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'flte telrestlial planetsare all relativcly snralt, denseolrjects.They inhabit the inner regionsol'the Solar Systerrand have teuuous?rtnlosplleres if, indeed,they have any at all. -llte predominantn)aterialswhich nrake up the cornpositionof theseplanetsare silicate c o n r p o u n d sa n d n r e ta l s,e sp e ci a l l y i r o n a n d n i cke l .'fh e vo l a ti l e su b sta n ce s,su ch a s gaseousatnlospheres and the water containedin Earth's oceans,were probably deposited by cttlliding conretsafter the planets had fonned. Volatiles are substancesrvhich can changcstateeasjly,e.g.gas to liquid, solid to liquid. The asteroidbelt rnarksthe boundary bctr.veen the inner and outer Solar Systerrrand representsa planet which was prevented li'onrIbrnringby the gravity of giant Jupiter. 'l-heouter Solar Systcnris the donrainol'(he Jovian planets.'l-hese are giganticrvorlds, nrilny tinlos la|gcr and nror(jrrassivethan the terrcstrialplancts.'l-heirconrpositionsa|e very dill'erentand are predonrinantlylight gasesand volatiles.l'his nreansthat, although the planetsare very nrassivecolnparedlvitlr the Eartb,they are not very densesincetheir bulk is spleadmuch r11ore sparselythroughouttheir over-sizedvolumes.{n point of fact, the averagedensityof Saturnis lessthan tliat of water! 'l-he fulthel out into the Solar Systenlone venturesthe more prone to volatiles the rvorldsbecorne.Uranusand Neptulte,for instance,are gas giants with very high proportions of astrorronrical ices,e.g. water,ntethane,and ammonia. Pluto, a tiny icy rvorld rvith a sinrilarlyf igid moon, Clraron,representsthe start of the Kuipel Relt and the Oort Cloucl.'flre Kuipcr Belt is a flared disc rvhich extendsinto a spl)ericalcloud, the Oort Cloud, surroundingthe Solar Systerl. Together,they contain vastrttnllters,oficy cornetswhich are thoughtto be the rerlainso1'themateriall'romwhich thc Solar Systenl was formed. I'}eriodically,membersof thcse 'reservoirs' fall inwards torvardsthe Sun and their gasesare boiled offby the heat. In general,however,they re,lrainin the furthestreachesof the Solar System. 'l-hentotion of the planetswas finally described in 1609 by Kepler when he presented his thlee ernpiricallaws of planetaryrnofion: 'fhe orbit of'a planetabout the Sun is an ellipsewith the Sun at one l'ocus. A linejoining a planetand the Sun sweepsolt equalareasin equal intervalsof tirrte. 1'hesqualesol'the siderealpe|iodsofthe planetsare proportionalto the cubes o l ' t h e i r s e rr r i - n r l j oar xe s. As ve't,tltcre \vereno theoreticalfbundationsupon rvhich his larvs(see Fig. l.l) could be based,yet their validity was beyonddoubt becauseofthe rvay they could be usedin order to predict the ntotion of the planets.A theoreticalflamework within which these'laws could be lturtgwas finally forth-comingin l68T when Newton publishedhis three laws of nrotion. 'l'ulning our allentionback to the centreof the Solar Systenr and to gain some kind of pcrspectiveon it, intagineif everything,except for the Sun, were placed o,none side of a scalebalance.l'he Sun is then placedon the other side. Despitegrouping all the planets, nloons,asteroidsand cornetstogether,the Sun would still outweigh them by over seven hLrrtdledtirnes.In fact, the Sun contains99.8 per cent of thc ntasscontainedwithin the Solar Systenr.So, the lnatterwhich constitLrtes the planetscannoteven be thouehtofas the i c i n s o n t h e S o l a r Svste mca ke !
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Itig. L I . Kepler's laws of planetarymotidn representedone of the most fundamentaladvancesof his tirnc,(a) All orbits are ellipseswith the Sun at one focus.Equal areasare sweptout by the rndiusvector in equal times. The radius vector is an imaginarylinejoining the Sun and the orbiting body.(b) The squaresofthe siderealperiodsare proportionalto the cubesofthe seminrajoraxcs.(Adaptedfrom Kaufmann,W.J.,Universe,W.H. Freeman,1987.)
composedof the two lightestgasesin the Universe; Thc Sun itself is overwhelmingly hydrogenand helium.Thereforewe muststatethatthe SolarSystem,too, is overwhelmInglycomposedof thesetwo chemicalelements.We haveto disregardwhatour eyestell us fi'onrlookingaroundthe Earthandrecognisethat our entireworld, plus everlhing it corttains,is rnadeup of nothingmorethanthe cosmicflotsamproduced,as we shallsee, of stellarevolution. nsa by-product Our thcoriesofstar formationsuggestthatstarsareproducedby thegravitationalcollproceeds, the centralconcentration ofmatter npscofgiantcloudsofgas.As thecollapse a star.Otherfactors,suchasthe orbitalmotionof the cloud,mitigateto produce bccouros It is in thesediscsthat planetsform. n disc of nraterialaroundthe centralconcentration. Thesehaveranged Justrccentlytherehavebeena numberofextra-solarplanetsdetected. thestar51 Pegonessurrounding to themoreconventional li'olnthcexoticpulsarplanets naturallyout of starformationtheories. Secondly, lsi, In.short,planetscanbe predicted giventhe fact that the Sun,and henceotherstars,are far moremassivethan anyplanets to which may be in orbit aroundthem,it would seemmore sensiblefor cosmologists to understand theUniverse. switclrtheirattentiontowardsthestarsin theirattemDts I.2 ]'t'IE SUN AND OTHER STARS 'l'hc Sunis a star.It is no differentfrom the pinpricksof light in the nightsky exceptthat it is ntuchcloserto us. In principle,a staris nothingmoreexoticthana vastcollectionof
888 (b)
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Fig.l. t ( b) hydrogen andheliumgasheldtogether by theforceoI itsorvngravity.lt contains so much matter,however,that tlre pressurein its centralregionis .nor,rrou, and the tenrperature soarsto millionsof Kelvin.Thecombination of thesefactorsallorvsnuclearfusionto take place'Thisprocess produces theenergywhichcauses a starto shineand,in llrevastnrajority of stars,thechemicalelementrvhichis undergoing lusionis hydrogen, thesirnplest atomrvhichcan exist.In stars,hydrogenatomsin the coreare fuscd lnto hcriurn,the sophornore element of narure. The fusionof hydrogen takesplacevia theproton-proton chain.Thecondirions at the coreof a stararbso intense thatatomicnucleiarestrippedofthcir surrounding electrons. In thecaseofhydrogen, itsnucleus is a singleproton.-liheproton-proton chainrcpresenrs the collisionswhichmusttakeplacebetrveen the hydrogen anrjothernucleiin ordcrto bui l da hel i urn n ucleus.
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r)uclci (protorrs)collidc to fbrrn a heavy hydrogen nucleus In stcp orre. trvo hl,clrogc'n (knorvrras dcrrtcriurrr). a positronand a neutrino.In steptrvo,anotherproton collidesrvith the dcutcriurnnuclcusto fbrrn a liglrt hcliunr nuclcusand a ganrniaray. The final step of t hc rca ctio ninvolvest hc c ollis ionof t r v o t r it iur ns\ v hic h f o r n r sa h e l i u m n u c l e u sa n d r e lcascslrvo pro tolls. A lcrv, rnorc unlikcly routcsto furnr lrcliurnare also possible,but in a star such as the Sun thc abovc rcaclionroutc is tlredorninantone.'l'hcenergygiven out by thesereactions ofnlass into energy.lrt all cases is produccdttccausetlrc rcactionsconverta snrallarrtourtt tlrs surnnrcdntassol'tlrc rcilctants(thoseparticlcson the lcli-handside of the arrows) is lc.sstlra nth c sun rrnc dnt as sol' t lr e pr oc luc t s( t hos epar r i c l e so n t h e r i g l r t - l r 4 n ds i d e o f t h c arro*'s).'l'hisdifl'crcnccirr ruassis krrorvnas lhe nrassdef'ect,Anr, and is ttrrnedinto energy. l:. irr n ccortla nc rcv it lrI ' lir t s t c ir t 'fsat t t ot t seqt lat iot t, [: = Arrrc:
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'l'hecorrstarrt of proportiolrirlityin tlriscquntionis tlrc sclualeof the speeclof light. difflcrenttypesof starstrervnthrougltspace.An Studl,lrassltorvntlrattlrcrcarc a rrryriacl cxcc llcn t rva y irr rvhi c lrt o c las s ili't hc r n ir r it iallyis by t l r e i r c o l o u r , s i n c e t l l a t i n s t a n t l y yields thc stirr'ssrrrlhcetenrl)cratul'c. f'or exarnplc,l,ellorvstarssuch as the Sun have surof about4,000 K, lircc tcnrpclatulcsof 6,000 K. Cool red starshavc surlaceternperatures rvhilst tlre llottcst stars irr tlrc Urrivcrscare blue rviilr surfacetemperaturesin excessof 20. 000K. ' l'h c prcciseclassil lc at iolrdc s pc nduponot hc r c har ac t e r i s t i cssu c ha s l u m i n o s i t y ,r a d i u s c o p e r t i e sh e l p d e t e r n t i n et h e m a s s and a co rnp lctca na ly s isol' t hc s t ar ' ss pc c t nun. ' l- hespr ol' thc stilr irr qu cstionand t lr r :lir s ior rr c ac t ior t st ak ir r gp l a c e i n i t s c o r e . T o h e l p i n t h e ltusselldiagrarnafter its inventors,has classillcatiorr a diirgraur,krro*' as thu l lcrtzsprtrrrgbccn clcvclopcd(scc [:ig. 1.2).LJpontlris diagranrevcry knorvnstar has a place which is As a starevolves,the nuclearreacdctcrnrinedby its brightncssand surfaceternperature. tiolls tilking placc rvitlrirrit eharrgcin accordancervith rvlriclrelernentsare availablefor lirsion,and thc star clrangcsits classification.The changescan be chartedon the H-R diasra rrran d pro cltrccc v olr r t ionar yt r ac k s r v hic h r epr es e n tt h e d i f f e r e n t c l a s s i f i c a t i o n s , star hasa Iife a stlr occu pics d urirr g it s lif et inr c .J us t lik c an Ear t lrp l a n t o r c r e a t u r e a cycle; it is irritia llylir r r nc d and c v c nt ually dies . Dur in g t l l e c o u r s e o f i t s l i f e , a s t a r rnan ulircture spro gre s s iv c lyheav ic r c henr ic alelenr en t sb e c a u s eo f t h e n u c l e a r r e a c tions ta kin g p lace in i t s c or e. 'l'he eventuallatc of a star is virtually sealedby the nrassit containswhen it is formed. A star rvhiclrcorrtainsless than llve timcs the mass of the Sun rvill fuse hydrogen into heliunrfbr rnanyrnilliorrs- irr sonrecasesbillions - of years.When its supplyof hydr"ogen runs out. intcrnalconditionsrvill changeand the star rvill becomea red giant star, fusing heliurnirrto ca rbo n.A s t hc hc liur n r uns out , s o t he s t ar r v i l l d i e . I t w i l l r e t u r n i t s o u t e r laycrso l'lryd rog cnarr dhc liur r rint o s pac e,c aus ings or ne t h i n gw h i c h i s d e c e p t i v e l yc a l l e d a plarrctaryncbula.What is leli is a snrall,conrpactobject known as a white d,'varf.Stars of rnassgrcatcr than fivc tinrcs tlrat ot'the.Sun are individually more significanton the cosnrologicalscale.1'heyare prescntin tlre Universein far fewer numbers,and have much shorlcr lives than thcir lcssnrassivccousins.Whereassrnallerstarscannotfusethe carbon producedby heliurnlusion,thcsclargcrrrrassstarscan. In fact,they can fusea great many
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Fig. 1.2.Everystar in the Universehas a placeon the Hertzsprung-Russell 1H-R) diagram.The sweepingband ofstars runningfrom top left to bottomright acrossthe centreofthe plot is the mainsequence, wherethe majorityofstarscanbe found.It represents thosestars,suchas theSun, rvhich are in the stablehydrogen-iirsing stageof their existence.The numbersalons the main sequcnce arestellarmasses, in unitsofthe Sun'snrass. chemical elements through a complex pattern of interactions which are made possible bv
theextremeconditionsin theirinteriors.Iron,however,is a chemicalelementwhichmarks a watershedin nature.All elementslighterthan iron can be fusedin order to give out energy,but liom iron up*ards,energyneedsto be suppliedin orderfor the elements to be iused. In the heartsof stars,iron buildsup like ash in a fire. This is becausenowherenear enoughof the amountof energynecessary to firseiron is available.Whenthe amountof iron reachesaboutone-and-aJralf timesthe rnassof the Sun,its atomicstrucfurebreaks downandcauses thestarto collapse.Materialfrom thestar'souterlayersfallsdownwards
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known as a superA hugeexplos.ion' towardsthe shrunkencoreand impactsits surface' excessenergyrethe all supplies piece,s-and nouu,,ut., placewhich blows the starto originalstar,it heavierthaniron. ff anythiniremainsof the quiredto fuseall th" "t"*.n1, m ay beaf r agr ne n to fi ts c o l l a p s e d c o re k n o w nasaneutronstar.A l ternati vel y,thecol hole' havebeen iutgt that it becomesa black i;;;.;-.;.;';y In short,they elements. 'o heavier with starsseedspace ,rr"r. whqn tHgyexplo.de, '*ii* c hanget he' c om p o s l tto n o fth e U n i v e rs e ' W eknow fi -ommeasi rrementthatthecomposi 2 per cent(at heliurn-and ,oOuyi' f S per centhy$roge1'23 per cent tion of the.IJniverse hydrogen fromthe apart all the atoms most)everythingelse.rili, z p.i l""t consists-of System' Solar the and Earth the us, make u"Jfr.riut, whiih wiih time dueto the actionof stars'An changed hu' if" Uiiut"" of Sothe cornposition have that starsin the earlyuniverseco.uldnotpossibly immediateconsequence "r,rri"i, hadplanet s s uc h a s .r' " e u n r.i " o rb i ta ro u n d thembecausetheU ni versedi dnotcontai n enoughlieav ie r" t.' .n t,to * w h i c h to m a k e ro c k yw orl ds.P l anets,w hentheydi dform, bodies'similarto Jupiter' woulclhavebeengaseous T hedis t r ibuti o n o fs ta rs w i th i n th e U n i v e rsew asofmaj orconcefntocosmol finally de- ogi stsof ofsuch greatcontentlonthat it was only thc 1700sand 1g00s.The issuewas shapley. thanksto the work of Harlow cidedin the secondo."ua" ortnis century,
I.3 TH E GA L AXY space'Withthc througlrotrt randorilly thatstarswerepositioned Originally,it rvasbelieved Milky casc.'fhc thc rvas not obviousthatthis it bccame however, uduintoith. telescope, tfue agoss rvhich stretched liglrt of band historyasbeinga nristy Way,knowntlrrougliout ollaint hundrcds uporl hundreds of composed to be sky,*as shownbybalileo'steiescope obviousto him rvhenhe peercdat thetn,thatstarsrvcregroupedtogether stars.It.seemed or anotlter. in sonte'uvay groupingof stars itr. .ugi.rtlon tliatthe Sunu,asparlof a muchlarger,disc-slapcd of the Universe' 7"heor1' work' published in his Wright rvasfirsttua" itt 1750bi'Thornas lTSO sandf ounddif f er ' at t ent pt edt oniapt hedist r ibut ionof st ar sint hc W i i l i arnH erjchel sky ofthe areas ofdifferent densities stellar the in of600 encesofup to a factor oI the groupirrgof starsi-nthe Calaxyand in our understanding The breakthrough, rvhen c-cntury, of thctrvcntic(h theSun'i placewithinit, cameat thebeginning especially called of stars' collcctions spherical distant of studiedthe distribution HarlowShap.tey Milky Way' thatrrtostlay in thedirectionof thcsoutherrr He discovered globular "trsnupl.y,s the ccntreof "trit.iS. thelt by a giganticsphcrc, wereto be enclosed globularclusters to l0'000 25,000 sonte rvould bc it not be centredon theSun.lnstead, thatspheier.v*ould concluded and asstrmption bokJ a nrade Shapley ofSagittarius. iighty.urcin thedireption
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tltat this ntarkedthc ccntrc ol'the Galaxy sincethe globularclustersmust orbit around it. -l-lrisconclusiorrrvas,indecd,the correct one to dra\v and changedour view of the Universelionl bcing helioccrrtricto galactocentric. ln thc mid-trventicthcenlury,seriousattenrpts\verenradeIo map the structureof our Calaxy.lvlanl,lincsof invcstigationhaveshorvnthat the disc containsspiral 'arrns' of,stars rvlrichsu'irl aro un dthc c c nt r cof our Calax y lik e an oc to p u so n a t u r n t a b l e( s e eF i g . 1 . 3 ) . N4orereccrrtrvork on thc ratcsat u,hichstarsorbii the galacticcentrehas thrown up some st arllingco nclusion saboutt lr enat ur eof r nat t erc ont ain e dr v i t h i nt h e G a l a x y . It appcarsthat the starsare bcing gravitationallypulled by a vast quantityof matter in a splrericalhalo surroundingthe disc and nucleusrvhichtraditionallymake up the Milky \\/iry. It has provcd irnpossibleto detect this nrattervia any other mednsexcept by the gravitatiorralinflucnceit rvould appcarto exert on the starsin the Galaxy's disc. Llence, its c.xactrratrrreis sonrcrvlratcontrovcrsialat presentand nrany theoriesabound. What seenrscertain,horvever,is that the visible rrratterin the Galaxy, such as that which is containedin tlre stars,is vastlyoutrvcighedby the invisiblematerial.This inequalitymay be as rnu clra s 9 9 to l, and s o we c an no longert hink of o u r G a l a x ya s b e i n g j u s t a c o l l e c lion of stars.Irrstcad,our nrodcrncosnrologicalvierv of the Universepicturesthe Galaxy as being r regiortol tlrc Universervhich has a denser-than-average collection of nratter rvithin it. ll'rvc cxtcrrd this lirrc ol rensoning,stars are then nothing nrore exotic than dcttscr-tltan-avcrage rcgionsol'tlre Calaxy. lJ,xactlyhorv thesegalacticregionsbecameso dcnscis o nc o l'thc dri v ir r gquc s t ionsin c os r nology .
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A t abo utlh c san lctirnc as llallo* ' Shapley r v asm ak ingh i s b r e a k t h r o u g hw s ith the Milky War', anotltcrdr'batervasraging.The use of large telescopesover two centurieshad revcalcd a con sid era blcr r unr bc rof c c les t ialobjec t sr v hic h r v e r en o t s t a r s .T h e y b e c a m e knou'rtas ncbulac,and the brightcstofthese non-stellarobjectshad alreadybeen catalogucdby Cha rlcsMcss ic rir r 1781.M any ar e s t ill k nown t o d a yb y t h e i r M e s s i e rn u m b e r s , suclras lvl^12, tlrc Orion rrcbula. In thc carly part ol'the trventiethcentury,observations had divided the Messierobjects into trvo distinctcategories. Sornervereobviouslycloudsofgas, and theseseemedto congr!-galencar the lvtilky Way. Othersshorvedan elliptical or spiral shapeand seemedto occur at rartdonttltrougltoutthe sky. l'his latter classof object becameknown as spiral ncbulaeand sorucastrononrers suspectedthat they rverecollectionsofstars, just like the It4ilkyWay, onl), \,ie\\,cdfi'onra much greaterdistance.Controversyragedbetweenthese as(ronoll.rcrs artd thosc othcrs \vho thought tlrey rvere gas fornrationsor hazy stars rvithin thc Milky Way. lntcrcstirrglycnough,I-larlowShapley,rvho had shown such renrarkable ittsiglttcortccntirtgour orvn Calaxy, rvas vehemently(and incorrectly as it turned out) opposcdto tllc point ol'viov rvhichstatcdthat spiral nebulaewere in lact galaxiesin their orvrrrigh t! As thr bnck as l7-55,plrilosoplrerInrnrariuelKant had expressedthe vierv that these distantobjcctsrvcrepcrlcct analogicsto the Milky Way. Yet the matterlvas only finally cndcd in 1924 rvhcn Edrvin Ilubblc shorvedthat sonle ofthe nearby spiral nebulaecont aincdvaria blcstarssil nilart o t hos er v it lr int he M ilk y W ay b u t m u c h f u r t h e ra w a y .H u b b l e \\'cnt on to classili,galaxicsaccordingto their appearance. He found three broad types:
Fig. 1.4.This schenratic ofthe LocalGroupshorvsthat it is dorninatedby two spiralgalaxies:our orvnMilky Way and theAndromedagalaxy.Eachof thesegalaxiesis attendedby snlallersatellite galaxies,and a numberofdwarfgalaxies are also pr€sent.M33 is anotherspiral galaxy,and a recent addition is the barred spiral Dwingaloo l. (Adapted from Ferris, T., Galaxies, Stewart, Tabori andChang,1982.)
spirals,barredspiralsand ellipticals.Any galaxywhich did not fit into this schemewas ten.nedan irregular.Flubblemeticulouslymappedthe sky, looking for faint galaxiesin how they weredistributedthroughspace.Statisticalanalysisof his orderto understand nrapsshowedhim thatgalaxiestendto clumptogetherinto groupsand largerclusters. The Milky Way is partof a smallgroupof galaxies,knownastheLocalGroup(seeFig. 1.4).lt consistsof approximately thirty knownmembers.The hierarchydoesnot stopat groupsand clusters,however.ClydeTombaugh,the discovererofPluto, recognised that evenclustersthemselves tendto clustertogether!They form massivecollectionsknown (seeFig. 1.5)which,as hasbeenshownin the lastfew decades, as superclusters stretch throughspacein chainsandfilaments.This represents sucha fundamental departurefrom therandomdistribution ofgalaxies,thatit providesoneofthe moststringent constraints which must be placeduponany moderncosmologicaltheory,if it is to be successful in , explainingthe Universeasa whole.Anotherimportantquestionfor cosmologyis whether t'thegalaxies,or theclusterswhichcontainthem,formedfirst.
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instance,astronomerCarl Seyfert noted a nurnbcr of spiral and barred spiral galaxies which appearedto have nuclei much brighter than nornial. l'lresc bccanie knotvn as Seyfertgalaxiesand were the first of the active'galaxies to be discovcred.'l'hc tcrnractive is used to describea galaxy which is producingvcry muclr nrorc radiationthat that produced by its stars. The following year, in 1944,anrateurastrononlerCrote Reberrvasobservingthe heavens with a home-maderadio telescopervhen he detectedan incrcdibly porverlul radio soltrceemanatingfi'om sonretlringin the constellationof Cygnus.This rvasthc first recognition of the radio galaxiesrvhich,as the name implies.radiatethe nrajorityof their energy output at radio rvavelengths. In the 1950s,the positionofCygnus A rvasgraduallyrefined until it was finally identifiedrvith a fairly dinr ellipticalgalaxy. Unlike a Scyfertgalaxy, the radiation from a radio galaxy docs not come directly fi'onrtlrc nuclcus,Ralhcr, it is r e l e a s e df r o r n g i g a n ti c'l o b e s'r vh i cl re xi st o n e i th e rsi d c o f tl r e h o stg ,a l a xy.'fl r e ya p p e a r to be fed by a pair ofhigh-energyjetsbeing squidedin oppositcdircctionslronr the radio galaxy'sactivegalacticcentre.
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Moclerpcosmologystudiesthedistributionof mafteron scaleswhicharefar largerthan. inclividualgalaxies.This meansthat for manypurposeswe can imaginethe galaxiesas that lrciugtlremostfindamentalobjectsin thelJniverse.In fact,cosmologyoftenassulnes I many gas' are so There perfect a canbe thoughtof as in theUniverse tl)crllattercontained questionof how they however,thatthecosmological clifferenttypesof individualgalaxies, important. is still bccanrcthe way theyare I . 5 A CT I V E G AL A XIE S A N D QU AS AR S interestin galaxies,and they The first lralf of this centurysalv a fluny of astronomical to noticethat,,in terms began astronomers time, this werestudiedin greatdetail.During others.In 1943,for fi-om difterent galaxies were distinctly some of theirradiationoutput,
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Fig. 1.5. This schentaticof the Local Superclustershows how the Local Grorrp is totally 4oilinatedby the othermuch largerclustersofgalaxies.Oftheseotherclusiers,the Virgo Cluster is tlic nrost conspicuousfronr Earth becauseits memberscan be readily seen in a ntodest The figuregiven Virgo and Coma Berenices. tclcscope, set in the directionofthe constellations for cachclusteris its distanceaboveor belowthe X-Y planein millionsoflight years.(Adapted liont Fcrris,T ., Galaxies,Stewart,Tabori and Chang' I 982.)
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lrr 1 96 i, a rhirtl classof ac t iv e galax y was f inally ide n t i l i e db y a t e a r no f r a d i o a s trononlcrslcd bl,Cyril llazard.-l-hescpcculiarcelestialobjects,knorvnas quasars,appear 'sirpc.rficialll,as starsbut, underanall'sis,revealthat they areextremelydistantand incredibly. lunrinousgalactic objects (see Fig. 1.6). They sharenrany of the same f'eaturesas Scl,fertand radio galaxicsbut crnit cvcn rnore radiation.Curiously,quasarsseem to be rnuchnroreprevalcntthc furtherinto spaceastronolnersIook and it is this fact which has The lact that they once existed led to thc bclief that thcy arc of cosrnologicalinrportance. in greatnurnbersbut norvrro longerdo, nraybe of,crucialimportanceto our understanding of ' horvg ala xie sca rnein t o beingand ev olv edwit h t ir ne. Orr average,one in every tcn knorvngalaxiesis active,i.e. the majority of its radiation output is no t bcing pr oduc ed by s t ar s . I ns t ead, s or ne o t h e r p h y s i c a l m e c h a n i s m i s rclcasing copious anrountsof radiation,up to 1,000tinresgreaterthan that emitted by entire gnlasics,olien fi'orun lcgion rvith approximatelytlre sanrediarneteras our own S olarSystcnIr There arc nranydiflcrent rvaysofclassiSing activegalaxies,over and above the three t1,pcsrvlriclrhavc been nrentioncdherc. The crucial questionis: were all galaxiesonce active?Perhapsall of the so-callednorrtralgalaxies- our orvn Milky Way included- once passedtlrroughan activeplrasc.Norv,horvevcr,the activecore has fallen dornraritand the galirxics'ern issionarc s dor ninat c dbl, s t ar light .lf t his is t he c a s e ,t h e n i t w o u l d s e e r na s i f all yourrg galaxiespass through an active stage becauseof the distribution of quasars tlrrouglroutspace.l{, on tlre other hand, active galaxiesare intrinsicallydifferent frorn norrnal galaxicsthen tlris conclusiontoo \vould give us valuable insight into the early Univclsc. Wlry, for cxarnplc,rvould tlre Universepromotc the evolution of quasarsbilliorrsol-ycarsago but not norv? : So, activc galaxiesarc lhscinutingobjects to study becausetlre anslversto sonre intcnscll,perplexingcosrnologicalpuzzlcsseenrrvlappedup in their ruysteriouscores.
coNl'rNUUrvr r.6'nrEspACE't'rMri In tlrinkingaboutthc [Jnivcrse,nroderncosrnologydernandsthat we considernot only the objr:ctsil corrta irrs. As rvc ll as t hir r k ingaboutt he r adiat ionc o n t e n to f l t h e U n i v e r s e( w h i c h rvc shall covcr in lhe ncxt chaptcr)\vc lnust also considerspaceitseli. Kepler's laws of planctarl,nlotion\vcre thc llrst to describehorv objectsnrove throughspace.They rvere kirrc'rilatic irr rraturcbccnusctlrcyntadcno atternptto explainrvhy the planetsmoved.Newton went one stagefurtherby consideringthe forcervhichrvascausingthe motion, nan.rely gravlty. Ncrvton'slarysol-nrotionlcd hinr to theoreticallyderivehis universallaw of gravitation rvhichgives the nragnitudcol'the glavitationalforce, F, betweentwo masses,m, and nt,. rr'hicharc scparatccl by a distancc,r.
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thetaskof uniling nature'sdiverse of unification and,aswe shallseein thenextchapter, phenonenacontinuesto this day.Newtonusedhis equationsto deducethat orbitscould parabolae Theseareknownas conicsections.bepause or hyperbolae. . be circles,ellipses, I '' :' by slicingthrougha cone(seeFig. 1.7). canbe obtained I theirshapes Hyperbola Parabola
AA
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Fig. 1.7. All orbits.arerepresented by one oftheconic sections.Different conic seclionsare obtainedby slicing a boneat differentangles.Closedorbitsarecirclesand ellipses,obtainedby slicing the coneat ziro or shallow anglestb the symmetryaiis. Open orbiu are the parabolaeand hyperbolae,obtainedby 3licing the cone at steepanglesto the symnretryaxis. (Adaptedfrom Kaufmann,W.J.,Universe,W.H. Freentan,1987.)
Anothergreatunificationtook placeearlyin this centurybetweenspaceandtime.This rvasmade possibleby the conceptof spacetimewhich was developedby Hermann with time as a sepaMinkowski.Insteadof thinkingof spaceas beingthree-dimensional, postulates rateproperry,spacetime a four-dimensional frameworkin whichthe time ordinateean be given the sameunitsas distanceby multiplyingit by the speedof light. In the generaltheoryof relativity.This 1915,Einsteinbuilt upon spacetimeand presented wasalsoan extensionof Einstein'spreviouswork - the specialtheoryof relativity- and a tool with which to studythe Unihelpedto explaingravity.It finally gaveastronomers ' In 1929a very importantconclusionwasieached,basedupona setof interesting observations.Hubble'swork on galaxiesyieldedtheresultthatall thegalaxies,apartfrom those in the Local Group,wererecedingfrom the Milky Way.The furtherawaythe galaxy,the fasterit wasreceding. The recedingmotionof thegalaxieswasdescribed by Hubble'sequation,whichrelated Ithe recessional velociryofa galaxy,v, to its distance, d: v =H d
( 1. 4)
l{ is knownas the Hubbleconstantandhasa valuewhich is thoughtto lie somewhere in therange50- I 00 km./s/megaparsec. The generaltheoryof relativitycould be madeto agreewith this conclusionif one ,majorcaveatwere placedupon the explanation.Althoughit appearedas if it were the galaxieswhich were rnovingthroughspace,in actualiryit was the spacebetweenthe galaxieswhich was expanding.So the galaxieswerebeingdrivenapartin the sameway
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thatraisinsin a doughmixturearemovedawayfromoneanotherwhenthebreadrises(see Fig. 1.8).lnterestinglyenough,whenEinsteinhadderivedthe equationswhich definethe spicetime continuum,the equationsdid not allow the Universeto be static; it had to be eitherexpandingor contracting.Since,at thetime,Hubblehadyet to provethe expansion so that theyincludeda for presentation ofthe Universe,Einsteinhadrecasthis equations presented his results, When Hubble static. the Universe would hold new constantwhich mistake constantandcalledit the greatest removedhis cosmological Einsteinimmediately ofhis life! Generalrelativityprovidesus with a way to visualisehow gravity is created,by exThe theory statesthat massiveobjects plainingthe way massinteractswith spacetime. distort the spacetimecontinuuminto curvesin muchthe sameway as a heary ball might deforma rubbertabletop (seeFig. 1.9).Anyttringwhich getstoo closerolls downthe curveas if it werebeing attractedto the massiveobject.Thus,an intimaterelationship continuumcaused betweenspaceitselfandmatterexists.The curvatureof the spacetime by massin turn createsgravlty, which tells othermasseshow to movethroughit. havehad to dealwith is that, alOne of the universalpaladoxeswhich cosmologists thoughgravity is by far the weakestof the four fundamentalforcesof nature,it dominates the Universeon its largestscale.The stong nuclearforce andthe weaknuclearforce only operateover*re distanceof an atomicnucleus,whilst the elecfomagneticforcecancels out over largedistances.With nothingleft in competition,gavity andthe motion it causes cansculpttheUniverseon all but the smallestof scales(seeFig. l. l0). Indeed,it is graviin this tationalforceslvhichareresponsiblefor everystructurewe haveso far discussed fate of gavity sealed the has also is concerned, chapter.As far asthe future of the cosmos is! what fate work exactly that to out cosmologists is for the remains All that the Universe. all scalesof the Universe.The Cosmoloryis a rich field of studywhich encompasses only by thinking in termsof quantumtheory,the method Big Bangitself is understandable the Universeon its smallestscale.The long-termfutureof the we havefor understanding the only ifwe usegeneralrelativity:a theoryfor understanding Universeis understandable Universeon its largestscale.Cosmologyis, literally,universalin contentandscope.It is to it by takingourmindson thesciencefromwhichall othersarebom, andwe gainaccess joumey of the Universe. the towards edge from here a
The tools of the trade The astronomical censuspresentedin chapterI hasbeenmadepossibleby the collection of electromagnetic radiationfrom space.Astonomy, by its very nature,is an observational science,not an experimental one.As muchas theywould like to, astronomers are not freetojourney to thesefar distantobjectsin the exoticdepthsofthe Universeandset up experiments to learntheir secrets.Instead,they mustrely on collectingthe radiation whichhasbeenreleasedby thesecelestialbodies. The detectionofelectromagnetic radiationis, by far, themostadvanced ofour methods for examiningthe Universe.Sincethe dawnof humanexistence, mankindhasdonethis quite naturally,sinceour eyesarereally rathersophisticated detectorsof visibleelectromagneticradiation.Technologically, thestudyof visiblelight beganin 1609whenGalileo useda telescopeto look at the night sky. Today,a plethoraof collectingand detecting devicesis capableof samplingtheradiationfrom manyareasof theelectromagnetic specrrum. 2.1 ELECTROMAGNETIC RADIATION In the sameway that thevery fact of theUniverse'sexistence hascausedmanyto wonder aboutit, so t}renatureof light hasalsopuzzledmankindthroughouthistory.plato, Aristotle andPythagoras all wonderedaboutit but nothingreally cameof their pontifications. Betweenthe 1300sand i600s,European researchers concentrated on thedevelopment of lensesandmirrorswithoutreallywonderingwhatconstituted the light theywerestudying. Whilst doingthis, however,manybecameawareof theway in which raysof light moved throughthe air andinteractedwith otherraysoflight. Gradually,curiositywasraisedand thephysicalnatureoflight waspondered. In 1665,whilst attemptingto understand a seriesof observations which generated the phenomenon of diffraction,RobertHookeproposedthat light is a rapid vibrationofthe mediumthroughwhich it is passing.Hooke'spresentation marksthe beginningof the wavetheoryof lightwhichis still in useroday. Manyexcellent contributions weremadeto theburgeoning science of optics,butpossibly the nexttwo greatestmilestones werethe proofthat light traveiledwith a finite velocity and that it was a type of electromagnetic wave.Both conclusionswere finally and irrefutablyreachedin themiddleof thenineteenth cenhry.
20
lch. 2
The tools ofthe trade
From the daysof Galiieo,scientistshad beentrying to measurethe speedof light. Thoseearlyattemptsnow seemridiculouslycrudeandtheir failureto showanytime delay in light's propagationfrom one locationto anotherled someto believethat it navelled Ole Christensen R.smerobservedan infinitelyfast.In 1675,however,Danishastronomer phenomenon whichhecouldonly explainif thespeedof light werefinite.He astronomical wastrying to measure the orbitalperiodof Jupiter'smoonIo, andkeptobtainingdiffering results.lt wasthe fust directevidencethat light did not propagateinstantaneously and it evenyielded a crudeestimatefor its velocity.Just over fifty yearslater, anotherphenomenon,knownas aberration,wasdiscoveredby the EnglishmanlamesBradley.This, too, was explainableonly in termsof light travellingwith a finite speed.Like Rsmerbeforehim, Bradleyalsocalculateda speedfor light. of the speedof light wasmadeby Frenchman The first relativelyaccuratemeasurement ArmandHippolye LouisFizeauin thesuburbsof Parisduring 1849.His calculatedfigure was 315,000km/s which,comparedwith today'sacceptedfigureof 299,792km/s,is prettygoodfor the technologyofthe day. in optics were taking place, another At about the sametime as thesemeasurements unrelatedfield of physicalstudywasalsomakingprogressin leapsandbounds.Michael Faradayhadappliedhis greatmind to the studyof electricity andmagnetism.Within Faraa link berweeneleckicityandmagday'slifetime,HansChristianOerstedhadestablished netismwhen,in 1820,he noticedthatanelectriccurrentin a wire affectsa magneticcompassneedle.F4ladayhimselfnoticeda link betweenlight andelectomagnetism whenhe thatrastong magneticfield couldalterthe propertiesof a light ray. discovered Buildinguponthis informationandthe collectedresultsof manyotherexperimentalists anotherphysicist,JamesClerk Maxwell,expertlyextendedthe work and eventuallydistilled the behaviourof elecfomagletism into a seriesof four theoreticalequations.His work standstodayasoneofthe greatestpiecesoftheoreticalphysicsever,secondonly to thegeneraltheoryof relativity.In thecourseof his investigations, Maxwellbecameaware predictedthatelectromagnetism couldtheoreticallytravelin theform of thathis equations waves.Solvinghis equationsto give the speedof the wave,Maxwell discovtransverse
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eredthat it ravelled at Fizeau'smeasured speedof light. This wasso big a coincidence thatMaxwelrfelt compelled to drawtheconclusion th;t light*u, *.r..iorugnetic dis_ turbancepropagatedby a wave (seeFig. 2.1). Not only tiat, but light *ur-"oi..nour.o into sucha restrictedsetof wavelengths thatothertypesof electromagnetic radiation(with greaterand smallerwavelengths) could be predictid to exist. r" rsag, .-prii*.nulir, HeinrichRudolfHertzdramaticallyprovedMaxwell'stheoryuuou, .r..uo*'ugnetic radi_ ationby producingthe fust radiowaves.
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electromagneric specEum.All rypesof electromagneuc wave are similar to one flq-,22 Th: anotheri all that separates them is their wavelength,which dictatis how the wave interacts with = matter. I nanometre(nm; 194. Man-madedivisionshave been drawn to reflect these differences,arthoughth€ transitionfrom onetype-of€lectrorugn"ti. wave to anotheris l;r;;ii; smoothlycontinuous. (AdaptedfromKaufmann, w.J., Untverie,w.H.Freeman. 19g7.)
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T h e to o ls o fth e tr a d e
lch. 2
Electromagneticspectra 23
Sec.22l
divisions:radiowaves, radiationinto sevenman-made Todaywe split electromagnetic there microwaves,infrared,visible,ultraviolet,X-raysandganrmarays.Fundamentally' freand wavelengths have different they simply radiations; these is no differencebetween (seeFig.2.2). quencies The definingpropertiesof the wave,namelythe wavelength,1",andthe frequency,f, areinterlinkedby thespeedofthe wave'spropagation, C= IA
(2.1)
Radiationemitted
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R adi ati onpa through c l oud
2.2 ELECTROMAGNETICSPECTRA
ll
specradiationis knowntodayastheelectromagnetic The entiregamutof electromagnetic trum. The word spectrumwas first coinedby IsaacNewton,who wasthe first personto produceandstudytheopticalspechum.Theword itselfis Latinfor'ghost' or'apparition" patternofcolourswhichdancedon the andwasusedby Newtonto describetheephemeral wall of a darkenedroomwhenhe placeda prismin thepathof a light bearn. Initially, the spectraobservedweresimplycontinuousbandsof colour.tn 1802w.H. Wollaston observeda few dark lines in the solar specffumand assumedthat they were magnifieda spectrumofsunlight sapsbetweenthecolours,but in l8l4 JosephFraunhofer trat it was full of the dark lines of the absorptionspectrum.Later that Ld discouered century,emissionspectrawere observedby fwo chemists,RobertBunsenand Gustav Kirchhoff.Theypassedthe light from chemicalflameteststhrougha prism anddiscoveredthat their specta were simplepaftemsof colouredlines ratherthan dark lines superimposedupon continuouscolours.Furtherinvestigationsshowedthat eachelementhad a patternof theseemissionlines.It wasalsorealisedthateveryemissionspeccharacteristic absorptionspectrum(seeFig. 2.3). trum hada corresponding It appearedthat, in someway, atomscould only absorband emit at specificwavethat a truly continuousspectrum lengthsof radiation.By now, physicistsalsorecognised wai only producedby heatingan objectandlettingit radiatethat heatas electromagtetic radiationbecameknown as radiation.Thus,this methodof producingelectromagnetic it impossibleto understand made however, a wave, as light thermalemission.Thinkingof why atomsandradiationshouldbehavein this way.The productionof thermalradiation by threeempiricallawswhich assumethat the objectbeing heatedis a is characterised perfectabsorber(and perfectemitter)of radiation.Sincea perfectabsorberwould not reflectanyradiation,its colourwould be black.Thus,an objectofthis typehasbecome knownas a blackbody.All radiationabsorbedby the objectwill be convertedinto heat As well as a solid object at a specific energyandthenre-radiatedat lower frequencies. as a blackbody if its constituentatomsand radiate gas canalso tempirature,a denseideal andcosmologicalcases,it is astronomical most In equilibrium. are in thermal molecules emissionby a denseidealgasin thermalequitibriumwhichproducesblackbodyradiation. as beingblack bodiesand,as we shallsee,the For instance,starsarewell approximated by a black body curve. is alsocharacterised radiation background cosmicmicrowave Hence.frorn now on, this book will assumethat Planck(black body) curvesare being by denseidealgasesin thermalequilibrium. produced
Absorbtion Spectrum
3;::i?xil Fig. 2.3. The productionof emission,absorption,and continuousspectra.The contlnuous sp-ctrumis producedby a hot, solid bodyor by a hot, densegas.Emissionspectraareproduced by a hot, tenuousgas,andabsorptionspectraareproducedby cold cloudsoftenuousgas. The first law which describes the process of black body thermal emission is known as law. It gives the total radiated power per unit area, R, for a black the Stefan-Boltzmam body at a given temperature, T.
R =o To
(2.2)
The proportionality is maintainedby the Stefan-Boltanarm constant,o:5.67 x 10rWm2K4. The second law is known as the spectral radiancy and describeshow the intensity of radiation changeswith wavelength and temperature. Graphs constructed for &e spectral radiancy at specific temperaturesare known as Planck orblack body curves (seeFig. 2.4). When the spectral radiancy is integrated ovel all wavelengths it equals the Stefan-Boltzmann law.
t 24
lch. 2
The tools ofthe trade
iantly and presentedhis theoretical equationwhich perfectly matched the spectralradiancy curves.
su b m illim e tr e fa r in fr a r e d r a d io
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k = 1.38* lo-"Jn( and theBoltanannconstant, narnely, usedtwo newconstants, Hisequation t lnor der t opr oducehisequat ion, Planckhadt o 10- r oJs. theP i anckconst ant , h=6, 63 abouttheway in which atomsreleaseradiation.Classically,it makea radicalassumption that atomscouldemitradiationof anyenergy.Max Planckintroduced hadbeenassumed Albert Einthe ideathatatomscouldonly releaseradiationat certainpredefinedenergies. photons and, as particles known of as be thought steinproposedthatlight couldsometimes of thought be sometimes matter could proposed that Schrodinger turningtiretables,Erwin as wa;es.Usingtheseideas,which becamegenericallyknown as quantumtheory,Niels I Bohr explainedthe possiblepositionsan electroncouldassumearounda hydrogennucf energy the photon allows concept The sPectra. emission leus by ionsiderationof their caniedby eachphoton,E, to be calculatedin termsof the light's frequency,f' (2.5) E: hf
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Fig .2 ' 4 .Pla n ckcu r ve sa n d th e wie n d is pl acement.l aw .A nyhotbodygi vesoutl adi ati oni n moreradiationis emlttedand the u.zo.aun." with thesePlanckcuwes.The lrotterthe body, the peak emissionis of wavelengtlr in the change This peak emission of ;h;;; th. wavelength law' describedby the Wien displacement law' It states that the waveThe third and final, empirical law is the Wien displacement
proporlengthat which the maximumintensityof radiationis released,1.'o, is inversely body' radiating ofthe tionalto thetemperature
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is equalto 2898pm K' The Wien constant,w, which At thetum of this century,physicswasfacingthe challengeof findinga formula The best basis' theoretical a from could fit the Planckcurvei and be totally derivable Lord by made the attempt was offer could physics classical attemptat fitting thecurvethat fit thecurvesat very longwaveRayleighandlaiermodifiedby JamesJeans.It could_only but lengths.A secondattempt,madeby WilhelmWien' fittedbetterat shorterwavelengths however, theory, classical from somewhat Wiendeparted faitia to fit at tongwavelengths. and the by assumingthat there *ui * analogybetweenthe spectralradiancycurves gas' ideal of an molecules the for curves distribution Maxwellspeed presentMax Plancksolvedthe problemby interpolatingbetweenthe two modelsand his derive to then set out He wavelengths. at all ing a formulawhich fittedthe radiation brillHe succeeded assumptions. theoretical of set a simple from time this .q"uutionagain,
The key to quantumtheory is wave-particleduality. It statesthat light, traditionally be a particleandthatelectrons,traditionallythought thoughiof asa wave,cansometimes we arefree behaveaswaves.As physicistsandastronomers, of aJparticles,cansometimes at hand' problem the to solve to regardlight andelectronsas particlesor wavesin order andthe part the scientists the of on to take liberty This seemslike quite a fundamental The answer particle? wave or a it a Is really? an electron, is what arises: naturally question is that,just like light, it is bothandyetneither. particlenatureand a wavenature' Quantumtheorystatesthat everythinghasboth a formationaswell. The key to why wave is a just but object solid a This very book is not very muchmoremassivethanan it is is because however, object, a solid like it behaves that whenthe quantumtheoryequationsfor electron.Electronscontainsuchtiny masses their behaviourare solved,neitherwavenaturenor particle natureshowsdominance' Hence,it displaysthe qualitiesof both. If the quantumequationswere solvedfor this book,however,it's solidparticle-likenaturewouldoverwhelmthe wavenature. The conceptof quantizationand wave-particledualityhas shownthat electronscan only exist aroundaiomicnuclei in certainstatesdefinedby the quantumnatureof the atom.Whenradiationcomesinto contactwith electronsaroundatoms,thephotonwill be absorbedonly if it containsenoughenergyto allow the electronto jump to a newenergy state.Later,whenthe electronjumpsbackdownto its original level,the energyis given back out as a photonwith a specificwavelength.Thus,the processresponsiblefor the andthe reason productionof absorptionand emissionspectrais finally understandable, why thereareline spectrafollowsnaturallyfrom the explanation' quanalejumpingbetween theelectrons occursbecause ofline spectra Theproduction with their association their losing electrons the stage are no at but tized energylevels, (seeFig'2'5)' transitions areknownasbound-bound parentnuclei.Thus,theseffansitions An idealgascan radiateeithera continuousblackbody spectrumor a line spectnrm, beuf,onthe densityof thegascloud.A tenuousgashasnegligiblereactions depending
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way in which radiationis eitherabtweenits constituentatomsand so the predominant sorbedor emitteddependsonly upon the way in which the electronsinteractwith the surroundingphotons.This leadsto emissionand absorptionspectra.In a densegasthe energylevelsarealteredby theproximityof the atomsto oneanother,andthis smearsthe radiationout into a continuousband,producinga continuum. profile.This is because shapeknownasa Gaussian Spectrallineshavea characteristic there is a naturaltendencyfor the lines to spreadout over a small rangeof wavelengths. For the atomsin an ideal gas,the temperatureof the cloud will ffanslatedirectly into a velocitydistributionfor its constituentatoms.Whenan electronabsorbsandthenre-emits a photonof radiation,the wavelengthof the photonwill be slightlyalteredby the individual motion of the emittingatom.When the cloud is studiedas a whole,the statistical profiles.Theprodistributionof velocities(describedby Maxwell)createstheseGaussian ln the caseof turbulentmotionwithin the cessis knownasthermalDopplerbroadening. will alsotakeplace.Theanalysisof the cloudbeingstudied,turbulentDopplerbroadening by the shapeof spectrallinescanthereforetell us whatphysicalconditionsarepossessed cloud. emitting(or absorbing) the atomsbecomemorecrowdedandthe amount As the densityof the cloudincreases, of interactionbetweenthembecomessignificant.Our frst clue can be foundby rememberingthat oneof our conditionsfor blackbody radiationwasthat the cloud mustbe in thermalequilibrium.This impliesthat theremustbe a largenumberof atomic interactions in order to spre4dthe thermal energyevenly betweenatomsin the gas.In the courseof thesecollisions,the atomswill interactwith eachother.This occursbecausethe wave natureof theelectronsallowsit to actasif i* chargeis distributedevenlyabouttheatomic nucleus.Thustheregionin whichthe particulateelectronmustbe locatedis knownasthe electroncloud.The atomsin a denseidealgaswhich is in thermalequilibriuminteractby feelinga repulsiveforcebetweentheirsunoundingelecton clouds.This altersthemotion changeto the energyof the system. of the interactingelectronscawing a corresponding we canthink ofthe energies Thatenergyis lost in the form ofa photon.For our purposes involvedin theseprocesses asbeingunquantized andso theradiationis emittedin a congivesa Planckcurve. tinuumwhich,because ofthe distributionofatomic energies, So,the carefulanalysisofthe spectrumfrom any celestialobjectcantell us a a great dealaboutthe mattercontainedwithin the objectunderscrutiny.The shapeofthe spectrum, the presence or absenceof spectrallinesandthe intensityof radiationall help in by whichtheradiationwasemitted. understanding thephysicalprocesses
2.3 ELECTROMAGNETIC RADIATION EMISSION MECHANISMS Having lookedat thermalemission,it is now importantto considerthe other types of for electromagnetic radiation.Considering emissionmechanism bound-boundtransitions,it becomes naturalto wonderif it is possiblefor electronsto completelyescapethe influcnceof their atomicnucleisimplyby absorbingphotonsof suffrcientlyhigh energy. 'l'his is a processknownasphotoionisation andis definedasa bound-freefansition. The energyrequiredto ionisea hydrogenatom,if its electronis in the lowestenergyor groundstate,is l3.6eV.(An electronvolt is a measure of theenergygainedby an electron il'it is accelerated througha potentiaidifferenceof I volt.) Photonscontainingthis amount
Sec.2.3l
Electromagnetic radiation emission mechanisms 27
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Fig 2.5. Energylevelsandtransitionswithin the hydrogenatom.ln the simpleBohr picture ofthe atom, energylevelsaresaid to be quantized,i.e. the elecbonsmay take ui only certainspecific energies-For the hydrogenatom, an energylevel diagramcan bi drawn'showingall available energy levels and the s€riesof spectral lines (e.g. Lyman, Balmer, paschenInd Brackett) producedby transitionsbetween.them.. Electronsjumping from higher to lower energylevels produce emission lines, white thosejumping from iower to hig-herenergy levels"produce absorptionlin€s.
ofenergy or morecanbe absorbedandusedto ejectthe electronfrom the atom,leaving an atomicnucleuswith a net positivechargeknownas a positiveion. Energyover and abovethe 13.6eVneededfor ionisationwill be convertedinto kineticenerg/ty the free electron.As thephotonenerryincreases pastthe ionisationlimit, however,th! probability that the photonwill be absorbeddecreases and so absorptionbandsare createdin the spectrumwhich havea sharpdiscontinuitycorresponding to the energyof ionisation(see Fig.2.6).Several suchbandsarepossible withinthesamespectrum because ionisation can takeplacefromelectrons in anyenergylevel.A gascloudwhichis largelycomposed of positiveionsandelectrons is knownasa plasma.
t 28
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The tools of the trade
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freeelectronscanbe captuledby positiveionsandtheir energygiven out Conversely, asphotons.This is the processofrecombinationandis knownasa free-boundtransition. is a rangeof mechanisms which to be considered Thefinal typeof emissionmechanism the elecfronsare uncould be classedas free-freetransitions.In all ofthese interactions boundto atomicnucleiandremainthatway,evenafterthe interactionwhichproducesthe radiation. The most obvious of the free-free transitions is known as thermal by an interactionwith This occurswhen a free electronis decelerated bremsstrahlung. anotherchargedparticle.The otherparticlemay be a positiveion (i.e. an ionisedatomic nucleus)or anotherfree electron.Whateverthe precisesituation,the energylost by the electronin the interactionis releasedas a single photon of radiation.A thermal spectrumis continuousbut of a very differentshapefrom a black body bremsstrahlung emissionof a tenuousplasma' curve.It is the characteristic is Magnetobremsstrahlungalsopossiblebut usuallygoesby the nameof synchotlon involvesparticlestravellingat relativisticvelocities radiation.This emissionmechanism theelectronto loseenergyby in circulartrajectoriesthrougha magneticfield. This causes mechanisms theradiationproemission other Uniike radiation. givingout electromagnetic of being that, instead randomlyorienmeans This polarised. is highly way ducedin this placedin the samedirection. tated,the electricvectorsofthe photonsareconsistently The compton effectoccurswhena high energyphotoninteractswith a lower energy andknockedinto a lower electron.lt is convenientto imaginethatthe photonis scattered Theinverseprocess occurs to higherenergies. energystate.whilsttheelechonis boosted when'-ahigh Energyelectroninteractswith a low energyphotonand boostsits energy' Describedin this way it soundsrathersimilarto synchrofionradiation,with a photonfield replacingthe magneticfield. Althoughwe havereferredto theseeffectstakingplacebetweenelectronsandphotons,whichwill applyin the majorityof asfophysicalcases,the electronscouldbe replacedby otherparticles. The wavelengthshift, Al., sufferedby a photonin the inverseComptoneffectis given bv theequation: Al" = tr"(1 - cosg)
(2.6)
whereg is the scatteringangleof the photonand l" is the Comptonwavelengthof the the photoninteraction.The Comptonwavelengthis the wavelengtha particleundertaking if it caniedtherestenergyof theparticle;henceit is defmed: photonwouldpossess ^h I
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wheremois the massof theparticleinvolvedin the scattering. 2.4 WINDOWSON THE UNIVERSE As the previoussectionhasshown,differenttypesof emissionmechanismareproduced mechof eachemission Withintheboundaries to differentphysicalconditions. in response can alsobe produced.Obsewingthe Unianism,a wide rangeof radiationwavelengths andscrutinisingspectracanthereforegive us an insightinto verseat differentwavelengths presentthroughoutthe cosmos.ln the differentphenomenaand physicalenvironments
S ec.2.4l
W i ndow s on the U ni v ers e 29
some ways, we have becomeso usedto seeingthe night sky at optical wavelengths,that spacecraft images of it in anything other than visible light often take us by surprise. It is important to remember at all times, however, that visible light is such a tiny part of the electromagneticspectrum that to ignore the rest would be folly. If we start at the lowest energies of electromagnetic radiation, the Universe becomes the realm of the radio galaxies. The entire sky is dotted with their tremendouslypowerful radio emitting lobes. Also visible at radio wavelengths are objects from our own Galaxy known as supernova remnants. These are the glowing remains of exploded high mass stars. In the direction of Sagittariuswill be the centre of the Milky way. At certain radio wavelengths, vast clouds of molecuiar gas can be seen. These also exist within our own Galaxy and are the clouds out of which stars eventually form. The different wavelengths of radio trace out different molecular species.By mapping the strength of eachmolecule's radio emission, contour maps of the clouds can be obtained, which show the number of each type of molecule at each point throughout the cloud. The nearestmolecuiar clouds would appear to be enormous to us. For instance, the molecular cloud with which the Orion nebula is associatedencompasses the whole of the constellationat radio wavelengths. At the next man-madedivision - microwave wavelengths- the view is totally different, since the cosmic microwave background dominates.Insteadof a dark slcypunctuatedwith both point and extendedsources,the entire sky is bright and glowing with energy. Superficially, the brightnesswill look the samein all directions. There are variations in the radiation however, and the first, most obvious is known as the dipolar anisotropy. It is produced by the motion of the Earth relative to the cosmic microwave background radiation. When all the componentsof the Earth's motions are summed, such as the component due to the Solar system's motion aroundthe centreof our Galaxy and the Galaxy's motion within the Local Group, the resultant velocity increasesthe temperature of the cMBR in the direction ofthe Earth's motion. It also decreasesits temperatureby a corresponding arnount in the antithetical direction. Underlying this is the microwave contribution &om the material and objects in the Milky way. If all of these are removed and the remaining microwaves subjectedto very careful analysis,fluctuations, which coincide with the emergenceof Galacticstructure,would becomevisible. Changing our observationsto the next, more energetic bands ofradiation, we arrive at the infrared. The sky is once again dark and starshave reappearedon the scene.In general these are stars cooler than can be easily seen at optical wavelengths. They are the red dwarfs and red giant stars.Also presentare the nascentstars in stellar nurseriessuch asthe orion nebula. These protostarsand other young stellar objects are obscured from view at optical wavelengthsby their dusty birth clouds but, at infrared wavelengths,shine through. The Milky way continuesto stretchacrossthe sky again, illuminated not so much by stars but by the infraredglow ofwarm dust clouds.A secondbandalso stretchesacrossthe sky. This one intersectsthe Milky way at an angleofjust under 80oand marks the planeof our Solar System.lt is glowing becausethere is warm dust in interplanetaryspace. Beyond infrared, the familiar optical spectrumoccurs. our view of the Universe at thesewavelengthswas describedin chapterl. At higher energies,the ultraviolet,the very hottest stars in the Galaxy dominatethe view. They are the o and B-type supergiantstars which havesurfacetemperatures of 20,000K or more.Using wien's law l,.o can be calcu-
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asdo otherregionsof of galaxiesglow faintlyin X-raysthanksto thermalbremsstrahlung, hot, tenuousplasmaspresentin our owr Galaxy.The generalbackgroundglow is also punctuatedby point sourcesof intenseX-rays.Someof thesearethe nucleiof powerful activegalaxies.Othersmarkthe positionsin our Galaxywherestarsarebeingrippedto areexplainedtheoretipiecesby incrediblystronggravitationalfields.Both phenomena cally asbeingdueto the actionof blackholes. spectrum,the If we wereto continueto thehighestenergyrangeof theelectromagnetic night sky would look perfectlyblack againexceptfor the occasionalflashof an elrant garnmaray. As yet, thesebursts,which occuronceeveryfew daysfrom totally random directions,are unexplainedand makeup one of the mostfascinatingaspectsof modem highenergyastronomy. weredesignedto illustratejust how biasedour view of the The precedingparagraphs wouldbe if wewereto persistin myopicallypeeringat it with opticalwavelengths cosmos would be ableto tunehis telescopeto pick up alone.ln a perfectworld, an astronomer certainfactorsmitiwhateverwavelengthof radiationhe wantedto detect.Unfortunately, gateagainstthis. Oneis thatdifferentstylesoffocusingdevicesanddetectorsareneeded in orderto receivedifferenttypesof radiation.Anotherfar moreseriousproblemis that, evenif you wereto build a detectorfor eachkind of radiationandmountthemin a field, stops the Earth'satmosphere only someof them would receivesignals.This is because certaintypesof radiationfromreachingthesurfaceof our world (seeFig. 2.7). Photon endrgy {eV) 'to3
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regionof the spectrum'Thus' latedto be 70 nm; a wavelengthin the extremeultaviolet in the Galaxywould bestars brightest the obscurity, to whereasmoststarswould faje the spectrum' comeevenbrighterif we couldseethe ultravioletregionof around.This is knownas As well asthe individualstars,thereis alsoa glow from all rhe SolarSystemand ,bubble' which within 'cavity' andis a rougtiiy spherical the local explosionlong supernova a by produced been have thoulghito is ,urro*oing starssit. It a bubbleshape into atoms ugo.ff,e siock wavefrom thatixplosionhassweptinterstellar *hi.h no* glowsat ultravioletwavelengths' the sky continuesto glow faintly at passrngon to evenmore energeticwavelengths, the X-raybackgroundcomesfrom ultraviolet, the locally*produced X_rayenJgies.Unlike fromdistantgalaxies'Clusters andis thoughtto 6. tn. combinedemission vastdistances
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Sec.2.5l
Telescopes,detectors and spaceprobes 33
Abovewavelengths of 20 metres,radiowavesarereflectedby the Earth'sionosphere. Most,but not all of the infraredradiationis absorbed by molecules in the atmosphere. Opticalwavelengths, obviously,passthroughwithouthindrance.Apart from theultraviolet radiationwhich causessuntans,all the high energyphotonsare blockedby various interactions Thesetake placebetweenaltitudesof a few with atomsin the atmosphere. tensto a few hundredsof kilometres.The typeof radiationwe wishto observedetermines the style of detectorwhich hasto be built and whetheror not it hasto be madeinto a satelliteandsentinto space. 2.5 TELESCOPES.DETECTORSAND SPACEPROBES
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FromEarth-based astronomers can detectpredominantlyopticaland radio observatories waves.Usingtelescopes for opticalashonomybeganwith Galileoin 1609.He appliedthe designof HansLippershey,a Dutchspectaclemaker,andimprovedit. His telescopeallowedhim to makethe mostremarkable discoveriesin his dayandage,includingobservathe Copemicanview of a heliocentric tions of the moonsof Jupiterwhich strengthened thosewho followedhim to build biggerandbetterteleSolarSystem.It alsoencouraged scopesin an effort to discovermoreandmore.Newtonalsodesigreda styleof telescope which is still widely usedtoday by amateurastronomers and, indeed,is known as the Newtonian. areenormousin sizecomparedwith those Today'splofessionalastronomytelescopes original ones.Many existingtelescopeshavemirrors which are 4 metresin diameter, whilst a new generationoftelescopesis cunently underconstructionwhich possess 8-metremirrors.The largesttelescopein the world is the Keck Telescopeon the extinct volcano,MaunaKea,Hawaii,whichpossesses a primaryminor l0 metes across.It is so largethat it wasunrealisticto build a single,continuousmirror of the size.Instead,it is constructedlike an insect'scompoundeye,with 36 hexagonalmirror segments held in place by electronicsupportarmsto createthe giant mirror. The Keck Telescopehas provedto be so successful thata second,identicaltelescopeis currentlyundergoingconstructionon the summitof MaunaKea. This siting of the telescopeis not unusualfor modemobservatories diffrcult conditionswhichworkingat altitude despitethesometimes cancreate.Mountaintopsarean idealsituationbecause thetelescopes areelevatedabove msstofthe weatherandturbulentair, whichobstructobservations from sealevel. Atmospheric turbulencecanalsobe combatedin otherways.For instance, a technology knownasactiveandadaptiveopticsis just provingitselfviable.Active andadaptiveoptics form a systemwhichallowsa reflectingsurfaceto be controlledby mechanical actuators.The qualityof the imagebeingproducedby the telescopeis continuously monitored andanydeviationfrom perfectionis registeredso that stepscanbe takento makeconections.A computerdetermines howto movethemirrorto maketheimageperfectagain(see Fig.2.8).Thissystemhastwo advantages. Thefirst is thata largemirrorcanbe manufacturedandsupportedin manyplaces.Formerly,the rigid construction of a miror to a level which preventedflexuremadeit prohibitivelyheavy.The secondadvantage is that,providingthesystemcanreactfastenough,it candetectimperfections in the imagecausedby atmospheric turbulenceandcompensate for themby manipulatingtheminor. This typeof technologylookscertainto be installedin moreandmoreobservatories overthe coming decades.
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Fi g 2.8 S c hemati c di agramofanadapti v eopti c s s y s tem.Thek ey c omponenti s thew av efront detecror.which sensesthe distortionin the incomingwuu. rront,ito*ini,r,. the mirror to comDensate ""rp"i"ri"'.q*,
All a telescopeprimarilydoesis collectlight. It is up to the astronomer . what is done with that light onceit hasbeencollected.originatly, viiual observations weresufficient, butcontemporary sciencedemands hardfactsanadatato backup anyassertions whichare made.A plethoraoftechniquesanddetectorshassprungup to help astronomers record theirfurdings. Two basictechniques ofanarysing the light colrected by telescopes arethoseofspec_ troscopyandphotometry.A spectroscope splitsthe incominglight into a spectrumso that its spectrallines can be studied.As discussedearlier,the pattem of spectrallines can indicatethe chemicalspresentin the objectunderinvestigation, andthe iize andshapeof thespectrallinescanleadto conclusions aboutthemotionofthat object.Aboveandbelow the spectrum,the spectroscope superimposes referenceemissioniin"., .o that accurate wavelengths for the observedspectrallinescanbe measured. Devicesknownas micro_ densitometers canbe usedrostudythe intensityof radiationalongthe spectrum, andit is fromthesetracesthattheshapes ofthe spectrai linescanbe founj(seenig.2.9i. It is fair to say that the vast majorityof astronomers usespectroscopy to studytheir chosenobjectsbecause the level of informationreturnfrom a singleobservation canbe veryhigh.However,spectracanbe time-consuming to recordbecalse,in traditionarspec_ troscopes, the light froman objectis passedthrougha slit aperfureandthenexpanded into its constituentwavelengths. This can dramaticallydecreiseits brightnessano thus in_ crease thetimenecessary for theexposure. Photometry is a technique wherebythe brightness ofa celestialobjectis takenat variousdifferentwavelengths. Thosewavelengths areknownasphotometric bandsandhave
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FrequencY by a specificshapeknown as a Gaussian Fig. 2.9.Absorptionandemissionlines arecharacterised profile, which can be obtained by tracing with a microdensitometeracrossa spectral line. (Adaptedfrom Kitchin, C., Stars,Nebulaemd the InterstellarMedium'Adam Hilger' 1987.)
They havealsobeengiven letternames:for to specificwavelengths. beenstandardised of 2.22micronswhich is in the the K photometricbandrefersto the wavelength instance, practised by placingfilters betweenthe is The technique infraredregiol of the spectrum. telescopeandiome form ofphotoncountingdevice.The filters only allow specificwavelengthsoflight throughto the counter,which recordsthe intensityoflight at that wavelength(seeFig.2.10). it canrevealtheirblackbodytemperaPhotometrycanbe usedto classi$ starsbecause tures.It is very usefulat trackingvariationsin theamountof radiationwhich is outputby celestialobjectsover a periodof time. A goodexampleof wherephotometryis particularty usefulis in the classificationof variablestars.Photometryshowsjust how they vary (seeFig. their light outputoverthecowseof time andallowslight curvesto be constructed analysisof photometricdatacoveringa wide rangeof wavelengths 2.11). Sophisticated can yield many ofthe sameconclusionswhich can be derivedfrom spectoscopybut, than the the collectionof photometricdatais evenmoretime-consuming unfortunately, data.Thus, the consfuctionof highly complicatedspectrocollectionof spectroscopic scopesis still favouredoverthe useof the simplerphotometers. A third, lesspopularthoughno lessvalid,techaiqueis thatof polarimetry.Thismethod of observingcelestialobjectscollectsinformationaboutthe orientationofthe electric It canbe a powerradiationbeingcollectedby thetelescope. vectorin theelectromagnetic ful tool in probingregionswhereradiationis beingscatteredby dustor electrons.It can alsohelpto showup regionsof spacecontainingmagneticfieldswhichhavealigneddust grains.Thus,the techniqueis excellentfor probingthe interstellarmediumin this and othergalaxies. astronomer. The light caparenow insufficientfor theprofessional Visualobservations the above techniques must now be processed via of one telescopes and large tured by recordedfor later analysisand publicationto scepticalcolleagues.Photographyis still usedby some,but by far the mostrapidly developingtechnologyis in a type of detector
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WaVelength{nm} Fig.2.10.Thespectral response ofthedark-adapted eyeandoftheU (ultraviolet), centred on365 nm,B (blue),centred on440nm,andV (visual,i.e.yellow-green), centred on550nm,pass-band filtersusedfor photometry in theUBV system. known as a ccD, or 'charge coupled device', an instrument which is so sensitive that it records almost every photon which strikes it. It is a computer chip which usesa detection mechanism,similar to the photoelectric effect, to record the number of photons striking it. These are instantly tumed into an elecfrical signal which can be read out into a computer memory for later analysis and display. Another way of saying that a ccD has the ability to count almost every photon which strikes it is to say that it has a high quantum efficiency. This is a ratio which can be easily understood as the number of detected photons divided by the actual number of incident photons. In other words it gives the percentageof photons which are actually detected when they strike the detector. A ccD will typically have a quantum effrciency in excess of 75 per cent, whereasa photographic systemwill rarely be more than I per ceht. ccD chips are made of semiconductors,the choice of which determineswhich part of the electromagnetic spectrum will be detected.ulfiaviolet, optical and infrared can now all be observedwith the correct CCD. The collection ofradio wavelengths,however, takes place with totally different t,?es oftelescopes and detectors. A radio dish works in exactly the same way as an optical telescope.The reflector still needsto be parabolic but, becausethe wavelengthsofradio radiation are so much longer, it no longer needsto be silvered. The detector is placed in the prime focus position on the radio dish, where a secondarymirror is usually, but not always, found on an optical telescope. Radio astronomy has pioneereda techniqueknown as interferometry, which effectively increasesthe resolving power of a telescope by linking it in tandem with another. The
36
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Otherwaysofobserving theuniverse37
The resolvingpowerof a telescopeis proportionalto the wavelengthof radiationdividedby the apertureof thetelescope. Thuswith an increasein the wavelength, theresolving powerof the telescopecanbe maintainedonly if a commensurate rise in the apertwe ofthe telescopeis alsoachieved.The radiowavesgivenout by neutralhydrogenaresix ordersof magnitudelongerthanvisiblelight so, in orderto get the sameresolutionfrom the aperhrewould needto be one million timesthe sizeof opticalteleradiotelescopes Obviously, anotherwayhadtobe found. scopes! Interferometrywas that otherway. It was pioneeredat CambridgeUniversityin the 1940s.It allowsan objectto be observedsimultaneously by two or moreradiotelescopes. The signalscollectedby the dishesarethen combinedand interferencepatternsare obpatternscanbe usedto constructdetailed tained.UsingFourieranalysisthoseinterference imageswith muchgreaterresolutionthana singledishon its own couldachieve.Lnterferometryin theradioregionof the spectrumhasbeenso successful thatthemethodhasnow too. A pioneeringteamof astonomersat Cambridge beenappliedto optical telescopes hasappliedthe technologyto producean imageof the starCapellausingfour smalltelescopestogether.Now, a numberof much larger observatoriesare under construction aroundtheworld which all hopeto exploitopticalinterferometry. The impenetrability ofthe Earth'satrnosphere makesit necessary to sendspaceprobes andsatellitesinto orbit in orderto collectthosewavelengths from which we areshielded. High energyradiationis almosttotally blockedout by the atmosphere. Apart from the smallamountofultravioletradiationwhichpenetrates theatnosphereandcausessuntans, the vastmajorityofultraviolet radiationhasto be collectedby spaceprobessuchasthe IntemationalUltravioletExplorer(IUE). At evenshorterwavelengths, the EinsteinX-ray Observatoryhas surveyedthat region of the electromagneticspectrum.Thesespace probesrequirea slightly differenttype of mirror systemknown as a grazng incidence mirror.This type of mirror is an annulustakenfrom the cylindricalwall of a paraboloid ratherthanfromthebowl asin opticaltelescopes. In orderto maximisetheamountof high energyphotonscollected,annuliof successively smallerradii are nestedwithin one another. Molecularabsorptionblock a lot of infraredradiation,but this too hasnow beensampled from spaceby the Infra-RedAstronomicalSatellite(IRAS) and the InfraredSpace ObservatoryQSO).Evenwavelengths which can be studiedfrom Earthhavebeencollectedin space.High abovethe Earth'satrnosphere, the starsremainsteadyandunwaver(HST) is currentlyperformingmagingly sharp.The celebrated HubbleSpaceTelescope nificentlyby collectingunprecedented imagesof thecosmos.
200
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resolving power of a telescope is simply a measureof how apparently close two celestial objects can be to each other before the telescope is incapable of showing them as two distinct objects.For optical telescopes,the resolvingpower can often be so good that the distortion of the images through atmospheric trubulence is the biggest source of image degradation. For radio telescopesthis is not the casebecausethe wavelength ofradiation is so much larger.
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2.6 OTHER WAYS OF OBSERVINGTHE UNIVERSE Whilstit is trueto saythat90 per centofobservations areundertaken by detectingelectromagneticradiationfrom space,thereare otheremissionswhich can be studied.One methodis the detectionof tiny particlesknownas neutrinos.Theseparticlesarea fundamentalconstituent of the cosmosandcany excessenergyawayfrom nuclearreactions. Neutrinodetectors havebeenverysuccessful in detectingthesefleetingparticlesafterthey havebeenproducedin the heartofthe Sun.Additionally,andperhapstheir greatestcollectiveclaimto fame,is thatthe detectorsidentifieda burstof neutrinosfrom thenearby supernova of I 987,exactlyaspredictedby theory.
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detectors. Undeniably,they are still very crudewhencomparedwith electromagnetic they sky the ofthe neuffinos area which tell from to For instance,they cannotbe used powerprovide will another devices ofthese refinement The continual come. have detect detail' ful resourcewith whichto probethe Universein everincreasing which is in its infancy at the moment,is the instrumentation, of tecbnology Another gravitationalradiationdetector.Gravitationalradiation is predicted,by the generaltheory of relativity,to be releasedfrom massivebodieswhich are changingtheir gravitational continuumin the throughthe spacetime relationshipwith oneanother.It wouldpropagate andrarefacpattern compressions of (i.e. a repeating wave motion form of a longitudinal tions) and distortany objectsin its path.The distortionswould manifestthemselvesas minusculevariationsin the lengthof objects.As yet,however,technologyis insuffrciently to be ableto detectthesewaves,sincethe sizeofthe variationsthey induceare advanced is of the diameterof a hydrogenatom.Meanwhile,research vanishinglysmallpelcentages foreveradvancingand the sensitivityis graduallybeingpushedcloserand closerto the detectionlimit. Gravitationalradiationis the final testofthe theoryofgeneralrelativity.Thereis even radiationsimia hopethat it maybe possibleto detecta cosmicgravitationalbackground lar ti ttre cosmicmicrowavebackgroundradiation.If this wereto prove possiblethen, a view of the Universeas it existedonemiltheoretically,it would afford cosmologists Bang!. Big the after a second of lionthof a millionth
2.7 PARTICLE ACCELERATORS AND THE ARCHITECTI]RE OF MATTER Oneof the mostinnovativewaysin whichphysicistsstudythe beginningof the Universe This technologyis is to usegiganticpiecesof equipmentknownas particleaccelerators. the perfectsynthesisof the very small,namelysub-atomicparticles,with the very big' namelythe entireUniverse.Insidethesedevices,streamsof sub-atomicparticlesareacceleratedto velocitiescloseto the speedof light, which suppliesthemwith similarquantiduringthe earlyUniverse.To simulatethe ties of energythatthey wouldhavepossessed beamsof particlesarethen densityof matterfrom thoseearlytimes,highly accelerated a liberation of energy cause result which collided with eachother. The annihilations populated the earlyUniparticles must have which of creation to the leads which,in turn, versein largenumbersbut no longerexistnaturallyin ourpresentdaylow energycosmos' to testtheirtheories,particlephysicistshavedevThroughtheuseoftheseaccelerators almostall particlesandtheir interactions.The explains elopeda standardmodelwhich go to makeup matterfall naturally into two famiwhich particles nature of fundamental lies. Theseareknown as the leptonsand the quarks.Both familiescontainsix particles of pairs.The mostfamiliar leptonsarethe first genwhich aresplit into threegenerations neutrino(usuallyreferredto simplyastheneuelectron the pair: and the electron eration arepopulatedby heavierversionsof both the electron trino). The othertwo generations (themuonandthetau) andthe electronneutrino(themuonneutrinoandthetauneutrino). heavierversionsof the up anddown of successively arecomposed The quarkgenerations quarks;the charmandthestrange,thetruth andthe beauty(seeFig.2.12). particlescancombinein manywaysto becomethe mattercontent Thesefundamental chargeof -1. The up an electronhasan elechomagretic of the Universe.For example,
Sec.2.7l
Particle acceleratorsand the architecture of matter
LEPTONS z o
E
4
g
{ g a = o
e -a
39
HADRONS vso Eslron lleufim
El€atm Rosponsiblo tor slectricity wilhnoelectric and Particle charge redctions. chemical lhstrar€lyinteracts withoth6r matter. your It hasa charge of-1. Billions tlythrough bodyov€rywond,
lla Up Oulrk li€sanelectric charge ol +28, Protonrhavetwoolthem,while neutrons naveone.
O. DowtrO[ork Hasanelectric charge of -1/3, Protons haveon6of thom,while nsutrons havstwo.
vpa lluor ilautritro iluon rslative A heavi€r ofth6el*tron Crested alongwithmuonswhen $m6 particles dtray.
co
so
E g 2 E
Cham Ourrl A heaviflrelative ol theup.
Strrnge Ouail( A h€avier rslative of thsdown.
z o
rf
I
E c a 2
E u 2 g
o a e
p'a
Tru H6avierstill.
a v1 Tru Nautrino yst Not dismveredbutbeli€vsd to exist.
o n:ii'I,
Top tne
quarkol all.
bo Eottom Ourrk fleavigrstill.
Fig.2.l2. Leptonsand hadrons,the fundamentalparticlesof the Universe.(Adaptedftom gig Bang Science,ParticlePhysicsandAstronomyResearch Council.)
quarkhasa chargeof +213whilst the down quarkhasa chargeof -ll3. In orderfor the quarksto combineinto themorefamiliarsub-atomicparticles,neufionsandprotons,they mustcometogetherin the right combinations. Two up quarksandonedownquarkmake up a protonwhich possesses a chargeof+I. Oneup quarkand two downquarkscome togetherto form a neutronwhich caniesno charge.Thesehybrid particlesmadefrom quarksare lnown as hadrons.Hadronscan be subdividedinto quark fiiplets known as baryons,suchas protonsandneutronsandmesonswhich consistof a quarkand its antimattercounterpart.Electrons,protonsandneutronsthen combineto form atoms.The exactnumberof electrons,protonsandneutronsdefinesthe atom'schemicalidentity. Thereare very few stablepaniclesin the Universetoday.Only the electronand the electronneutrinoare truly stable(photonsof radiationcan also be consideredstable). Neuffonswill decayinto an electronanda protonin about896 seconds, if removedfrom an atomicnucleus.Protonsmay or maynot be stable.If they arenot stabletheydecayin lifetimesof aroundl03ryearsandbecomea positronanda pi-mesonwhich,itself,decays into trvophotons.Althoughtheirvastlifespansmakethemstablefor all currentproblems, the very long-termfutureofthe Universecould be affectedifprotons do decay.All the otherhadronshavelifetimesof a merefractionof a second. All the particles,be theyleptonsor quarksandtheir composites, interactwith oneanothervia the exchangeof a third groupof particlesknown as gaugebosons.It is these particleswhich carry the forcesof nature.Throughouthumanhistory,what were once thoughtto be totallydifferentforceshavebeenshownto be differentmanifestations ofthe sameforce. For instance,Newtonshowedthat the motion of the planetscould be explainedby the sameforcethatcausedtheproverbialappleto fall to theEarth:gravity.On thefaceof it, two totallydifferentphenomena which,in realiqv,weremanifestations of the sameunderlyingprinciple.Earlierin this chapterwe sawhow electricity,magnetismand light wereunified.Later,Einsteinshowedan interconnection befweenspaceandtime in specialrelativityandthenlinkedthis work to gravityvia his generaltheoryofrelativity.
40
The tools ofthe trade
lch.2
forces.Theyare Todaywe recogniseonly four forces,which we tenn the fundamental the weaknuclearforceandthe strongnuclearforce.Eachone gravity,elecffomagnetism, ofthem actsdifferentlyfrom the others.Theyarecarriedby gaugebosonsin the standard is carriedby the photon,which we havealreadymet,andthe model.Electromagretism weaknuclearforce is canied by threedifferentparticles,the neuftalZ" andthe charged to thephoton W" andW-. Theseparticlescanbe thoughtof asbeingsomewhatanalogous mass.The stong nuclearforceis a chargeandtheyall possess exceptthatthe Ws possess also mediatedby a gaugeboson,known as a gluon,which transmitsthe force between quarks.MesonsthenFansmitthe forcebetweennucleons.As yet,thereis no convincingquantumtheoryofgravity, althoughthehypotheticalgaugebosonhasbeennamedthegraviton. forces The massof thegaugebosonsaffectsthe distanceoverwhichthesefundamental uncertainlyprinciplewhichstates: ofthe Heisenberg canact.This is a consequence
Sec.2.7l
Particle acceleratorsand the architecture ofmatter
4l
i
E
E
-P E a
aEAt=I
(2.8)
2n
Sincethe energyAE to createthe gaugebosonsis bonowedfrom the energyfield ofthe spacestrrounding the interactingparticles,that energyhas to be paid back before equation(2.8)is violated.Equation(1.2)tellsushow muchenergyneedsto be borrowedand so the timethe particlecan'live' for, At, is givenby a combinationof thetwo equations. A t= -\ 2{nd
Q.e)
Therangeofthe force,r, canthereforebe shownto be inverselyproportionalto themass ofits gaugebosonbecause,accordingto specialrelativity,nothingcantavel fasterthan the speedof light in a vacuum. r-< c At=
1 h * 2nmc m
(2.10)
The weaknuclearforce is canied by massiveparticleswhich limit its rangeto approximatelylO-r?m.Themesonswhich carrythe strongnuclearforcearelessmassiveandcan canexistforeverandsotherange reactovera distanceof l0-r5m.Photons,beingmassless, forceis theoreticallyinfinite.Overlargeregionsofspace,however, ofthe electromagnetic forceis, in fact,confined.Gravitons electricalchargeis neutralandsotheelectromagretic which canbe positiveor negaand,unlikeelechomagnetism, aretheorisedto be massless cannot be cancelled out. This is the reasonit thus it gravity athactive, is only ever tive, shapesthe Universeon its largestscales. canexaminethe behaviouroftheseparticlesandforcesin condPanicleaccelerators itionswhich mimic the early Universe.By doing so, a remarkabletheoryhasbeenconandthe weaknuclear firmed.A groupofphysicistshad proposedthat electromagnetism in the Confidence forcewouldactin exactlythe samefashionat sufficientlyhigh energies. by theparticleaccelerator Salem,WeinbergandGlashowtheoqywasboostedenormously andthe weaknuclear confrrmations oftheir predictions.Fromnow on, electromagnetism force.This success hasIedphysicistsand forcewouldbe foreverlinkedastheelecffoweak cosmologists to believethat the strongnuclearforcecould alsobe unified with the electroweakforce.It is postulatedto takeplaceat evenhigherenergiesandis explainedby a
t t t
1015
10rs (Planckscalo)
(GeV) Energy Fig. 2.13. Unification offorces. Centralto most cosmologicalideasis the notion that, as the temperatureof the Universewas higherat earlierald earliertimes in history, so the distinction betweenthe separateforcesofnature waslessand lessapparent.(Adaptedfrom Silk, J..A Short HBloryof the Universe,W.H. Freeman,1994.)
setof ideasknownasthe grandunifiedtheories(GUTs).This is a set of theorieswhich setsout to uni! all the fundamentalforcesexceptgravity. A numberof GUTs exist, but asyet nonehavebeenproven.GUTspredictthatprotonsshoulddecay. Somephysicistsand cosmologists believethat, following a successfulGUT, gravity wouldbe unified andeveryinteractionin the Universewould be describedin termsof a singlefundamental forceof nature.Thislevelof unification,if it evenexists,is a longway intothe future.A quantumtheoryof gravityis requiredfust (seeFig. 2. I 3).
t t t t t t
L L
F
Observationalcosmology Cosmologyis, by its very nature,an observational science.It is passivein that we must wait for eventsto happenin the Universewhich we canthenwatchandlearnfrom. Not for the practisingcosmologistis the relative easeof making a universein the laboratory,although simulationsof the early Universeare partially possible in particle accelerators. havephysics,an experimental Luckily, as pointedout in chapterl, asfronomers science, on their side. Every piece of cosmologicalinsightgainedis achievedby painstakingly usingthe physicsgleanedfrom laboratory modellingobservedcelestialcharacteristics, experiments. The first fundamentalobservationwhich canbe madeaboutthe Universe,as a whole, is that it containsmatter.The radiationcontentis not so surprising,aswe shallsee,but the fact that solid lumps of matter aboundis rather a shock! The reasonfor the surpriseis currentlybeingconducted because ofthe resultsfrom experiments in particleaccelerators, mentionedin chapter2. In theseexperiments, the interchangeability of massandenergyis explored.Energy,caniedby photons,canbe changedinto massundercertahconditions: for example,if the photongetscloseto a heavyatomicnucleus.Whenthis happens,two particlesare produced- one of matter,the other of its anti-mattercounterpart.This is necessary to conservechargeamongotherquantities.For the purposesofthis example, imaginethat the two particlescreatedarean electronandits counterpart,a positron.Eventually and usually soonerratherthan later,the positron comesinto contactwith.the electron (or anotherwhich is just like it) andthey annihilateeachother,returningtheir energy backinto photons(seeFig. 3.1).Ifthis processholdstue univefsally,thenfor everypadicle of createdmatter,thereshouldbe an antimatterequivalent.Eventually,mutualannihilationeventswill returnall themassenergybackinto photons,leavingnothing&om which to makestars,planets,you or me.Couldit be thatthe antimatterhassomehowbeensegregatedfrom the matter?This is a ratherunsatisfactoryexplanation,sincethereis no obserfrom the point ofview ofthe cosvationalevidenceto supportit. It is alsounsatisfactory mologicalprinciple,aswill be explainedshortly.Somewayhasto be devised,within the knownlawsof physics,which enablesthe ratio of matterparticlesto antimatterparticles to be greaterthan l. Currentapproximations, baseduponthe ratio ofphotonsto matter particles,suggestthat the asymmebyof matterto antimatteris probablyonly onepart in a billionl Very smallindeedbut, asinsignificantasonein a billion may sound,it hasled to a profoundlydifferentUniversethanonefilled with radiationalone.
lch. 3
44 ObservationalcosmologY
/ \ Two photons collide
a -
€./._A
/ \
-i=-*^
v
/ \ / \
)
Positronand electroncreated
/ \
Sec.3.ll
Look-back time
45
aneously,over somethingaslargeasthe universe,however,eventscantakea longtime to propagate.so long in fact,thatthethe moredistantthe object,the morein thepastwe areviewingit. To quantif,thischaracteristic ofthe universe,astronomers havedeveloped a distanceme4surement systemknownasthe light year.This is the distancefavelled by light in a singleyearandis equivalentto 9.4607x l0r2kilometres.If two starsareseparatedby a distanceofone light yeartheneventswhichtakeplaceon onestellarsurfaceare only apparentto the other after a period of .oneyear,during which time the light released by the eventhastravelledthe9.4607x l0r2 kilomehesbetweenthe two objicts. closer objectswill be ableto observetheeventbeforemoredistantobjects.Thus,a galaxywhich is onebillion light yearsawaywill appearto us as it did onebillion yearsago.This phenomenonis knownaslook-backtime (seeFig. 3.2). The informationthat an eventhastakenplace propagatesoutwardsin a sphericalvolumearoundthe eventwith a radiuswhich increases with the speedof light. The ,surface' of the sphereis knownas the particle'shorizon.over smallvolumesof space,an event whichtook placeat time,t,, will havea presentday(i.e.time = to)particlehorizon,r", of: r.= c( h*t r ) (3.1) Over largedistancesof space,relativisticeffectswill destoy the simplicityof this relationship.Diagrammatically, this behaviouris represented by a light cone(seeFig. 3.3).
{
i, t,
i
I
Positronand electroncollide
\
n/ @-1.-c
This image is only one quarterof the way to Earth.
lI.,tr
\
ir
/
lt i
\
i,.
I
i
li
i',
This is how the galaxiesappearnow.lt will takeone billionyearsfor this imageto reachEanh.
)
Thi s i mage i s one hal f of the way to Earth.
Two protons
Produced
Fig. 3. L Pair production:the creationof a matterparticloand its antimatt€rcounterpart,resulting fiom photon interaction.
3.1 LOOK-BACKTIME At fust, thevery ideaof cosmology,i.e. observingtheUniverseasit existsnowsothatwe It would be like taking a snapshotof a can tell how it all began,seemspreposterous. personand telling his or her entire life story from that one singlephotograph.Yet the aim feeljustified in doingthis. A key element, of this chapteris to explainwhy cosmologists is that light and all ofour consideration, the beginning right at introducing which needs radiationcanonly travelat a finite speed. otherformsof electromagnetic with a value in chapter2, the speedof light in a vacuumis uhsurpassable, As discussed almostinstant' of 3 x l0Em/s.On terrestrialscales,this meanseventsare communicated
AQ) One billionlightyears
6
(t)
This image is three quartersof the way to Earth. Thi s i s how thes e galaxies appear to us on E arth. The i mage i s one bi l l i on y ears out of date!
Fig. 3.2. The finite speedof light causesthe phenomenonof look-back time The deeper astronomers look into space,the moreanciontthe objectstheysee.
t t t t t i
t L
; ; ;' l ll
,l
lt bl
rt,i
I
LJ
I
,i
_l l
46
ObservationalcosmologY
lch. 3
namedafterthe physicistwho Light conesare drawnon Minkowski spacetimediagrams, exists in the universe can be which first proposedthe conceptof spacetime.Anything as 'world lines'.For unacknown paths will follow they diagram. spacetime ;;;;" themto becomecurves' causes " acceleration but straigbt are lines world ieleratedtravel, is travelling' For exartobject fast the rrr" gaoie* of a world line is an indicationof how or infinity depending zero either gradient of line world objectwillhave a ;;, ;;;r;"rry thg* in the Universe' fastest the being rays, Light axis. time the of orieniation ;;ilr; .geodesics,through6e spacetimecontinuumandhavea set gradient iJrr"* p"a, called i'e. arecausallyconnected, ro. trr.i,.world lines.objectswithin iach other'slight cones their during to occur effects ian cause hence and photons ,h.y i";. beenableto exchange Objects a timelike seParation' ,"rp".iiu. lifetimes.The two |Uitttt *. thensaidto have separation. space-like possess . noi wittrinoneanother'slight conesaresaidto obviousthat Universe,thenit becomes the ligfi coneofthe observable Ifone considers becauselight from themhas theie could very well be objectswhich we do not know exist
Sec.3.2l
Olbers'paradox 47
not reachedus yet. Sincethe light coneofthe Universeis defuredby its age,any object from us cannotpossiblyhaveinfluencedour evolution. whichhasa space-likeseparation Theseunknowableregionsaretermeddomainsand could,conceivably,havetotally differentlawsof physics.The limit of our observable Universeis knownasaneventhorizon. we cannotobserveit because thecosmicmicrowavebackground Unforhrnately, blindsour sight,aswe shallsoondiscover. 3.2 OLBERS'PARADOX observation which canbe made,andis possible Olbers'Paradoxis anotherfundamental with nothing more than the naked eye. Ask anyoneto describethe night sky and the chancesarethat oneof the first thingstheywill tell you is that it is dark. Kepler,whoselaws of planetarymotionwe encountered in chapterl, pointedout in 1610that if the Universeis infinite, with starsscatteredrandomlythroughoutit, why is it dark at night?After all, in whateverdirectionone caresto look, our line of sightwill, sooneror later,cometo reston the surfaceofa star.Although light suffersfrom an inverse squarereductionin its intensitybasedupon its distance,the further one looks into space, themorestarswill appearin our line of sight,compensatingfor the dimming.This curious phenomenonwaspopularisedover a centurylater by Heinrich Olbers,andnow bearshis name(seeFig.3.4).
I
I
I
Porticte hor'zon If oneeventis situatedwithin Fig. 3.3. Light conesshowthe propagationof light from anevent' event is situated outside the it E'rigiti .o"ni of *t" other,.then the/are causall-yconnected.If one other's existence (Adapted each yet of awate nbt are events two the then o*er, of tfre iiJfrllone 1994') to Cosmologt,Wiley, lztoduction M., frim Roos,
Fig. 3.4. Olbers'Paradoxaskswhy the Universeis dark at night.If it were infinite in extent,then our line of sight would eventuallymeetwith the surfaceofa bright star.The reasonthe night sky is dark, therefore,is that the Universeis not infinitely largeand that the redshiftmakesdistant objects more and more faint.
t 48 Observationalcosmology
lch. 3
The most obvioussolutionto the problemis that starsare not distributedrandomly throughspace:insteadthey form galaxies.This providesonly temporaryrespiteandthe aswe shallsoonsee,on thelargestscale,galaxproblemreappears with galaxiesbecause, iesandclustersofgalaxiescanbe thoughtofas beingspreadrandomlyt},roughoutspace. One solution to the problem,which gives us our fust fundamentalinsight into the naof look-backtime.Imagineour Galaxy ture of the Universe,comesfrom a consideration and anotler more distantone to be plotted on a spacetimediagram.We only become awareof the other'sexistence(andvice versa)whentheir light conecrossesour world line. If the Universeis not infinitely old, thentheremust be distantgalaxieswith light conesnot yet in contactwith us. ln orderto resolveOlbers'Paradoxwe havebeenforcedto assumethat the Universe maynot be infinitein age.In doingthatwe havetakenour first steptowardstheBig Bang, becauseit impliesthat at sometime in the pastthe Universemust havebeencreated. resolutionalsoexists,aswill be explainedin thenextsection. Anothercomplementary
Sec.3,3l
lineswhich havebeenshiftedfrom their measuredlaboratorywavelengths. This can be explainedastheopticalequivalentof the Dopplereffect.we areall familiarwith theway in whichbellsandsirenschangepitchastheypassus.Insteadofthinking ofcarsandtrains which emit sound,let us transpose the ideato starshipsandlight rays. Imaginetwo starshipsheadingout into deepspace.Initially, they are both travelling with the samevelocity,althoughstarshipA is in front of starshipB. Atop eachof the spacecraft is a flashinglight.Bothregularlypulseon andoffwith a frequency,f. someone on starshipB canseeboththe flashinglight on his ship andthe oneon starshipA. Ifthis personmeasures the frequencyof both lights it will be found that they arethe same.If starshipA suddenlyincreases to anothervelocityandthe frequencies ofthe two flashing
#
time = tnr
-+
3.3 THE DOPPLER EFFECT The galaxiesin the night sky appearstatic until they are studiedspectoscopically.AstronomerVestoSlipherdiscoveredthatthe spectaof galaxiesdisplayspectal absorption
c
<;-
ti me = tBl
I-B I
i
TheDoppter effect 49
t
A
@
t t t t t
\z
fl
tAl
=+ b
time = tnz
)> An observer heresees a redshift
le l +€
Ad
#
I J
_->
a J
ti me = tB2
IB I@
c
<_
/4. -v__ l^l
--*
Fig. 3.5. The Dopplereffect.Motion ofeither the sourceor the observercausesa Dopplereffect to be impartedto radiation.(Adaptedfrom Kaufmann,W.1., Universe,W.H. Freeman,1987.)
Fig. 3.6. stanhips A and B are separatedby a distance,d, which is getting larger all the time becauseA is moving awayfrom B with a velocity,v. Ifan observeron A and ariobserveron B comparesthe length of time betweenflashesof a light on A, it will be noticed that the time recordedby the observeron B is longerthan that recordedby the observeron A. (Seemain text for a full explanationofthis phenomenon andthe underlyingmathematics.)
.J
l
50 ObservationalcosmologY
lch. 3
lights arecomparedagain,it will be noticedthat fo is smallerthanf but that fr remainsthe same(i.e. equal to f). Thus, a fundamentalchangein the way observerson starshipB thereis now a differencein velocity perceivestarshipA hastakenplacesimplybecause betweenthetwo vessels.This conceptis at the heartof Einstein'sspecialrelativityandis a finite invariantvelocitythrougbspace.Does of light possessing a direct consequence this meanthatthe flashinglight hasactuallysloweddown or doesit just meanthat starship B perceivesit to slow down?This is wherethe conceptof relativitycomesinto play.The in motionawayfrom flashinglight on starshipA appearsto slow downonly to observers it. It doesnot matterwhetherthe observeris moving awayor starshipA is moving away or both are moving away from each other. All that mattersis that they are in relative motion awayfrom one another(i.e. the distancebetweenthemis increasingwith time). The cxactamountby which the flashinglight slowsdown is thendependentuponhow fast they are separating.Sinceit doesnot matterwhich starshipis moving, from an observer on starshipA's point of view,it is the flashinglight on starshipB whichhassloweddown, mathenot the oneon starshipA! The conceptis easyto graspthroughsomeelementary matlcs. If two observers- on€on eachvessel- agreeto time the flashesof starshipA's ligltt, then observerA recordsa time tAr, as soon as the light flasheson (seeFig. 3.6). The obscrveron starshipB beginstiming after ttre the light has crossedthe distance,d, betweenthetwo ships.Hence,the time recordedby observerB is rd
(3.2)
t9 1 = ta 1 *-
I
Whcn observerA seesthe secondflasha secondtime,tA2is recorded.Thusthetime betweenflashes,astimedby observerA, is
(3.3)
t= t4 2 - tAl
it is the time of the flashesas observedfrom the t is knownasthe 'propertime' because light's own frameof reference(i.e. thereis no relativemotionbetweenthe light andthe observer).The observeron starshipB recordsa time of
(o+ la)
ili
tB2 = tr,2 *t-;-
(3.4)
This distance,Ad, is how far the starshipshavepartedin the propertime,t. From equaby observerB can tions(3.2) and(3.4),thetime interval,At, betweenflashesasmeasured be seento be a t-r+ -
Ad
(3.s)
Thus,the increasein the lengthof time betweenflashesis proportionalto the increasein distancebetweenthe two shipswhich,in turn, is proportionalto the relativevelocitybei.e.the starships aregettingclosertogether, tweenthetwo ships.Ifthe distancedecreases, thenAd will be negativeandAt
Sec.3.4l
Redshift 5l
B. This reinforcesthe fact that theseareobservationaleffectswhich haveto be taken into accountwhenwe observeobjectsin relativedotion to us. 3.4 REDSHIFT The next step is to imaginethat the flashing light on starshipA is replacedby a light source.Insteadof the flashperiodgettinglonger,thetime betweenelectromagnetic wave crestswill increaseasthe two shipsbecomefurther apart.This will obviouslyincrease the wavelengthof the light andhenceshift it towardsthe lower energyendof the electromagneticspectrum.In visiblelight,the lowerenerrycolouris rea ani so this phenomenon is knownasthe redshift.If the distancebetweenthe two starshipshadbeendecreasing, the shiftwouldhavebeento theblue,higherenergy,endof theelectromagnetic specfum.The redshift,z, is quantifiedby equatingtherestwavelength,1,,with the o-bserved wavelength, trol
"=+L=*-'=*
(3.6)
Equation(3.5) showedthat the increasein flashperiodwasproportionalto the distance travelledby the starshipsbetweenflashes.This distanceis obviouslyproportionalto the radial velocity, v., of the starship.If we now equatethe flash period to ttre time between wavecrests,the increasein theflashperiodbecomesanalogous to theredshiftandwe can rewite equation(3.5)to be z-v'
c
(3.7)
Earlier in this chapterwe statedthat equation(3.1) neededto be modifiedto take into accountrelativisticeffects.This equationalsoonly holdstrue for certainrangesofvalues, specificallyI v | < 0.lc (seeFig' 3.7).Abovethis velocityrange,relativisticitodifications mustbe madein the following way. Imaginetwo framesof ieference,s and s,, moving awayfrom one anotherin the x direction.If we are observingfrom S, then s, appearsto be moving with velocity v. The t:meordinateis setat zero when S coincided*itt s,. an extemaleventoccursat somefurthertime, t, andis measuredby us andan observerin S,. In orderto compareour measurements to verif, that they arethi same,someway of transformingour coordinates from s to s' mustbe found.ciassicalphysicsur.. u r"t of.quutionsknown asthe Galileantansformation: x'= x - v t y'= y z'=z
(3.8)
t' = t
This implicitly assumesthat light travelsbetweenthe eventand the observersinstantaneously.on the everydayscaleof thingsthis is quite a reasonableassumption,since whenan electric light is turnedon in a roomeveryone,regardless of ttreirpositionwittrinthe room,simultaneously sees.itlight up. when light travelsover largedistances, time delays will be noticedbetweenobserversat differentpositionsin diflerentfiamesofreference. This is becauselight does,indeed,havea frnite velocity.It is extremelyfast, covering
lch.3
52 ObservationalcosmologY
Sec.3.5i
TheHubble flow 53
It is implicit in this transformationthat time is affectedby velocity. This is a phenomenon which hasbeenchristened'time dilation'. Sincethe wavelengthis relatedto the time betweensuccessive emissionsof a wavecrest,it becomesobviousthat time dilationmust alsocausea redshift.Insteadof beingthe radialcomponentof velocity,time dilationdependsuponthe overallvelocityofthe sourceor observer,v. Whenthis is takeninto acc(3.6)becomes: ount,equation
10 Velocityin relativistic units(c=1)
(3.1 0)
i i
If the velocityis entirelyradial,v = v,, the equationsimplifiesto:
This canbe rearranged to givethevelocifyofseparationbetweenthe sourceandobserver basedupona measurement ofthe source'sredshift:
Redshift Fig. 3.7. fhe linear redshift approximation(solid line) _canbe made only when velocitiesare bel-owone tenthof the speedof light. Abovethis figure,the full relativisticformulamustbe used (dashedline).
(3.r2)
approximately3 r lOt nrls, but finite nonetheless.As soon as the relative velocities of sourcesand observersgrow to more than 10 per cent of the speedof light' a totally new set of fiansformationsmust be usedwhich relies on the fact that different observersin different framesof referencemay not recordthe eventat the sametime. It alsotakesinto accoult the observationallyverified fact that light appearsto havethe samevelocity regardlessof the velocity of the observer.Thesewere originally derivedempiricallyby Lorentz to explain the failure of the Michelson-Morley experimentto detectthe ether. Later, in his specialtheory of relativity, Einsteinderivedthem again,but from a formdation of soundtheoreticalarguments.Nevertheless,they go by their original nameof the Lorentztransformation: .
(* -u t) l)
lt-u1l^ c2 v' = v
(3.e) /It--t vx) I c2)
t t t t t
Usingthis equafion,redshiftslargerthan1 no longeryield theunphysicalsolutionthatthe distancebetweenthe sourceand the observeris increasingat a velocity greaterthan the speedoflight.
3.5 THEHUBBLE FLOW Slipher'swork showedthat, in the majority of galaxiesstudiedby him, the shift in the wavelengthof the spectrallines was to the red end of the spectrum.only in a few rare casesdid the lines shift towardshigherenergies. slipher's observations wereextendedand finally explainedby asfronomerEdwin Hubble.As well as developinghis morphologicalclassificationschemefor galaxies,he was also dedicatedto determiningjust how fu awaygalaxieswere. In l9z+ he fnally showedthat the AndromedagalaxyandM33 weretoo far awayto be containedwithin our Milky Way. He wenton to determinethe distances to othergalaxiesand,in the process, beganto realisethat a trend in the data was becomingevident.The further awaythe galaxy,the greatertre redshiftseemedto be. with the help of fellow Mount wilson astronomer,Milton Humason,Hubbleinvestigated this dependence andfoundit to be a linearproportionality.With the exceptionof a few nearbygalaxieswhich aregravitationally boundto the Millqy way, every other seemedto be displayinga redshift, indicatingthat the distancebetweenit and the Milky way was increasing.The linear natureof the
t i
t t I L
L L
54 ObrcrvationalcosmologY
[ch.3
proportionalityindicatedthat if two galaxiesexisted,one at doublethe distanceof the othcr,the nearergalaxywouldbe movingawayfrom us with only half the speedof the The factthatthe Universeis furthcrone.This is a propertyknownasuniformexpansion. oxpandingaroundus,causingthe galaxiesto move awayfrom us, is knownasthe Hubble of theBig Bangtheory. flow, It is a comerstone law also finishesour resolutionof Olbers' Hubbleand Humason'sredshift-distance Poradoxby consistentlyreducingthe energyof the light coming from distant galaxies. This makesthemappeareverfainterandhencemorediffrcultto observe. ln tho oarly half of this centurythe RussianastronomerAleksandrFriedmannand the predictedthe Bolgianpriestand cosmologistGeorgeLemaitreboth, independently, verification.Lemalte wenton to postulate Hubblcflow two yearsbeforeits observational thEttho Univcrsemusthavebegunas a compactedprimevalatomwhich thenexploded rnd rcattcrcdmatterthroughoutspace.He basedthis ideaon the fact that sincethe galaxlol woroall moving awayfrom oneanother,theymustoncehavebeenvery closetogether. Wlth thh concept,Lemalte plantedthe ideaof a creationeventin the mind of the scientlflc community. I.6 THE DISTRIBUTION OF GALAXIES TIIROUGHOUT SPACE Ar woll as his other pioneeringwork on galaxies,Hubble also soughtto understandhow SalaxioJworc{istibuted throughoutspace.lndeed,*tis Wpeofwork still occupiesa huge Surveysof everincreasing cosmologist. rmountof timespentby themodernobservational numborrof galaxiesareattemptingto elucidatethe way in which thesecollectionsof stars of redshifts uo dirfibuted throughoutspace.The surveysall rely upon measurements whlchcanthcnbe convertedinto distances. into groups Ar oxplainedin chapterl, it hasbecomeobviousthat galaxiesaggregate which aresfrewnthroughlnd clustcrs.Theseclustersarethengroupedinto superclusters out rprco sunoundinghugevoids.Pencilbeamstweys probedeeplyinto the Universe rhowing tho distributionof galaxiesalongvery specificlines of sight. The surveysof Brbadhurstand Koo have clearly shownthat gala:
Sec.3.7l
Theisotropy andhomogeneity oftheUniverse55
containroughlythe samequantityof galaxies,its linear dimensionsmustbe increased beyond100million light years.The preciseamountby whichthe scalemustbe increased is still a matterof somedebatebut, baseduponthe Las campanasDeepRedshiftSurvey, whichhascollectedover 12,500galaxyredshifu,thescaleis in the orderof between300 and600 million light years. Ifthe entire contentsofthe universe weretaken apartand spreadthroughoutspaceas a unifonnly tenuousgas- a conceptknown asthe cosmicsubstrafum- eachcubic metre of spacewouldcontainonly onenucleon!Thedensityof this cosmicsubstratum wouldbe approximatelyl0'' timeslessdensethantheEarth'satnosphereat sealevel.This hasled cosmologiststo make the assumptionthat the matter contentof the universe can be thoughtofas a perfbctfluid, i.e. onewhich doesnot resistchangingits shapeunderexternal influence. Thus,on a scalegreaterthan 100million Iight years,the Universecanbe thoughtofas homogeneous, i.e. it is the sameat all pointsthroughoutspace.This resultis reachedno matterin which directionthe observerloola. A cosmologistlooking due north would reachthe sameconclusionas a cosmologistlooking due south.This meansthat the Universelooks the samein all directionsandso is saidto be isotropic.An isotropicUniverse adheresto the Copernicanprinciple which statesthat the Universehasno preferredlocation within it. No matterwherewe are in spacewe will seea totally representativeselection of the Universe.Nowherewill we be able to seea different classof star or galaxy because they areall scattered homogeneously throughoutthe cosmosand so no location takesprecedence over any other.An isotropicUniversecanhaveneithera centrenor an edgebecause to do so wouldviolatetheisofopy. Ifone werelocatedon anedge,theview wouldbe very differentthanif onewerelocatedin thecentre(seeFig. 3.8).
The Universe
This Universeis homogeneousbut not isotropic.Thereare more galaxiesin directionAthan in directionB.
{a )
Fig. 3,8. The isotropyofthe Universc(a) impliesthat ir hasneithera centrenor an edge,and the homogeneity(b) meansthat astronomerscan make sweepingstatementsabout the cosmos becausewe live in a representative part of it.
[' lch.3
cosmology 56 Observational
uo(.') = vo( r - r ") = uo( . ) - uo( . ")
On what scale is our Universe homogeneous?
This is a volume of space split into cubes. Thereis an unequalamount of galaxiesin eachindividualcube, but four in everblock of eight cubes.So the Univerceis homogeneouson the scaleof the eight-blockcubes.
Fie.3.8.(b)
3.8 TIIE coJvTOIOCICAL PRINCIPLE The observationalconclusionthat the Universeis both isotopic and homogeneoushas beenraisedto the levelofa guidingprinciplein our studyofthe Universe.It is knownas proven the 'cosmologicalprinciple'.From it we can actuallydeducethe observationally Hubbleflow in the followingway. lmaginetwo observers, A andB, situatedin differentgalaxiesin theUniverse(seeFig. the meandensityof galaxies,p, in two differentdirections 3.9). ObserverA measures principlemeansthat so long asobserver alongradiusvectorsr andr'. The cosmological A doesthis at the samecosmicepoch,
po(r)=oe(r')
S ec.3.8l
The cosmological principle
(3.l 6)
Equation(3. I 6) only holdsfrue,however,if vo(r,t) = r(t)r
(3.17)
Herewe haveexplicitlystatedthetime dependence of the equations by insertingthevariable, t, into the functions.For the presentepoch,time is a constantandso equation(3.17) reducesto theHubbleequation(l.4). Thefunction,f(t) canyieldeithera positive,negativeor zeroanswerfor anygiventime. Negativeanswerswould correspondto a collapsingUniversewhereaspositiveanswers wouldmeanthatthe Universeis expanding.The third possibility,namelythat f(t)=O,can be discountedif we takerecoursein the followinganalory. Imaginespaceships blastingawayfrom the Earttr.Any vesselwhich doesnot reachthe Earth'sescapevelocity(-l I km/s)will be draggedbackby the gravityof our world.This is said to be a closedgravitationalsystemand corresponds to f(t)<0. Any craft which its velocifybeyondthis will escapethe gravitationalinfluenceofthe Earth,creincreases atingan opengravitationalsystem(f(t>0). In the specialcaseofthe spacecraftachieving just the escapevelocity, it goesinto an orbit aroundthe Earth. This is known asthe static (t)=0. solutionbecause If the staticsolutionis appliedto the Universeat large,it impliesthat thereis a prefened location aroundwhich bodies can orbit. This is expresslyforbidden by both the Copernicanprincipleandthe cosmologicalprinciple.Thus,by a simpleconsideration of what we know aboutgravitationalsystemsand applyingthe cosmologicalprinciple,we haveshownthatthe Universeis expectedto be eithercontractingor expanding. The otherreasonwhy the staticsolutionfor the Universeis highly unlikely comesfrom a consideration ofgravity.Sir IsaacNewtonfonnulatedhis now famouslaw ofgravity and
t t t i
t t t t i
t
(3.l3)
the meandensityof galaxiesin directionr' in the same Similarly,if observerB measures epochasobserverA,
-p"(r')= p"(r) = po(r)= po(r')
57
(3.14)
Thus, if A and B turn their attentionsto anothermeasurablecosmicquantity,suchasthe thecosmological velocitydistribution,v, ofthe galaxiestheycanobserve, principlestates that: v "( r ' ) = v o( 1' ;
(3.I s)
IfobserverB hasa relativevelocityofvo(r") asmeasured by observerA, providingthat thevelocitiesarebelow 10 per centthespeedoflight,
Fig. 3.9. The cosmologicalprinciple allowsus to predictthe Hubble flow. (Adaptedfrom Roos, M., Introductionto Cosmologt,Wiley, 1994.)
I Lr
i-'"
LJ
58
0bservational cosmologY
lch. 3
expressedthe concernthat the Universemight be collapsingunderthe force of its own self-gravity.ln otherwords,he wonderedhow the cosmoscouldpossiblybe staticwhen it containsmassivebodieswhich would nahually pull everythingtogether.He failed to pursuethis line of reasoning,however,and the static Universemodel persisteduntil Slipher,HubbleandHumasonprovedotherwise.
3.9 THE HELIUM PROBLEM
,l
l. rj il,.,1 lll
It' I |lir' ul. 't !
ncl wll ,,!i q; q, I
q;
Having looked at kinematicconstaint we shall now turn our attentionto a compositional to deducethechemicalabundance hasallowedasfronomers ono,The useof spectroscopy of clemcntsin the Universeat large.This work hasled to the infriging problemof how the Universecameto be populatedby the chemicalelementsin the relativeabundances foundby spectoscopists. haveshownthatif onewereto sample100atomsfrom anaveragecosmologEstimates lcal environment,i.e. not from a planetsuchasEarth,the breakdownwould be that about one 93 of thc atomswouldbe hydrogenwhilsttheother7 wouldbe helium.Occasionally, or porsibly two of the atomsencounteredwould be from a heavierelement. Translatingthis into the massof the chemicalelementswhich makeup theUniverse,75 por contof the cosmicmasswould be hydrogen,23 per centwouldbe heliumand2 per contwouldbe eyerythingelse.This is far too muchheliumfor it all to havebeenproduced Insldestars,If it had,the massof heavierelementswould be far largerthanthe 2%owe obsorvetoday. It is now known that starsproducetheir energyby the nuclearfusion ofhydrogen into holium.Hydrogenis the simplestelementof nature,consistingofjust a singleelectronin by addingparticlesto the orbit arounda singleproton.The fruion processbuildselements atomicnucleus.Thus,an analysisof the chemicalcompositionof a starshouldbe ableto StarsareknownasPopulationlstarsiftheycontainarelatively tollustheageofthestar. whilst earlierstarsaretermedPopulationII. Someastlargoamountof heavierelements, ronomersalsobelievethatanevenearlierpopulationofstarscanbe found.ThesePopulatlon Ill stars,however,haveyet to be conclusivelydiscovered. problem.Whilstthe Analysisof the oldeststarsavailableto us presentsan interesting the amountof heliumcontainedby thesestars lovclsof heavierelementsareacceptable, lr fnr greaterthancouldpossiblyhavebeencreatedin their violenthearts.It is as ifthe to heliumwhich was quite out of proportionwhencomllnivcrsc had a predisposition pnrodwith theotherelements. 'l'his excesshasbecomeknownasthe heliumproblem,andis oneof the fundamental propertieswhich mustbe takeninto accountby any viable cosmological observational weretakenby GeorgeGamowin the 1930s. thcory,Thc first stepstowardsan explanation l le soughtto understandhow chemicalelementshad beenforrnedin the quantitiesin which thoywereobserved.At ftis stagein history,the role of nuclearfusionin starswas Gamowknewthat the chemicalidentitiesof differentelementswere not yet understood. detcrulincdby the differingnumberof protonswhich populatedtheirnuclei.He alsorenliscdthatby addingor subtactingneutronsandprotonsto a nucleusonecouldartificially crentedift'erentelements.The problemwasthat,evenif you startedwith a basicmixture of ncutronsandprotons,how couldyou forcethemtogetherandmakethem'stick?
Sec.3.10l
The cosmicmicrowavebackgroundradiation 59
The answer,Gamowdiscovered, wasto subjectthemto extemely high temperatures; billionsof K, in fact.His nextproblemwasto answerthe question:wherein theUniverse could one find sucha titanic infemo? Gamowrealisedthat, at the time, the answerwas nowherebut, buildingon the work of Lemaitre,he exercisedone of his greatestinsights by likening the Universeto a bicycle pump.If air is compressedin a pump,the atomsand moleculesin the air heatup. If the Universewerecompressed in sucha way, as would havebeenthe casein the early Universewheneverythingwas very much closertogether, then, reasonedGamow,it must have beenvery, very hot indeed.So hot, in fact, that it providedthe temperaturesnecessaryfor nuclearfusionto takeplace. Unfortunately,Gamow'stheoryonly workedwell for explainingthe 23 per cent of helium.The other,heavierelementscould not be explained.As a resulthis theorywasnot ascelebrated asit shouldhavebeen,andtheideawasonly slowlyaccepted. We now know that almostall of the other elementsare producedin the heartsof massivestarsand retumedto spacein supernovaexplosions.Supemovaealone are incapableof synthesizing the abundanceof helium in the Universe.In essence,Gaurowhad successfullysolvedthe helium problembefore it had ever really escalatedinto one! In doing so, he was the frst cosmologistto ever seriously(and quantitatively)considerthe first momentsafter creation, and he alsoprovedthat the Big Bangwasnot only a densephasein the Universe's existence but a very hot onetoo! The conceptofa hot Big Banghadbeenborn. 3.IO THE COSMIC MICROWAVE BACKGROUND RADIATION The conceptof look-backtimehasallowedusto view theUniverseat successively earlier andearliertimes in its history, usuallyrefenedto by the genericterm 'epochs',simply by looking further and further into space.If the Universehasexistedforever then, in principle, oneshouldbe ableto observefurtherandfurther into space,seeingnothingbut galaxies which look exactlythe sameas thosearoundus. What we actuallyobservein the cosmos,is thatthe typesof celestialobjectchange,the furtherinto spacewe look. This implies somesort of evolutionaryeffect andperhapsindicatesthat the Universeis of finite age.Ifthis is thecase,thenthequestionnaturallyarises:canwe view theepochofcreation if we look far enoughout into space?Unfortunately,the answeris'no'. A fundamental barrierhasbeendiscoveredto exist,which blocksour view ofthe early Universe.The barrier is characterised by the emissionof microwaveradiation,blinding us to earlier even$. The releaseofthis backgroundradiationsignifiesa fundamentalchangein the characteristicsof our Universeandwasactuallypredictedby Gamow'scolleagues RalphAlpher andRobertHermanin 1948.It is furtherproof of a hot Big Bangbecauseanyhot object givesout thermalradiation(asdescribedin chapter2), andifthe constituents ofthe Universewereat billionsof K, theymusthavegivenout copiousquantitiesof radiationin the gammaray regionof the spectrum.AlpherandHermanpredictedthatthe radiationwould now look like a thermalsourceof about5K. Microwaveradiationwas discovered,serendipitously, in 1964by Arno Penziasand RobertWilson (seeFig. 3,10).Whilstpreparingtheradiohom at Bell Laboratories, New Jersey,for usein radio astronomy,thepair ofresearcherscould not get rid ofa stubbornly persistentsignal.This arnoyinghisswaseventuallyshownto be the first observedpoint on thegraphof the cosmicmicrowavebackground radiation'sspectrum!
l"' f
[: 60 Observationalcosmology
l ch.3
S e c3. . 1 0 1
The cosmic microwave background radiation
61
who Fig. 3.10.Dr. Arno A PenziasandDr. RobertW. Wilsonof theBell TelephoneLaboratories, in 1954 discoveredthe microwave background radiation while using the hom-shapedantenna partially shownin the backgound ofthis picture.The antennawas designedto relay telephone calls to communicationssatellitesin Earth orbit. (Photographreproducedcourtesyof Bell Laboratories.)
Penziasand Wilson's datapoint was actually a measureof the CMBR's intensityat a wavelengthof 7.35 cm (seeFig. 3.11).Work was swiftly begunto measurethe background intensity at other wavelengths,but experimentswere severelyhamperedby the fact that the atrnosphereabsorbsquite strongly closeto the theoreticalmaximumof the backgroundradiation.Nevertheless,more andmoredatapointswere being added to the curve all the time, and graduallya thermal curve beganto take shape. Absoevidencethatthe CMBR wasa blackbodycurvewas obtained lutely incontrovertible by the CosmicMicrowaveBackgroundExplorer(COBE),a satellitelaunchedby NASA in 1989. the microwavebackgroundradiationit found it to be characWhenCOBE measured of 2.726+0.005K, whichwasalmostexactlywhathadbeenpreterisedby a temperature hasallowedthenumberdensityof CMBR dictedby AlpherandHerman.Thistemperature photonsto be calculated.It tumsout thatwe canexpectto find an averageof 400 cosmic photonsin everycubiccentimeteof space.This is an overwhelmmicrowavebackground ing numberof photons.It totally dwarfsthe numberof photonsproducedby starlightor radiationis thedomianyothercelestialprocess.Thus,thecosmicmicrowavebackground nantsourceofradiationin theUniverse. I J
Fig. 3.I l. The spectrumofthe cosmicmicrowavebackgroundradiationis fitted very closelyby a blackbody curve of a thermal source at 2.7 K. (Adapted ftom Silk, J., A Short History of the Universe,W.H. Freeman,1994.)
Whendiscussing,at the begiruringof this chapter,the conceptof the substratum, we statedthatthe averagematterdensityof the Universeis just onenucleonper cubicmetre. This leadsto the ratio statedearlier that for every particle ofmatter there are approximately1,000million photons.So eventoday,the contentof the Universeis totally dominatedby the leftoverradiationof the Big Bang. This doesnot mean,however,that the energycontentof the Universeis dominatedby theCMBR.As we sawin chapter2, the amountof energycontainedby a photonis propor(equation(2.5)).Microwavesare,energettionalto the frequencyofradiationit represents ically speaking,ratherweak.If onecompares thetotal energyboundup in the microwave background,e,,usingequation(2.5) with the energyboundup in matter,e,, usingequation (1.2),it is seenthat e,))e,. Hence,in the presentday Universe,mattercontainsthe dominantform of energy.This is why the Universeis saidto be matterdominated.This hasnot alwaysbeenthe case,however. If the cosmicexpansionis tracedbackthroughtime, the redshiftwhich hasbeenimpartedto theCMBR is reversedandhenceeachbackground radiationphotonincreases in
t t t t t t t t i
t I
T
62 Observationalcosmology
\"
il I I l q; I I ll l il{' l il{; \,
q;
E,
ql
4
t
fch.3
energy.Eventuallya time is reachedwhenthe dominantform of energyin theUniverseis in the form of the backgroundradiation.The approximateconditionfor this is wheneach photoncontainsonethousandmillionth the energyboundup in a proton. The proton is usedbecauseit is the dominant,stableheavy particle in the Universe; electons contain little massand there are too few neutronsto disturb the approximate natureof our calculations.The time at which the photonenerry densityandmatterenergy densitywereequalcorrespondsto the dividing line betweenour presentmatterdominated Universeandthe early,radiationdominate{Universe. This dividing line occurredat about100 secondsafterthe Big Bang.The fact that it happened beforespacebecameopticallythin to thecosmicmioowavebackground hasan importantconsequencefor the radiation.As we shall see in later chapters,the fact that mattercameto dominancebeforeit stoppedinteractingwith the CMBR meanstfin1i bO an imprint, showingus the primordial densitydistibution of matterin our Universe.These tiny fluctuationsin the temperatureofthe backgroundradiationwere detectedby the COBEsatelliteandgive us insightinto how galaxiesform. The observationspresentedin this chapterare the oneswhich havedirectly led to the Big Bangtheoryofthe Universe'screation.Theyarenot thebeginningandendofobservational cosmology,as we shall seein later chapters.The densityof matter in the Universe,the evolution ofgalaxies andthe searchfor dark matterare all importantobservations which, when analysedwithin the Big Bang framework,lead to somesurprisingand profoundconclusions. sometimes
The Big Bang in the previoussectionhasled cosmologists An analysisof the observations discussed to the currentlyacceptedmodelof the Universe'screation.It is known as the Big Bang;a phrasewhich was actuallycoinedas a term of derisionby Fred Hoyle. He proposeda different interpretationof the resultsknown asthe SteadyStatemodel, but wasultimately provedwrong by the detectionofthe microwavebackgroundradiation. GeorgeGamowwas the first cosmologistwho was sufficiently audaciousto believe what his equationstold him aboutthe early Universe.The Big Bang is, indeed,our best model yet of how the Universebegan,but it is importantto rememberthat it is not yet proven!This chapterwill providea largelyqualitativeaccountofthe Big Bang.It is here that we encounterthe applicationofquantumtheoryto the Universeat large. If the Universeis expanding- which our observationalevidencewould leadus to conclude- then, by extrapolatingthat expansionback through time, we arrive at a singular point in history at which the Universewascompactedinto an infinitely denseregion.This is what is known as the Big Bang.As we shall see,theoreticalphysicscaonotyet takeus back to the point ofthe Big Bang but, perhapswhen quantumgravity theoriesare perfected,they will. They may evenshowthat the initial Big Bang point can be avoided altogetherand insteadshow that the Universehad remainedin a quiescentstatefor an infuriteperiod of time beforesomethingsparkedthe cunent headlongexpansion. Discussionof an initial point of creationnaturallyleadsmostpeopleto wonderwhat therewasbeforethe Universeexisted.The answeris that spaceand time cameinto existenceat the momentof the Big Bang.This being the case,it seemsa little trivial to state that ipace and time did not exist beforethe Big Bang. It is an importantstatement,however,becauseit answersthe questionfor us.If time was createdat the instantof the Big Bang,the conceptof beforethe Big Bangceases to haveanymeaningbecause time itself did not exist,By a similar line of argumentit can be reasonedthat the fact that space expandsdoesnot meanit hasto expandinto anything, 4.1 CHARACTERISING THE EXPANSION The evolutionofthe Universeis drivenby its expansion. The interlinkedphysicalproperties of temperatureand energyare the oneswhich allow cosmologiststo calculatethe
(),1 'l'hcllig llang
l(--h.4
c()n(litions in rvhichthe carly Urtivcrscis thoughtto lravcexisted.In order to placeour tliscussiotl of tlratevolutiorrin contcxtwc lnust lilst corrsidcrhow the expansionof the lJnivcrsealtcrsits ternperature and energy. In physics,an adiabaticprocessis dcfinedto be onc in rvhichheat neitherentersnor luavesthc systcnrunderinvcstigation.'l'hcrefore, iftl)e systenlwe arestudyinghappensto bc thc Universcas a whole,it mustbc adiabatic. Thus,thc Universeexpandsadiabatically. Tablc 4.1. Particlcrestcnergiesand relativisticdomains.The rest cncrgiescan be usedto shorvrvlrcn,in the historyofthe Universe, thoseparticles1;ecies wcre relativistic(l{oos, 1994,Wiley) I)artrclervithantirnatter counterDart
f rri \ ' , , ' il ,
',; t,, il
l).n I
/;'
pnoron clectronneutrino Muon neutrino elcctron tau neutrino nruott p ion proton,neutron ta u W particle Z paticle
Rest l:ncrey (MeV) (K)
Relativistic domain(K)
0 0 < 1 0 -5
Always I x 106 3.1 r l0ro 5 . 9 3 x l 0 'o 3 . 6 x l 0 '2 1 . 2 3x l 0 r r 1 . 6 2x l 0 r r 1 . 0 9' l 0 r o 2.07 " llto 9 . 3I ' l 0 r 5 1 . 0 6' 1 0 1 6
lOe l0' 10rr 10t2 l0r2 l0rr 10rl l0ra l0r5
'l'heconccpt of the cosmicsubstratum, introducedin chapter3, postulates that op the liilgcstscalcs,the Universecan be thoughtof as an idcalisecl, smoothfluid. At earlierand cat'liertitres,this analogybecontes applicableover snrallerand smallerdistances. Before thc ageof300,000yearsthe Universeis thoughtto havebeenan excellentexampleofan idcal fluid. fhis fluid is non-viscous and all measurements are made frorn a co-rnoving {ianreof refcrencewlrich nreansthat it is at rest within the substratum(seeFig.4.l). The constituentsofthe Univcrse,i.e. the particlesofmatter and the photonsofenergy, are all irr thermalcquilibrium during the early stagesof the Universe.At any point in tie evolutiorr ol'thc univcrse, its temperature,T, can be specifiedwith referenie to its energy, E, by the simplelarv:
E=KT
(4.l )
n4rcrck is the larniliarBoltzmannconstant. -['hernrodynarnics definesa propertyknewn as entropy,rvhich is a measureof now casy it is for a systenlto use its internalenergyto do externalrvork..Foran adiabaticprocess, llrc ertl'opy of the systemdoes not changeand so the seco'd law of thermodynar'rcs recluilcstlrat
dE = pdv
(4 )\
C harac teri s i ngthe ex P ans i on 65
S cc.4,I I
dv, rvheredE is the changein energybroughtaboutby a changein the system'svolume. pressure the fluid, p, has remainedconstant.In a non-viscous assumingthat the pressure, is definedto be I
( 4. 3)
P=Jt
'"vheree is the energYdensitY. upon the energydensityof the radiation contentof For the momentwe will "on..nt.ut" the Universe,e,, becauseit drives the thermalevolution of the early Universe. If the As the Universe expands,both its volume and its energy density must change. linear size of the Universe is characterisedby the function R(t), which has the dimensions of this of distanceand increaseswith time t, the volume changesin proportion to the cube Iunctionbecause
4nR ttl " v = -------:-j-
( 4. 4)
J
given If we choosea small enoughvolume elementto study, then the energy density is element. each in is found photon one only very simpty becausewe assumethat F
hf
hc
V
V},
(4.s)
: -= -
'fhus, e, changesin proportion to R(t) a becauseit is not only dependentupon the expansion of the volume elementbut also upon the redshift sufferedby the photon. Retnembering, from chapter3, that as time passesthe Universeexpands,the redshift ofthe radiation is*proportionalto R(t). Flence,when the volume and the energy density are equated,the volumescancelout and we are left with
E ". n(t)-'
( 4. 6)
When this is substitutedinto equation(4. l) ,
' T cc R (t)
-l
( 4. 7)
So as space expands,the temperatureassociatedwith the radiation within it also decreases.As we stated in chapter 3, the cosmic microwave background is the dominant the [Jniform of radiation in the Universe,so it is this which governsthe temperatureof in placed object cold any that radiation photons ofbackground many so are verse.'fhere that of the spacewill be impactedby the photonsand raisedin temperatureuntil it mirrors CMBR. gas, l{aving statedthat our physical model for the early Universe is that of an ideal cosmolotsts have to keepitock of all the individual particleswhich make up that cosmic gas.Chalter 2 introducedthe Planck distribution (2.4) which allowed us to calculatethe equaiumber of photonswithin a specific frequency(i.e. energy)range.A similar type of of a freInstead velocities. at relativistic particles travelling for formulated can be tion quency range,this distribution gives the number of particleswithin a range of momenta (p+dpj.Momentum is used becauseit containsthe variablesof mass,m, and velocity, v,
t t I I
!
'l,
1 ,;
,;I
;r
l ,;
; 'l
r; F
't .li
T
ti
:l 1 1 'l 'l
66
'I'hc Big B:q,l
lch.4
Sec.4.I l
C harac teri s i ngthe ex pans i on 67
which are usedto definethe total energyof the particle,E(p),(i.e. restmassenergy+ kineticenergy):. {4,
/ \ r n(p)dp=
n-
(4.8) *'
"Etetlw
A s t h e U n ive r see xp a n d sso d o e s th e fr a m e o f r eference:_
hf
:l :l
(4.e)
As the Universe expandsand cools, the kinetic energy possessedby particles of matter will also fall. Eventually,the particleswill ceaseto travel at relativistic velocitiesand thc distributionbecomes tt' (2nmkr) -,,r, \r (4.r0) N=_ nrp,n .^ (*f
;.1 C o - o r d i n a te sr e m a in th e sa m e e ve n th o u g h d istancehas rncreaseo.
I1l
p2dp
z
The only variable not yet mentionedin this equationis that of n,o,n which is a measureof the quantum property, spin, of the pafticle being investigated.The equation is used for bosons(i.e. particleswhich do not obey the Pauli exclusionprinciple)by settingthe *l condition to -l. Fermions,which do obey the exclusionprinciple, are cateredfor by setting the conditionto + l . The Planck distribution can be easily derived fiom this equationby rememberingthat photons are bosons with an D,oin= 2. The particle energy, E(p), is replaced by the photon energy, hf, and the variables are changed from momentum to frequency, f, via v'
_l
8n ns pi n
I:ig 4 l A co-movingrranrcof refercncc nreans thattheco+rdinatesofan objectdo not crrangc thc Universchasexoanded. Justbecausc
where N is the number density of non-relativisticparticleswith mass m and spin states n,oin,irt i temperatureof T. This is known as the Maxwell-Boltzmann distribution. In general,a particle is relativisticwhen its kinetic energyis l0 times largerthan its rest mass energy(seeTable 4. l). The rest mass energy of a particle is very important in a cosmological context because, when the energy density of radiation in the Universe is greaterthan twice this figure, it meansthat the particle and its antiparticlecan be spontaneouslycreated.The fact that the antimatterparticle must always be createdis what gives rise to the condition that the energy density must be twice the rest massenergy of the particle to be created.The excess energy,over and above what is neededto createthe particle, is given to the particle as kinetic energy.Thus, at energiesgreaterthan twenty times the particlesrest massenergy, the particlesare createdwith relativistic velocities.As the temperatureand hence the energy densityof the Universedrops, so each individual particle speciesis createdwith less and lesskinetic energy until, finally, production stopsbecausethe Universe has dropped below the thresholdtemperature.When this happenstwo outcomesare possible. In the vast majority ofcases the particle speciesceasesto exist in any appreciablenumber, because its particles all annihilatewith the antiparticles.In the casesof particles such as neutrons,protonsand electrons,some processin the early Universe,which we shall discusslater, allowed the creationof particleswithout antiparticles.Thus when the Universe passedtheir thresholdtemperatures,not all of theparticles were destroyed,becauseof a deficiency in the number of antiparticles.Theseremainingparticles,which have gone on
6l{ 'I'hcBig l_}ang
lch.4
to fonn all of th6ltars and galaxies around us, wer.c and ail followed 'on-relativistic Maxwcll-Boltznrannd istributions.
(a)
T hi s m o l e c u l e h a s th e s a m e p hysi cal properties as i ts m i rro r i m a g e :-
The first l0-3 seconds 69
Sec.4.2l
Universeis when it reachesan age of approximately10t' seconds.This is a specialinterval in time which is known as the Planck time and arises from the fledgling quantum theories of gravity. Why searchfor a quantum theory of gravity when chapter I stated that generalrelativity can describeit? Even Albert Einstein refusedto believe that his generaltheory of relativity was complete. Late in his life, he questionedthe validity ofhis theory for certain astrophysical He pointed out that generalrelativity was only meantto be a valid approxicircumstances, mation for weak gravitationalfields. In formulating his theory, he assumedthat he could separatethe conceptsof matter and gravitational field. In a region of space where the maner densitywas incredibly high, Einsteinfelt that his theory would break down. Nowhere can there be a more severetest of this than at the beginningsof the Universe, when everythingwas squeezedtogethergiving the most incredibly high densities.In the sameway that Newtonian physics must give way to relativistic physics when objects travel fasterthan 10 per cent the speedof light, so there comes a limit after which a quantum theory must be usedto explain the behaviourof matter. For example,when discussinga planet such as the Earth in orbit arounda star such as the Sun, the Newtonian approximationor generalrelativity are capableof being used lf one changesscaledramaticallyand beginsto talk about an electron in orbit around a hydrogennucleus,quantumcorrectionswill becomehighly significant,and the previoustwo theoriesare inadequatefor the task. Startingwith equation(2.8), the Heisenberguncertaintyprinciple, it can be shown by dimensionalanalysisthat the Plancktime, to, is given by
(b) [hG
to =t/rnc
.^-d?-
-ru
( 4.rr )
This length of time is of fundamentalimportanceto us in our considerationsof the early Universe.It is so importantthat it can be usedto form a seriesof fundamentalunits including the Planckmass
rn"=-5=2.5xlo-5g '
(4.t2)
2 n c "l ,
and the Planck length Fig 4 2. Reflectional androtational symnretry fornroleculcs. A molecule behaves in exactly the samcwaytcgardless of itsrotalional stalcol s)'rnmetry. At a nlucllsmaller level. diflerent specics of sub'atonlic particles archelieved to behave in oneandthesamewayat highenergies. This concept isknownassymmetry. As we begin at the earliesttime in history about rvhich physics can say any4hing,the evolutionofthe universe is driven by its expansionand its effectsupon the eneigy density and temperature.Hence,in the following.sectionswe will frequentlyrefer to the ternperature and/orthe energyof the Universe,at the most importanteventsin its historv. 4.2 THE FIIIST I04] SBCONDS Modern day physicscan take the universe back to a split secondafter the Big Bang, but not earlier'The earliestageat which conventionalphysicscan say anythingat all aboutthe
l o= cto=1. 7xlo- 33cm
(4.r3)
why thissystemof unitshasbecomeusedandwhythePlancktime is so imporThereason tantwill becomeobviouswith thefollowinganalysis. In chapter2 we introduceda quantityknownas the Comptonwavelength(2.7), which if it caniedtherestenergyof a partia photonwouldpossess represented thewavelength principle(2.8),to give us the time for which a gauge cle. We alsousedthe uncertainty with anyparticleto give canbe usedin conjunction bosoncouldexist,(2.9).Thisequation the lengthof time it represents because important is very This time theComptontime,t". of energylaw. for whichthemass,m, canviolatetheconservation ,,-2n
I
h
(4.r4)
--
r,
t t t t t t t t t t t t t, t
'l 'l 'l 'l _l :il :ll _11
I I :il I -ll I -il il -[
-l l
-il
u..l
70
' l ' h c Itig Ba n g
lch.4
This kind of bchaviotrris callcclquantumfluctuation. It is usualfor it to takethe forrn of pair production.A pair of viftual particles(onc parlicle a of matter,the otlrerits antimatter counterpart)conle spontaneouslyinto existencebut annihilate themselves,returning the bor'orvcd energy belore they can rre cletectecl. r'his ail takes prace in a time of t . The conrpton time can easily be convertedinto a conrpton length, which is virtuaily indistin_ guishableI'romthe compton wavercngth,the typicir distani tiavelled by the virtual parti_ clcs bcforethey annihilateeachother: |
-^+ 'c - v , c
( 4 .I 5 ) so thc compton length can be thought of as the limiting distancefor any particre in the quantumregime.rn classicarphysics,a similarkind of iimiting distancecan arsobe de_ rived' It is known asthe schwarzchilclradiusanclis the classicaldefinition of the radiusof a blackholewlrichpossesses a mass,m. It is givcn by
,
2cnr
-J
)
c-
(4.l 6)
Nothingcan escapefrom within a radiusof r, around an objectof mass,m. Thus,r, is the boundarybetweenthe crassicarregime of giavitation and quantunrgravity. For conveniencewith comparisons,Iet us define a Schwarzschird time, tr, whici i, ,irnpry the time it would take.aphoton of light to travel the Schwarzschild radius: --l ts = c
(4.t7)
we can use tlresetimes and distancesto determine if we are in the classicalor quantum realnr.lf we takc a particrewith the pranckmassand carcurateits compton lengthand Schwarzschildradius, it will be noticed that the calculated lengthsare both equal to the Plancklengtlr.converting thesequantiiiesto time, both Schwarzschildand compton time are equalto the Planck tinre. ln other words, a particle of the planck massis a minuscule black hole which briefly existsfor r0-o'seconds;the pranck time. If the massof the parti_ cle is increased,then it entersthe realm ofmacroscopic entities.In this case,t.tr,l.>1, arrdquantumeffectsare of crucial importance.It is no rongeradequatero describethe serf-gravity u.bgoypossessing I;1. with generarrelativity. As we gf havesecn,this is the rearmof the brackhole, a bocly whoseself-gravityis obviousryof the highest importancebccauseit has crusheditserf out of existence!A theory of quantum gravity is necessaryto ruily describcthis behaviour and, althoughn,unyihy.i.irt. u.. currently working towards this, no-one has convincingly presentei unyttring*i,i.t .n.n resemblesa finishedtheory. Thus, on time scaresof the prancktime, brack holes of the planck masscan spontan_ eouslycome into existcncc!Via the processof lJawking radiation,the black hole can tlren evaporateback into energy.The characteristictirnc scale for this to occur happensto be approxirnatelyequal to the planck tirne.Thus,the Universeat r0-o!r".onJ.'in agewas a seethingnrassof energyin which brackhoreswcre continuousry formingandevaporat_
Sec.4.3l
The phas etrans i ti on era
7l
ing. The concept of distance,i.e. a measureof the amount of spacetimecontinuum between two events, can have very little meaning in the Universe at this stage. The continuum was squeezedinto sucha tiny volume of spacethat regionsof spacewhich would end up as being totally disparate,were in contact. This is best imagined as being like a flat sheetof paperwhich beganas a screwed-upball. Many different parts of the paperwill be in contactwith one anotherbut as the paper is flattenedso they will lose contact. The process of pair production is thought to have been incredibly important at these early times because,by the action of a strong enough elecffomagneticfield or a sufficiently non-uniformgravitationalone, it is possibleto separatethe two particlesbefore they recombine. The gravitational field which permeatedthe Universe at this stage in its history was exceptionallynon-uniform. Hence, many of the particles forged in pair-production escapedtheir initial annihilation.The density of theseparticleswas so high that it meant they soon met and annihilatedwith other antiparticles.This retumed their bound-up energy back into photons.The Universe,however,had begunto be seededwith matter. Thus, the age of l0-a3secondswas the first importantwatershedin the Universe'shistory. At this time, gravity was just becoming an individual force, separateand distinct from the other three which were still joined togetherin a grand unified forcc. The Planck era, as the time before is known, was the realm ofthe superforceand cannot be explorcd with our currenttheories.Betweenthe Planckera and the next watershed.which occurrcd at l0r5 seconds,the quantumgravitationaleffectsdwindled to become negligibte. From that age onwards,generalrelativity and the Newtonianapproximationbecomethe cosmologist's greatestallies in understandingthe evolution of the spacetimecontinuum.
4.3 THE PHASE TRANSITION ERA The separationofgravity from the superforcemarks the first known phasetransition in the Universe.As indicatedin the previoussection,physicscan say very little about this event becauseof the lack of a suitabletheory. The first phasetransitionwhich can be explored theoreticallyis the one which occurredwhen the Universewas l0-35secondsin age. This is when the grand unified force split up to form the strong nuclear force and the electroweak force. During this epoch of the Universe's existence,the way in which particles behaveand interactwith one anotheris describedby a grand unified theory (GUT). There are many approachesand, consequently,many different versions of these at present.None have been proved and so the behaviourofmatter during this phaseofthe Universe is still only conjecture. During the GUT era the strong nuclear force, the weak nuclear force and the electromagneticforce all actedas one grand unified force. This meansthat there was no distinction betweenhadronsand leptons.All particlesbehavedin the same way and interactcd through the exchangeofthe samevirtual particles.In cosmologicalparlance,theseparticles are said to possesssymmetry. Symmetryis a word that is usedto define a set of transformationswhich can be applied to a systemwithout altering any of its physical properties.For instance,if we switch momentarily to a much larger scale,moleculesexhibit reflectional and rotational symmetry
72
' l ' h c l l i g Ila n g
l ch.4
(sccliig. 4.2).The synulrctrics studictlirr clcrner)luf)/particlesare oftennrorcesotericarld not so casy to relatc to physicallrropclties.l'clhapsthe best rvay to tlrink of-it is that particlcswhich obey a syulrlrctD/ale indistirrguishable from one another.A brarrchof nrathenratics, knorvnas grouptheory.is usedto strxlytheseproperties. In gcneral,the tJniversetoday is a placcof brokerrsynrmelries.'fhere are nranydifl'crln the high-energyphaseofthe cnt particles,all o1'whiclract differentlyfrornonc arrother.
The phas etrans i ti on c ra
S cc.4.3|
' 71
abovetne Curietempcrature:fvfaqnet "
i ]
n +tr* {r, y\ +l/
+ + t/ --> {
,
v{
*t
,
+,
+
'r->,1 t tr--> + -> Yrr t/ \ I;
r; > t/ ** <-> y' A\
<-
jl
7z
I ; i l l ":..'"f::,;il:;.jil::;il'j'',#ii:1;:.fi;il1:],# # t t i, i' f f ii: i: f f i1 . ' } |.
1'he particlesweresaid to obcy the grand unified theory symmetry.According to this theory, it is hc'*1 at this stagein the Universe'shistory,that the propensityof nratterover grandunified antilnatter antimat|c|wAs wr$ introduced irtroduced into inlo the Universe. Universe.Tlrc The grand unified theories lheoriesrnake make leptons leplonsand hadrors cquivalcnl. rhereforc ou. Lodern nori., otbaryon conservalion in readions (whichresultsin particle-antiparticle pair production)no longerholdstrue. [n particular, certainexotic particlescould be forrred which rvould later decay into a proton without its
malchingantipmron.The prctoDwould tlen be brcken up iDmediately into qoark. Concredtiohofa biryonwithoutanantibaryon counlerparl ditionsvlich allowtheoccasional
; rr)-l*3 ; i: I *i *i :f rriL::>ii a +*i : L '. +^ i , : 4
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r
/
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Dipolesare totallyrandom,no overallmagnetism.
I i
i a rcth ercfor c pos s ible, under t his t hc or y , ina ( c a l c u l alt ci n de ) v e r y l 0 *t o l 0 ''c a s e s . T h i s pIo ce ssis s onr et it nes nanr edbar y os y nt lr e s i s . I t i s s t i l l h o t l y d e b a t e d a b o u t w h e r e 'i n t i n r e . .
baryosynlhesis look place.Somecosmologists bclieveLlut itwdberc h thesepantionof {,e grandunifiedforcctlidt lhc asynmetryw6s ir{roduccd.Othe.sbclieveil occutred
>
i i
f L t6mper6tu6: the Curie curi6temperature:Magnet belowth€ Magn€tbelow
r I I
,, .
later,at about l0-roscconds. Wlren tlre grand unifictl syllrnetry spontancou:;ty breaksbecar.rse the ternperaturehas
i{lN x\rr rr :;:T*lt"ltrt:*fi'"T::,Tx"?:i:',"f#,';""";r*jj#lilTr"il: i /irlil>9i*SN--Z:.tl
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produccd. prcduced.In with no change case,rhe the feroDra8net ferronragnetcould be tn this cde, be orientated oricntatedin ii any anyway $taywitl' chang. in properties.It its external could therefore Lresaid symmetry. any rny of lr could dErelorebe lo have hale a high highlevel levelof s)mmeLry. olirc exremalpropenies. srid to
z, z, /7-7
*/
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| | , A s lhc r c m p e ra tU rc d rc Ps b e Io w th e C u ri etenl pel aN re.thei nremi atpani cl es' sponran-| n.ei onso ldohinanlm 6gnet isFhavenowspont aneouslv|or m . couslyarangelhenselves reor'ertaling theferosolhatma$tetisation oc.urs-Suddenly, L matn m at nc clwo lwouIudc Idhangelheway c h a n g e l h e wr a I ryouls tIrcidewo o u rs iaew l | d p t rortop* c € i v c s icei l a nv* d l hi .* u soi i l si ." e a' irs* I i e' ri r s"yi 'm y.." m e.y| r r yfl i f e' l e '4 4ll''T Ttc!p.nh@ t c ! p . n h @ d dcrt 4 r t ioionof n o fr e n r em d kmlkm '( l l ^'(bll^w. .w .e !tr lhli n r o F dipd6-c rmdmh m.tul.d {b,{'henrhc ;;:i"i; ;ir;';;;;;;'l1.;sem,k hdsbccnbrcken(seel.rs.4.r). | lnlhc p.o c e s 5 o fs p o n l ' n e o U s s y i | c Ufbreati | | ei nrheferromagnet.l hefm| .di B ri oni #;* r* nr* ncWhDf iuf t h. ; 4iaEd|pol65Ddt . ndyd|9'( 'ding in whicl rheindivrdualdrpolearorns fiDdlhemsclve. D toiilly arb ikary.Oneregionofthe I magretwill be magEtisedin oncdirecrion,whilslolherr€gionswill be magn€li$din a I dif ! r nt dire c ti o n .Ea c h r8 j o D o l d o mi n a ntmagneti sati oni 5cal l edadohai nandbetw een| i nthehi ghener gyUniver scof t hkcosm icer a, t }qu'*+ad Itcm lbc mare ar b boundeies o u n d e i eofnagnetic s o fn a g n ediscondnuifics. ti c d i s c o n t i nui 1i cs' | | ..r." " i " a* i ,.al ks€xi stedassi ngir n,di v constitu' qudks th.ir constyt:::11: down int. into their brokendown b€enbroken wuld have havebeen ro.red fomed would postulal€dto il;';,fi;;;ffi;;;;-br*k grandun'tred ibrcet breakup, a simlar rhing is is posturatecr ro have have 41the il;i tjme ofthe similar thing I 'p, whcnth:
, I I
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,
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a l' l a'ppe oe u"i"nc or '- ;;;'n" whcnripli'i"e ,obe to bebroken broken began enort'crsvmmarbegan 'reT!:::T-:i.*-y'i:'i'T:-"fi* io''r trooc.v). "'."r tnrteprocesor*issvmme-trv-'ry11'-*l^':*'j.?*;::i:.
l
had l, i:r":"j:T:"1"j::ii:1*n;"1l1ffigftHf.s]',':i'j'ii$llT"'i: rv I 0-'r s€condsBv thc time thc temP€rature ag! or approximde
^;;r; ,'fi":L'li,3fi:'i:i:T,l1ili,i,l,llllil;'"ilTlXi happeDed couro come;;ililrr;;;i;yd .l':ii"TT#"1,1""i1J:|I inourun.ve6e. rhcscaisconlinulies
n"$:llX s,n8repo,n(detecr6*now"^"."**u",.*r"o.i;J#'l;;;ii;;;;;;;ilil
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'oi i ro6c.vl] r "'i"pr ocesof lhissym m esFD ^s in8|ep o i n (d e te c ti s k n o w n d a D a 8 n eL' cmonoN | e' A onedl mcnsj ona| t|a tedtsconnFl .i oi uiflis,cmedaco$ics,,i,,s^,wo-din*isiorJrdiscon,,nu,yaoesbyrhenameor domainwa1,and. rhrcc-dnn"".u,"",o'*"*u,"u, rhcscIravebeenobseNcd.
,, ioiij'if;;
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""'i" - toi'r (tc"v), *i" pt'*" r.unsitionwa! complet€-Dutinclhis prcce_s fa en"""r'"4 furtherto
i:f;..f:.;?]i;"""",sevo|ution,ou|discUsionofhadrnsalmostexctusivelyli;;i;;:;"q.,t"d*1".1-,t.1"1io";;1.";,t'",'
"#J'i1if"Lf1fT,;llfi}I.:i,:Ji:'i;;:if"i::H:;'Ji
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th6hadronem,andcosmo, i;;i;;;l;rkit;;Mev) rtmarksthebesinninsof
'l
ll
tl I "- . n! !' r !6 !EE'*..
tl 1
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-
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74
T h c l l ig lla n g
lch.4
can star[to becolneratlrcrtttorcconlldcnt about tho physicalprocesseswhiclr rveretaking placc.llvcrythingup until this point in historynrustlre regardedwith a healthylevel of sccpticisrn.Until the technologyof particleaccelcrators increasessufficientlyto allow thesecncrgiesto be nrorecloselysludied,detailsand perhapseven fundamentalideas rnightbc liableto changc. 4 .4 TIIE I I ADRO N AND LEPTO N ERAS At this point in the history of the Universe(200MoV), the quark-hadronsyrrrnetryfinally broke.'l'hc brokensyrnntetryaflcctedthe strongnuclearforce and actedin sucha way that it confincdthe individual quarksinto mesonsand baryons.Thus, as well as the leptonsand photonswhiclr donrinatedthe Univcrse,protons,neutrons,their antiparticlesand pi(pions)joined thc rn6lec,replacingthe frcc quarksand antiquarks. nresons 'l-hchadronera of thc Universcdid not last for very long. The strengthening of the ilttcr-qu:trkcomponentof the strongnuclearforcc nreantthat it was impossiblefor quarks to cxist on their own. when a proton annihilatedrvith its antiprotonthe vacuum energy was too low for it to be rcplaced,since the tlrresholdenergyfor the spontaneouscreation ofa proton-antiproton pair is about2GeV, which had long sincebeenpassed.Thus,the batTon content of the tjltiverse inexorably dwindlccluntil all that was left was the tiny rcsiducof'nlattercreatcdduringthe grandunifiedcpoch.For a shortwhile, pionsdominatcd, until their thresholdenergywas passedas well. Three types ofpion are possible; thcy can bc botlr positivelyor negativelychargedor neutraldependingupon their precise quark content.At this point, thc chargedpions annihilateeachother and are not replaced, whilst tlrc neutral pions decay into photonsand are not replaced.pion decay takesplace wlrcn thc vacuumencrgydrops below l30MeV and signalsthe end ofthe hadronera. The photon dcnsity of the Univcrse has been increasedenormouslybecauseof alt the mattcr-antirnattcr collisions."lhe residualhadronsrerrainin thermalequilibriumwith the leptorrsantl photons.Thc temperaturein the Universeat this point was approximately10,2K. 'rlro lcpton era lastedfor the period of time betrveenthe vacuum energiesof l30Mev to 0.5Mcv. The startof the leptonera beganwhen the Universewas l0-5 secondsold. The thrcsholdcnergyof the electronis 1MeV, whitst its heaviercousins,the muon and the tau, lravc thresholdenergieswhich are higher.The tau may actually be so massivethat it had illrcaclyllassedits thresholdtemperatureduring the lradronera. Wheneverthe exact time, tlrc llrst to annihilatewerethe taus,fbllowedby the muonsat l0r2K. 'l'hc annihilation of the muonshad inrportantrcpercussions forthe neutrinosin the Univcrse.Prior to this, the densityofparticles had beenso greatthat the neutrinocould travel only rclatively short distancesbefore interactingwith anotherparticle.Neutrinos interact with othcr particlesvia the weak nuclearforce,which meanstlrat they have to passwithin a distanceof l0-rTmetresbeforethey can exchangegaugebosonsani exert any influence upon onc anot\:r. In the rnodernday Universe.getringthis closeto anotherparticle is not casy bccausematter is so spreadout. Evcn in so-callcdsolid objects thcre is plcnty of room on thcsekinds ofscale. Tltc consoquence ol'this is that neutrinoscan passthrough solid objects such as this book, thc readerand evcr.rthe Earth itself, as ifthcv were not cven therc. In the early tJniverso;l.owcver,particlcsrveresqueezedso close togetherthat ncutrinoswere constantlypassingolhcr particlescloserthan l0-17metres.l{ence.thcv
The nuc l eos y nthes i of s hel i um
Sec.4.5l
' 15
interactedregularlyand maintainedthermalequilibrium. With so many particlesof matter being lost in antimatterannihilations,the density of matter was dropping precipitously. When the muonsannihilated,it proved to be the final straw for the neutrinos.Suddenlythe matter density was so low (by neutrino standards)that they could travel long distances without interactingwith other particles.when this happens,it is termed 'decoupling'. An important consequenceofthe neutrinos' decouplingwas that they beganto depart from the thermalequilibrium ofthe rest ofthe Universe.They beganto looseenergy independentlybecausethey no longer collided with other particles.Neutrino decouplingtook place at 3rl0roK. Another particle which can interactvia the weak nuclear force is the neutron.Ever sincethe creationofhadrons in the previouscosmic era, neutronshavebeen constantly interacting with the surrounding particles via the reactions e - +p <>ve +n
(4.r8)
v " +p <) e '+n As can be seen,reactionssometimesproduced neutrons,whilst at other tinres reactions changedthe neutronsinto protons.Each time, however,the reaction involved a neutrino. which is the signatureof the weak nuclearreaction. When the neutrinosdecoupled,the reactionrate of the weak nuclear force effectively plummeted.In fact, when comparedto the reactionratesof the other fundamentalforces, it is almost possibleto discountthe weak nuclear-forcefrom further consideration.At this point in the Universe'shistory, the number of neutronsand neutrinosbecamefixed. With sufficiently sensitiveneutrinodetectors,it should be possibleto detectthis neutrino backfor the next stageofthe ground.The numberofneutrons has very importantconsequences evolution. Universe's At the end of the lepton era the Universe is finally in its presentday proportions with photons vastly outnumberingthe matter particles.Interactionsare still so common between the nucleons,electronsand photons that all remain in thermal equilibrium. Thc nucleonsand electronsno longer equally participatein the thermal evolution of the Universe, however, becausethey are vastly outnumberedby the photons. This is why this event signifies the beginning of the radiative era of the Universe.This is not to be confused with the term 'radiation dominatedUniverse'; the Universe ceasesto be radiation dominatedvery shortly after this event. The radiation dominatedUniverse is a term used to desqibe the fact that it is the relativisticparticles(of which the radiation most certainly is) which govem the expansionof space.The radiativeera simply meansthat photonsnow vastly outnumber the matter particles and drive the thermal evolution of the Universe alone. 4.5 THE NUCLEOSYNTHESIS OF HELIUM ln chapter3 the subject of matter or radiation dominancein the Universe was raised. In order to define thesecosmic epochs,the energy density of radiation, given by equatiott (4.5), rnustbe equal to the energy density of matter,e.. This is given to first approximation by dividing the rest massenergy(equation( I .2)) by the volume, V: M c2 F
" mv=-
(4.te)
76
Thc llig llar'i! ,
fch.4
'l'histernrncglectsany kincticcnergythatthe rnatterlrarticles may have.This is not disastrous because,at the epoch in which matter becorncsclominant,any kinetic energy the particleshave will be snrallcornpireclto their rest nrassenergies. As statedin chapter3, the dividing line occurredat roughly 100secondsafferthe Big Bang.This is so closeto thc bcginningofthe epochofnucleosynthesis, that it becomesvery easyto rememberthat thc energydensityof the Universeceasedto be radiation dominatedand became rnaner don.rinatcd, when nucleosyntheqis bcgan.As we shall see later,the way in which the Universeexpandedchangedat this point. beginswlre. the ternperatureof the Universedrops to approximately . ^|:.1:gry"alesis l0'l(. This is the situationwlrich occursat a time of appr.oximately one-ano-a-nalfminutes after the Big Bang, or roughly about the tirne when the tjniverse becomesrnatter dominated'l'he nutlrberoftlettlronsand protonsis not equal.This is due to the fact that neutronsare nloremassivethan protons.'l'heMaxwell-Boltzmanndistributiol(4.10) cal be uscdto give the ratio ofneutronsto protonsat this tirne: .
\=til
( nr , ,- r no) ex'pl \ --l k]' )
(4.20)
This delay in the accumulationof deuteriumnuclei is known as the deuteriumbottleneck. Once past this hold-up, fusion begins in earnestwith reactionsbuilding upon the deuterium'building bricks' to forge quantitiesofanother hydrogenisotope,tritium, which containsone neutron and possessesa binding energy of 8.48MeV. Also favoured is the formationof a light isotopeof helium, known as helium-3,containingtwo protonsbut only one neutron,with a binding energyof 7.72MeV. Helium nuclei are then formed from combination of neutrons,protons, tritiums and helium-3s.The resulting helium nuclei, which have two protons and two neutrons,are extremelystablebecausethey have binding energiesof 28.3MeV. In this way, during the every neutronis bound up into a nucleusbefore the majority of epochof nucleosynthesis, them can decay into protons and electrons. The rate at which a fusion reaction,r, takesplace dependsupon the density ofreacting particlesand somethingknown as the Gamow penetiationfactor, which is a function of the energy bath the particles are immersed within, E, and the chargesof the two reacting nuc-
r ocexp
2Z&z\ alE
which is roughly0.1-0.2 at this stagein the historyof the Universe.In otherwords,protons outnumbern€utronsby between5 and l0 to l. Neutrons in isolation are not stable particlesand will radioactivelydecayirrtoa proton via the emissionof an electron(known in nuclearphysicsas beta decay).The nreanlifetinreofa free neutronis about l4.g minutes but' if it can becomebound into an atomic nucleus,the neutronwill no longer decav. It will renrainstablefor as longas it is containedwithin the nucleus. chapter I introducedthe proton-proton chain by which helium is synthesizedin the heartsof stars.Duringthe heliumnucleosynthesis of theearlyUniversethe initialcollision betweentwo protons is largelyreplacedby the collision of a proton and a neutron which fornrsthe deuteriumatornand a photon ofenergy:
lH+ n- + ]H + y
77
lei, Z, and Zr.
,J/
N ,' I nt,')"
The decoupling ofmatter and energy
Sec.4.6l
(4.21)
Nuclear fusion introducesa quantity known as the bintling energy.This is the quantity of energywhich is carriedaway by the photon in an exothermicfusion reaction.Foi instance, in the nuclearfirsion betweena neutronand a proton, the resulting deuterium nucleus is less massivethan the combined rnassof the proton anclthe neution. This difl-erence is known as the mass defect,arn, and rvhenthe energy equivalent is calculated using the Einsteinequation( 1.2),this is the qua'tity which is known as the binding energy. A deuteriurnnucleushas a binding energyof 2.22MeV which r.un, tr,ot,-u, long as photonscontainingthat amountofenergy are presentin the Universe,the reactioncan be reversed.when a deuteriurnnucleuscollides witha2.22MeV (or higher) photon, it will be brokenup into a neutronand a proton in a processknown as photodisint.gration. Even when the energydensityof the Univeise drops considerablybelow 2.22MeV, there is still a considerablenumber of lhesehigh energyphotonswhich can photodisintegrate the ncwly fol'rred deuteriumnuclei. So, despitethe fornrationof deuteriumbeing favolred whenthe cncrgydc.sity dropsto irs nuclcarbindingencrgy,the photodisintegrition stops Iargenumbersof the nucleipersistinguntilthe energyhasfallen,still further. io 0.07MeV.
(4.22)
./
andtheenergy also.Thismeansthat,astheUniverseexpands r decreases As E decreases, densitydrops,riuclearreactionbecomelessandlesslikely.Evenmoreseriousthanthis is i.e. As thenucleibecomemoreandmorecharged, r decreases. thatasZ, andZ, increase, protons,sothereactionratedropsrapidly.Thesetwo effectsconspireto virtuaccumulate ally halt nuclearfusionin the early Universeafterthe neutronshavebeenconfinedin of theelementlithiumareformedfrom thehelium. heliumnuclei.Only minutequantities five minutesin ageand the Fusionstoppedwhenthe Universereachedapproximately haddroppedto around6x l08K(52keV). temperature was of elements duringthisepochthattheprimordialcosmicabundance It is,therefore, forged.25 percentof the massof the Universeis helium,whilsta whopping75 percent helium-3and of deuterium, Therearealsoverysmalltraceamounts remainsashydrogen. lithium. 4.6 THE DECOUPLINGOF MATTER AND ENERGY theUniversenow entereda state five minutes, Afterthefranticevolutionof thepreceding to expand,andtheenergydensityandtemperaof relativelycalmevolution.lt continued of theUniversewasnow governedby the photure dropped4ccordingly.The temperature tonsof radiationwhich vastlyoutnumberthe particlesof matter.In fact, at the endof the nuclearfusionepochthe ratio of matterto radiationwas set in its currentday ratio of I matterparticleto everytwo billion photons. As well as containingthis vast amountof photons,the Universeat this stagein its of thenucleiforgedduring evolutionwasfilledwith a highenergyplasmawhichconsisted The hydrogennucleithemselves anda seaof freeelectrons. theepochof nucleosynthesis werenothingmorethansingleprotons. stateof Thenumberdensityof particleswasstill sohighthattheywereall in a constant radiationcannottravel very far througha collision.Whenphotonsof electromagnetic
t t t t t t t t t t t L
t L
' jl
l'! 1.il 1.il
tr.1 il.,1
78
'I'hc ttig
Bang
Chronologyof the Big Bang Era
f i. u (s)
n.'
Temp. (K)
The Big Bangoccurs. Planck Era
All four fundamentalforces unified; physicsof the Universeindeterminate, t = 10 a3
1ot'
n
t = 1o 3s
1or .
Electroweak Era
n.
t= 1 0
Hadron Era
l-epton Era
I
I., il
ll .,
it
I .,
4
ID o. d'
Strongnuclearforce separatesfrom electroweakforce. GUTsymmetrybreaks(hadronsand leptons no tongerequivalent). Baryosynthesistakes place. Inflationaryepoch beoins. (Universeincreasesit-ssize by 1Os times). -
=
o o
3 0)
o c
tt
10t s
Electroweaksymmetrybreaks. Leplonsacquiremass.
= I t ro-'o
1o''
Quark-hadronsymmetrybreaks. Protonsand neutronsare created.
t = 1 0 -s
l o to
Neutrinosdecouple.
t =102
1os
Nucleosynthesis begins.
t = 1025
108
Nucleosynthesisends.
lr
il . ;
Gravityseparatesfrom other three forces
G UT Era
['i l
['lr
lch.4
Radiative Era
t = 107s (t = 1 year)
Thermalisationbetweenenergy and matter ceases.
o d (D
_o_
tI
5g < = =B = oo
t = 1013 103 Decouplingof matterand energy. H 6' " (t = 300,000years) Universebecomes transparent'iophotons; these photonsobservedtoday as cosmic i microwavebackgroundradiation. F r g .4 ,4 .Kcycvcn tsin .th ce vo lL r tioonl thcU ni vcrscj ust aftertheB i g B ang.
Sec.4.6l
The decoupling ofmatter and energy
79
medium, before they collide with a particle of matter,the medium is said to be optically thick. In the Universe today, space is optically thin becauselight can travel acrossvast distancesof spacevirtually unhindered.This is why we can see distant galaxies.In the Universebeforethe decouplingof matter and energy,conditionswere optically thick. In this high energyenvironment,energywas being sharedbetweenthe particlesvia the thermal bremsstrahlungprocess(describedin chapter2) creating new photons to carry away excessenergy.Also, photonswere interactingwith mattervia Compton and inverseCompton scattering.This high level of interactionmeant that both matter and radiation were maintainedat the sametemperature.This processis known as thermalisation. When the Universebecamea year old, the expansionof spacehad lowered the density of matter sufficiently so that thermal bremsstrahlung ceased to be a dominant process. Thermalisationstoppedand the temperatureof matterbeganto evolve differently from the temperatureofradiation. The expansionofthe Universestretchedthe radiationto succcssively longer and longer wavelengths.This did not affect the shapeofthe photon energy distribution. lt still followed a black body curve; as the wavelengthswere lengthenedsn the temperatureof the radiation fell. The matter particlesbeganto evolve under the influenceof gravity which causedthem to start clumping together.In this way certain regions of the Universe became slightly denserthan the average,whilst other regions experienceda drop in density. Radiation continuedto interactwith matter via the Compton effect and so thesedifferencesin density beganto imposean influenceon the radiatign,which was no longer constantthroughout the whole Universe. For the next 300,000yearsthe Universeremainedoptically thick to the radiation.Matter continuedto slowly clump togetherand the radiation cooled according to the expansion of the Universe (with a slight influence from the density of the region in which the photons found themselves). The turning point betweenan optically thick and an optically thin Universewas the next major developmentin cosmic history, and it signalledthe end of the plasmaepoch. The plasmawhich penneatedthe Universecontinuedto be ionised.As statedin chapter 2, the processofionisation is a bound*freetransitionwhich liberatesan electron from its electrostatic attraction to an atomic nucleus. In the case of a hydrogen atom, an energy of l3.6eV is necessaryto be sure of removing the electron. As electrons continued to move around,the few collisionsthey did suffer inexorablydrainedthem ofkinetic energy,until they could be easily capturedby any atomic nucleus ifthey happenedto stray too closc. The atomic nuclei, being much more massivethan the electrons,moved very slowly in comparison. By this stage, as well, photon energieshad dropped considerably below l3.6eV, and so when the electronwas capturedit could no longer escape. Insteadofhigh energyelectronszipping about all over the Universe,making a nuisance ofthemselves by getting in the way ofthe photonslike errant children being gatheredup by their parents,so the electronswere being confined to the near vicinity of atomic nuclei. By rernoving the interferenceof the electrons,photons suddenly became able to travel large distanceswithout interacting(see Fig. 4.5). The Universe becameoptically thin at this point and the temperatureof the radiationwas approximately3,000K (energydensity 0.26eV). This is the point at which matter is said to have decoupled from energy. Thc photonsofradiation, which suddenlybegan to travel through the Universe at this stagc,
lch. 4
lJO Thc llig Bang
are thc self-sameones we observetoday as the nticrorvavebackgroundradiation. The tctnperaturcofthat radiationhas beenreducedby a lirctor of I,000, due to the expansion ol'the Universe.The differencesin matterdensityresultedin slight differencesof temperature in this radiation,whiclr were recentlyfound by the COBE satellite. BeforeDecoupling:-
(a)
Photons
/\^\P
@
I
Y
@
Prolons
@
Electrons
Sec.4.7l
8l Modclllngthe crpnndlngUnlvcrrt
4.7 MODELLING THE EXPANDING UNIVERSE the driving force behind the uniThe previous sectionsin this chapterhave shown that (4.4) we introduceda function R(t) which verse,sevolution is its expansion:In equation time passes,R(t) grows.in size for an as l'hus the linear size of the universe. characterised lscale factor",and we shall refer to it as the knorvn function is a expandinguniverse.'I'his ofthe Universedependsupon ofien froi now on. Equation(4.4) showeclhow the volurne R(t)'. over thi distanceso[ atomic we have seen how the strong and weak forces act only forces averageoutlo bezero nuclei and atoms.chapter I also told how electromagnetic Universesince a time of one the of over largevolumesof space.Therefore,the expansion m i c r o s e c o n d h asb e e n g o ve r n e d e xcl u si ve l yb yg r a vi ty.In ch a p te r 3 w e - r e m a r ke d th a t why it did not collapse becauseNewton thought the universe was static, he wondered has the potential to be through the gravitational pull of its constituents._lfsomething m o v e d b y g r a v i tyth i sca n b e q u a n ti fr e d ,a n d i ti skn o w n ,a p p r o p r i a te |y,a sg r a vi ta ti o n a l
<-@
@ Oplicallythick
AfterDecoupling:-
l:ig.4.5.O$cal thickncss of thc llnivcrsc.iustallcr thc llig llang.(a) llclbrc thc dccouplingol' mattcrand'cncrgy,photonsof radiationcould not travcl lar bclorccollidingwith particlcsol' mattcr.(b) Aftcr decoupling, thcclectrons havebccntrappcdby theatomicnuclciandthc photons canlravclfor largcdistanccs withoutintcracting.
Irig. 4.6. 'l'he Frictlnranncquarionoatrbc tlcrivcdby considcring,.a.-..-o-n:t:.,"_ltl:.::n::tul::* cxtrenrcedgcol lllc spncrc tliivcrse and exploringwhat would happcnto the malt€r-atthe iiont -sitr.,J.,i Shortl{isrory olrhe I)niverse'w'l{' Frceman'1994') iil;;il
' .1
''I
t t t t t t t t t t I L I
Lll
1l 'll
82
'l'hc Big llnng
lch.4
tl
1 ,l ,l al
I
:il
I' i l
tr.il I"'il 'll I I
it'I I
I
potcntial energy. Hubble discovcredthat thc Universewas expandingand solved Newton's problem. Anything whiclr nrovesis said to have kinetic energy.Hence, in our Univcrsc the kinetic energyofthe separatinggalaxiesis greaterthan the force ofgravity betwecnthem. This may not alwaysrernainthe case.however. In order to model the expansionof the Universethis inequality in energiesmust be fbrrnulatcdwith rnathematics. In order to do this r.veimaginean arbitrarysphericalvolume ofth eUn iv er , eandov er lay at hins plr er ic ash l e l la r o u n d i t . T h e s p h e r e i o n t a i n s a m a s s , m, whilstthe shellcontainsa mass,nrs(seeFig. 4.6).The spherehasa radius,d, rvhilstthe thicknessof the shell is negligible.In accordancewith the expansionof the universe, the nlattcr in the shell is travellingaway from the centreof the spherewith a velocity, v, given by the llubble expansionlaw,.(equation (1.4)). with theseas our basicparameters, the kineticcnergycan be calculated: Ir K. t1.=- tnsv'[he gravitational potentialenergycan alsobe calcLrlated: l'.E. = -
Gnrnr-
(4.24)
d 'l'ogctholthesecan be equated to find the total energyofthe shell by applicationofthe principlcolenergy conscrvation rvhichstates K.E. + P.E.= totalenergy
(4.2s)
I3eforcusing(4.25) to find the total energyofthe shell,we shall substitutefor the velocity in (4.23) using( | .4). we shall also substitutefor the massof the spherein (4.24) usingthe cquatiorr
n r=V p =1 n o 'o 2 I rr(r)2,t acnod2) totale.ergy "t'[--i* t )=
whetherit is positive or negative. The kinetic energyterm in the Friedmannequation(4.29), has reducedto the squareof with time becauseof the action of gravity. The potthe Hubble constant,which decreases ential energy is governedby the densityofthe Universe,which also decreasesas the Unibut, becausethe sign ofthe potentialenergyterm is negative,this resultsin u.rr. "*pund, an increasein the gravitationalpotentialenergy. The sign ofk dependsupon whetherthe magnitudeofthe gravitationalpotentialenergy is greaterthan the kinetic energy.If it is, the value of k is negative.lf not, then k becomes poiitiu". At the point where the kinetic energy is just equal to the potential energy, k becomeszero. When the Friedmanequationis derivedthrough useof Einstein'sgeneralrelativity, thc energy constant is given a different interpretation. Instead of an energy, it is thought t
(4.26)
Timel
(4.27) Times
'l'his cquationcontainsLhedensityof the Universe.p, which is proportionalto the inverse cubeofthe scalefactor,R(t)-'. and hencedropsby a lactor ofg ifthe universe doublesits lineardinrcnsions(seeFig. 4.7). If we replacethe totalenergy,E, with an energlz constant,k,
2ER(t)2
k = -------\-llnsd-
(4.28)
a n d e q u a t i o n ( 4 .2 7 ) b e co r n e s r rt,\2
8 lGP
k
r lt a I
r .
,.f
n (t)-
<--
(4.29\
83
in This is known as the Friedmannequationand describesthe expansionof the Universe present denthe H(t)=Ho, constant, terms of measurablequantities. These are the Hubble I sity of the Universe, p:po and the present scale factor which we can set to unity, R(t): ' betause it is an arbitrary measureof the Universe's size. Thus, if we can determinethe Hubble constantand the densityof the Universe we could solve this equationand find k' Unfortunately, the precise determination of these parameters is not that easy, as will bc seen in latei chapters.The actual magnitude of k is unimportant-the big question is
l'lrus(4.2-5)becomes
.
.l
(4.23)
Modelling the expanding Universe
Sec.4.71
R -->
<_-2R._.--.---->
Fig. 4.7. As the Universeexpandsthe volume increasesproportionallyto the cube ofthe scale faitor. (Adaptcdfrom Silk, !., A Short History ofthe IJniverse,W H. Freeman,1994)
.1 tl4
'l'hc llig llang
lch.4
thc Univcrscand the llubble constantwill be discusscdfully in the final chapterwhen we considclthc agc and the fatc ofour Univelse. The Big Bang theory is without doubt the best current interpretationof the cosmological observationsavailableto us, but it is by no meansproven.A nurnberof problemsexist within its structurewhich rray or may not prove to be solvable.As the final sectionin this chapterrvill show, the theory has alreadyundergoneone major revision,and it seems likcly thatotherswill follow as betterdataandtheoleticalideasbecomeavailable.
Sec.4.8l
The llatnessand horizonproblems 85
ln a negativelYcurved Universethe angles inside a triangle add uP to more t h a n 1 8 0 '.
4.8 THB FLATNESS AND TIORIZON PROBLEMS The flatnessproblemcrops up when presentday estirnatesofthe k term in the Friedmann cquation are attempted,This is wrapped up in the searchto discover the density of the Universc.l'his will be discussedin chapter9 but, for the moment, it is enoughsimply to statethat all analysesend up with a value for k which, within the boundsof experirnental accuracy,is equal to 0 and implies a flat geometryto the spacetimecontinuum.Simply statedthen, the flatnessproblem is: why should we live in a flat Universe?An infinite number of open (k>0) and closed (k<0) Universesare possible so why, out of all the valueswhich k could take, is ours so close to tlre one special case?- the dividing line betweenan open and a closed Universe.[t seemslikc an awfully big coincidence,and is sometlringto be investigatedfurther.Coirrcidencesusuallylead scientiststo a reasonwhy tliings are tlre way they are. Chapter3 introducedthe conceptthat any event has an horizon around it whose radius is given by the time since the event multiplied by the speedof light. At the decouplingof rnatterand energythe Universeis thoughtto have been300,000yearsold and so its horizon was about 300,000 light yearsin radius.It will be shown in chapter9 that the Friednrannequationcan be used to show that the dependenceof scale factor with time for a 'flat' Universeis 2/ R ( t ) c c t /3
(4.30)
If we assunrethat the Universeis currently 1.5* 10"'years old then the current horizon is l.5tl0'0 light years.Using (4.30) to calculatethe currentscalefactor and one for the Universcat the time of decouplingit can be easilycalculated that the sizeof the Universe at 300,000yearsis about 1350times smaller,which in termsof an actualdistanceis about lxl0' light years.So at the time of decouplingthe sizeof the presentlyobservableUniversewas at leastthirty times bigger than the horizon distanceat that age. This leadsto a problem with the microwavebackgroundradiation which has become known as the 'horizon problem'. As describedin chapter2, the CMBR possesses the same properties no matter in which direetion it is detected.Although there is the dipolar anisotropy,producedby the motion ofthe Earth though space,and the fluctuationsproducedby tiny variationsin the local densityof matter,in principle the radiation is entirely smooth. It possesses the sarneblack body temperaturcregardlessof its direction.Conventionally, this behaviouris only possibleif the radiationthroughoutthe entirevolurre of the presentlyobservableUniverseis in thermalequilibliurn. The only way in rvhiclr thermal equilibriurncould be rnaintainedis if energycould bc sharedbetweenall particlesof
(b) I n a E u c l i d i a nU n i ve r se t h e a n g l e si n si d ea tr i a n g l e add uP to exactly 180".
t t t t t t
( c) In a positivelYcurved Universethe angles inside a triangle add uP to less than 180'
upon the amountof matter Fig. 4.8. The curvatureof the spacetimecontinuumis dependent w i thi ni t:(a )thec |os edU ni v ers ec ontai ns enoughmattertoha|ttheex pans i onandc o||aps ethc .flat' maner tolralt theexpansion.but tg""iil"""l u"i".rse co"ntainsenough universe;(b) the matterto halt enough contain not (c) rhe openuniverse-d&s i"'ini.it. r*ltrl ;;i; Freeman' "iii.q "il iot"""i-'taOupitO from Kaufmann'W '!'' Universe'W H and so will expand "*p'onrion 1987.) decoupling becauseev€n photons, which matter. This was clearly impossible at the time of
to sharethe distances travelat the speedofiigttt, couldnot havetravelledthe required energy. ThelrorizonprobtemandtheflatnessproblemledtotheproposalbyAlanGuthinl9S0 duringits.earlyhistory'Alexpansion thatthe Universeentereda periodof exponential somework. The theoryhas thouehhis ideaswere,orrr.t, his basiclormulationneeded
1 il til til til JI
iil :]il 1.il
l.l ]
t-;
ri ri
t. ;
t.l:
{16 'thc llig l}ang
[Ch.4
InflationarYcosmologY
Sec.4.9l
now rcachedsuch a level olsophistication and acceptancethat it is almost invariably includcd in discussionsolthe Big t3ang.This additionrvastermed 'inflation'.
't'.:iit.:) 4
.t.'
87
1028c m
4.9 INFLATIONARY COSMOLOGY a.
The inflationaryepoch is theoriscdto havetakenplace at the end ofthe GUT epochwhen thc tjniversereachcdthc agc ol' l0 tr seconcls. I)uring discussionsabout the epoch of grand trnificationwc havc strcsscdhow all thc lirrces,apart frorn gravity, were indistinguishablc.'l'hisis said to be a period of high syurnretryand, in understandinginflation, we will draw the analogythat this era of the Universecan be representedby a lake of liquid water.'l-hewater in its liquid form is the sameeverywhereand, becausethere are no prelbrrcd locationsor.dircctions,thc water is saidto bc in a symmetricalstate.If the temperaturc ol' thc lake werc to lirll, it rvould start to freeze. In the processof freezing, water nrolcculcstake up positionsin a crystallinelatticeand it is no longertrue that there are no plelbrrcd locations.Thus, in ice the liquid water sylnnletryis broken.This changeof state is analogousto what happenedin the early Universe when the temperaturepassedthe critical value of I " 1028 K. The Universechangedstatebecausethe GUT symmetrybroke. No longerdid the strongnuclearforce act like the electroweakforce. Whcn the water in the lake freezesit gives out energyknown as latentheat.This heat must be complQtelygiven out beforethe temperatureof the ice can fall below 0oC, In our sccnariofor iri'lation, energyis given out by the GUT symmetrybreaking,and this holds the Universeat a constantcnergydensityfor a short period of time. Maintaining the Univclsc at a constantdensityallows it to entera period ofexponentialexpansionwhich is the 'inflation'ol'thisepoch'sname. This conclusioncan be easilyshownby recourseto the Friedmannequation.Ifthe scale factor R(t) is differentiatedwith respectto time rve gain the expansionrate of the Universe.Ifthc units ofscale factor arc appropriatelychosenwe can form the equation
.t
..r r. "
\;
:
a
'/';\
..aa .
I a l ./:.r 3.f o
'::,i2 .'.
.t.t
..
a
'.
X:':: "".
a ao a
a
I
aa
(b)
o
a,
I
. a oa . a o a'
aa a aa o o' ,ao ->- .
{:::'i:'I?
. :'ii;.i1'.i..1
.' i '.'...t.: j.. ;. '.--.^.]:j. .:'. 3 x 10-25c m
t'. .i:t.';'t t
.:
a
(4.31) a
lf this is substitutedinto the Friedmannequation(4.29)it can be shown that the rate of universalexpansionis proportionalto the scalefactor rnultipliedby the squareroot ofthe dcnsity,sincethe densityitselfis proportionalto the inversecube ofthe scalefactor
a
Today
n (t)* n %
(4.32)
ln thc inllationaryepochthe densityremainsconstantbecausethe energygiven out by the phasetransitioncan be convertcdinto nrafterby (1.2). This affectsthe expansionrate of the Univcrseand it becornes n (t)ccR
(4.33)
Ifthese two equationsare plottedon a graph it can be easilyseenthat the constantdensity ofthe inflationaryepochlcadsto an exponentialincreasein the sizeofthe Universe,i.e. it undergocsa period in which it continuallydoublesits size in a constanttime (seeFig.
-iegion Fig-4'g.Non.inflationaryandinflationaryexpansion.(a)lnnon.inflationarycosmology'today's about lmm acrossat l0-r5 seconds.Even.though observabteUniverse.,.p;;;1';;;;; (b) trorirondistanceof the universeat that time. i"rg.ittr"-nirl" this is very small it lr rtil ,ui to becomemuch period inflation of th€ during In an inflarionaryun,".rr.,-#..ir'.*pr"o.o larger the Universe-is-much i.tg"t iftt" tttl n6riron aisii#e ofthe Universe As a consequence' oJ the IJniverse,w.H. Freeman' rhan we can ousene. lniap-iJ i.. sitt , !., A ShortHistory t994.)
4.9),A tt hest ar t of t heinf lat ionar yepoch't hechar act er ist ict im einwhicht heUniver s Eventhoughinflationendedwhenthe Universe doublesits sizewasaboutl0-!aseconds. it hadtime to inflateby a reachedan approximateageof l0-32secondsit still meantthat
[' tltt
'l'hc llig llang
O u r t i n y r e g io n h a s a r a d i u s o f cu r va tu r e wh ich i s s o l a r g e it is vir tu a lly i n d i s t i ng u ish a b le fr o m t h e f l a t ca se .
T h e U n ive r se after inflation ------+-
Scc.4.9l
Inflationarycosmology89
r4 secondsthe Universe'shorizon was l0-34light seconds.If we were to extrapoAt l0 latebackwardsfrom our observedlrorizonusing (4.30) we would find that althoughsmall, horizon the size of the Universeat l0-14secondswould still be about l5 centimetres.The in thermal be to the Universe expect we can which upon scale gives the maximum distance these equilibririmand possessthe samephysicalconditions.Beyond the horizon distances, very ditf' be could and to communicate time no had disparateregioni of the cosmoshave grew exponenthe Universe within point every inflation, During each other. from erent the tially larger by a factor of 105n.Inflation then stoppedat l0-32seconds,by which time l016 to seconds light l0r4 from in size increased bubble ofthermal equilibrium had been with an light seconds(3x106 light years).This enorrnousexpansionhlled our Universe energy which was all at the sametemperature,and it solves our horizon problem. ln aaaitionto theseproblems,we mentionedearlierthat the GUT phasetransitioncould and lead to topological deiects in the spacetimecontinuum such as magneticmonopoles despite yet found, to be have defects these by theory, predicted Although cosmic st;ings. the fact that they have well-definedobservationalcharacteristics.Inflation provides a reason for theseobjectsnot to be found, in that, as the Universeinflates,most of thesenewly createdobjectswill be pushedfar beyond our cosmichorizon' Finally, the energy releasedby the inflation signifiesa fundamentalchangein the vacuum of spaceand allows matterto form. In the coming chapterswe shall refer.to inflation severaltimes and indicatehow it hashelpedshapeour ideas,especiallythoseabout galaxy formation and the cosmic microwave background.
t t t t t t t i
Fig.4 l 0.'lhellatrtess problcnr issolvcdbvinUation.rvhichpostulates thatourUnivcrse isa tiny regiorr onthcsurlacc ol'arnuchlargcr curvcd surl'ace. f'actorof some 1050 tinrcs!This rvouldsolveour lla{ncssproblenlbecausel'orall but thc mostextl'emegeometriesof spacetimc,the stretchingol'inflation would flattenthe surface (seeFig. . I 0). By vastlyinllatingtiny areasof the tJniversethe horizonproblemcan also be solved.
t t t t L
l'll
lt
'lI 'll til ']l
lI ll
;rl ,,1
The cosmologicaldistanceladder In previouschapters we havediscussed theway in whichthe Universehasbeenobservcrl to be expanding. This meansthatthescaleof the Universemustbe an importantthingt
tl
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,1 , ,
h;
5.I STANDARDCANDLES A standardcandleis anyobjectwhichcanprovideits distanceby a studyof its brightness. The estimateis then calledthe luminositydistance.As this namesuggests,the distance calculated by this methodis baseduponsomekind of estimateof how brightthe object shouldreallybe.Any deviationfromthisstandard brightness is thenattributedto thc fact thatthe objectis far away.This methodrelieson the inversesquarelaw for the intensity ofpropagated light.Thusifthe distance ofan object,d, doubles,thentheobservedflux. F, is quartered: F o c-
I
( 5. t )
d2 If the luminosity, L, of the celestialobject is knownprecisely then(5.1)canbe useddirectly to give a luminosity distance:
L
( 5. 2)
4nF Often the preciseluminosity is not known, and so other methodshaveto be found in order to estimate an object's distance. To this end, astronomers use the magnitude system to referencea celestial object's brightness.This comes in two different guises. Apparent magnitude,m, is the brightnessof a star (or other body) as it appearsin the sky. This
92
'l'hccosnrological rlistnncc lirrl
lClr.5
systcttrol'classiIicatton,ltorvcvc'r, givcs no considcfirtionto the distarrccol thc object trndcrscltttiny.it is vcry likcly tlrata faintclosc-byoh.icctrvill appearto be nruchbrighter 'l'hus,a bcttersystemfor measuring thana lar distantbut intrinsicallybriglrtob.iect. brightncsscsis krrurvnas the absolutenragnitudc.M. 'l'his is a measurement of the apparent ruagnitudcofa celcstialob.jcctif it rvclc placedat a clistance of l0 parsccs.'l'hus,it provitlcsa dircctcontparison lrctwecnthc brightness ol'ail known celestialobjects.Combining tlrcset"vo nragnituclcsysterllscarrlcad astronomelsto tlre distancemodulus. 'l-hcmagrritude systetrlcarnc into bcing during thc time of the Greek civilisation.In particular,tlrc Greekastrononler, Ilipparchus,ofthe latesecondcenturysc, decidedthat hc could rarrkthc starsin the night sky accordingto their brightness. He dividedthe stars into six dil'l"crentcategoriesand classcdthe brightestas being of first magnitudeand the laintcstas bcing of sixth magnitude.With the inventionof the telescope,this primitive systerlrhad to be revisedand extcndccl. AlthoughWillianr Herscheloriginallyundertook this cndcavour,our ntodertrtnagnitude systernis baseduponthe work of the Englishastronorner,NorrnanPogson,in 1856.'fo rnimic the eyc's response,pogsonsuggesteda rnathcnratical equationwhich used logarithms.In studyingthe classifications made by Ilipparchus,Pogsondiscovered that the dill'erence bctweeneachof his magnitudes was a factorof 2.5. 'l'hus,he castan cquationto rnirnicthis bchaviourby conrparingtwo apparcnt rnagnitudes, m, and mr, and the flux ol'radiantcncrgy,rvhichcould be nreasurecl liom tltc celestialobjcctsat thc surl'ace oftlre f:arth,F, anrlI:". l l t,
trl )
l"\ 2 .' ,1 ,,' ,( I,/
(' ' i t
l-lrishas bccomeknown as Pogson'scquation,and is the startingpoint for our derivation of thc distancemodulus.As a brief aside,it was the introductionof a rigid rnathematical Ibrnrulationfor ntagrritudewhich hascarrsedsomeobjectsto possessrnagnitudesin nrinus n urn be rs.Thu sa nob. iec t wit ham agnit r r deofis -l trvo-and-a-halftimesbrighterthanan object with a rnagnitudeof 0. This object is, in turn, two-and-a-halftinresbrighter than a magnitudeI object. lnsteadof the flux of energy reccived at the Earth's surface,if the actual energy relcasedper unit areafrom eachof the celestialbodies,i.e. their luminosity,is known, then tlreecluation givesabsoluterrragnitudes instead:
M -Mz =-r5r"c[*)
(5.4)
'flrc
lurninosityof the otrjcctand its nreasured flux arc linked by the inverse*square Iaw (cquation(5. I )) so that .L
r--..-....T
4 nd "
(5.5)
lf this is to be usedto.give an absoluternagnitudethcn tlre distance,d, is fixed at l0 parsecs. To obtainthe distancemodulus,inragineobservingan objectofa known celcstial typc which has an absolutcnragnitude of M. Observatiorrs of the flux for this objectcan givc an apparcnttnagnitudcby usingcquation(5.3) in coniLrnction rvith a standardrcf'er-
S tandard rul ers
Sec.5.2J
93
known for the object ence star. l-hus an apparentand an absoltrlcrltagnitudeare now equation(5'4) to give into Thesemagnitudesand their associatedfluxcs can be substituted
( r-an(ro)' )
----*m - M = -2.5 loel - [ L 4 r d './ I
( 5. 6)
This equationsimplifies in a few stages. m - M =- 5 + 5 l o g d
( 5. 7)
distance,in This is the distancemodulus equationwhich can be usedto give a luminosity known. lt is scrutiny under the object of parsecs,providing that the absolutemagnitude square inverse the is in brightness to diminish object the for reason assumesthat the only objects by law, which is not stiictly true. lntersteiar dust particlescan also dim celestial also be estimated scaiteringand absorbingphotonsoflight. This interstellarextinctioncan expression: modulus and added to the distance
rn-M =- 5+5logd+Ad
(s.8)
for lines of A is a constantextinction factor and is estirnatedto be about 0.002 mag/pc Pogson'sequation and modulus distance Galaxy.'l'he our plane of in the are which sight ladder because,in .r-op up time and time again when studying the cosmologicaldistance such as apparent objects, of celestial properties observable uuriou, guises,they link the distances. to fltxes. and nragnitudes 5.2 STANDARD RULERS which we can be Standardrulers are celestialobjects which have linear diameters,l, of is measured' 0, object faraway a of diameter reasonablycertain. Thus, if th! angular distance'd, can the and triangle, right-angled a conitruct used to then be can trigonometry be calculated .uiily b" caiculated.In its simplestform this so-calleddiameterdistancecan using the equation
o=
I 0
(5.e)
the mostaccuratemethodof dismodifoingthe standardruler approach, By somewhat parallax, is knownastrigonometric This to astronomers. available is determination tance the Earth As known' well is thediameterof theEarth'sorbit andis possibleonly because points throughout vantage different from usto viewtheUniverse orbitstheSun,it causes theEarthis on differtheyear.Thisdifferenceis at a maximumeverysix monthsbecause parallaxinvolvesan angularmeasurement entsidesof its orbit.In principle,trigonometric stars,whichcanthenusedto conof a star'sshift in positionrJativeto the background (seeFig'5'l)' calculated can be distance structa trianglefromwhichits of thestary l)raconis' parallax the to measure tried Bradley James ln lT2T,Englishman relativeto thebackposition its a shift in Overa six-monthperiodhe did indeedmeasure haddiscovBradley fact, parallax. In to great to be clue groundofstars,but it wasfar too speedand finite a at travels light because occurs which
t t t t t t t t t t t t L
it
il
tl 1t tl li ll ll ll :l ll
ll ll ll ll 'll
,.1
l ' h c c o s nr o lo g icllr lista n ccIn r ttle r
lch.5 V ery di stant stars
Ear t h X
XX X yX
aX X Xx X I:ig 5 r ''r'rigonomctricparailaxis the hcst method for (rctcrminingstclrardistanccs,but unfortuniltcly is verylirnitid in rangc. I)arallax rvas finaily measured over a century later by the German accountant_turned_ i r s t . o n o r n e r ,F r ie d r ich Be sse r ,wh o stu d ie d th e d o ubl e si ar 6r cygni . Thi s si ar w as found
t. havea rninuscule parallaxwhich indicatedit was ,onl. 6'lolii1;i;, A;;r; km) away. It is parallax which provides astronomers with their unit of distanc., tr,e pur.".. tr," ttanteis an abbreviationofparallax arc second and is definedas the distancea star would bc lionr llarth ifit were to dispraya parailax ofone secondofarc. This happensto equate lo a (listanccirf approximately3.26 light years. In actuality,all parallaxesare smailerthan ()'c .rc sccond becausestars in our cerestialneighbourhoodaie spreadso far and wide. l lrc rrca'cststarto us,cr centauri,possesses u pulilu* or.0.75arc seconds. 'l'his illustrates the only-problemwith the parallaxmethod.It is measurableonly for the starsncalcstto our Solar System.1'he displacements are so small that the calculateddis_ litttocsrapidlybecomeinaccurate, and so only about 1.000or so starshavehad their disl.r)ccsnrcasurcddi'ectry by this methocr.It is, however.,a good foundationupon which to bascthc cosnrological distancescale. 5.J I'IIIMAITY I NDI CATO RS A p'inrary clistanceindicatorisany cerestiar object which hasbeen
calibratedby observa_ ri,rrsofsinrira'objects withintheMirkyway.i,referautf ilil;."*;ir'nlrl. o..n .u,_
cttlatcdby palallax measurements, but ofteri other obscrvationalor theoreticalconsiderrrtirns will have to be nrade.Having estabrished the observationarpropertiesofthe prirrrirryindicatorin our own Garaxy.itcan then be conrpared,eitherby'using it as a stanaaro c;rncllc or rulcr,to sirnilarobjectsin othergalaxies. 5 .1 CEPIIBID VARI ABLE STAI TS '-l'hc very bcst of the primary indicatorsis the crassorvar.iable star known as cepheids. 'l'hcsc arc nar'cd after the prototypevariabrestar of this class,6 cephei. itr.y u""upy u rcgion of thc Hc'tzsprung-Russeildiagranrjust abovethc rnainsequen.. una-r.pr"r.n, ,n. llrst stagcin a star'sevolutiontowarclsbecorning a rcd giant. virtually all starsare thought (o enterlhis stageofexistence alter hydrogenb-eginsto run out in their cores. l.he break_ throughin usingrhesestarsas distanccn.roi.k.r, c-amcat the beginningof this cennrryand *'as rnadcb),thc astronorrcrI.lenrieilaLcavitt, workingat l.larvardcottege.she obtained
Cepheidvariablestars 95
Sec.5.41
photographicplates of the Magellanic Clouds which, in those days, were knorvn only as being incredibly dense star clusters. She identified many variable stars from the photographs and began to notice a correlation between brightness and the time taken to pulsate,a quantityknown asthe period.The brighterthe star,the longer it took to pulsate.She then comparedthe shapeof thesevariable stars' light curveswith variable stars in more immediate surroundings.She discoveredthat the shapeswere exactly the same as the Cepheid variable stars, only the brightnesseswere different. This she attributed to the variable starsin the MagellanicClouds being much further away.The distancesto nearby Cepheidshad yet to be determined,however,becausenone were in the range ofparallax The final piece in the puzzle was addedby Harlow Shapley,who realised measurements. that the variations in brightnessmust be due to variations in the size of the star during pulsation.He usedthis theoryto work out the sizesof individualCepheidsand calculate tlreir luminosities.As soon as this informationwas in place, luminosity distancesbecanre easyto determine.lt was the discoveryof Cepheidvariablestarsin the Andromedagalaxy which allowed Edwin Hubble to concludethat it was a galaxy externalto our own, and to proposethe redshift-distancelaw. The relationship between the average absolute magnitude of a Cepheid variable star, M,, and its period of pulsation,P, can be quantitativelyexpressedby the equation
(s.r0)
M u = - 2 .8 l o g P
-5
.= W VirginisStars
o- ? c
E 3-1 a +'l
0. 1
0. 25 0. 5
151050100 Periodin days
for Cepheidvariablestarsis oneofthe mostaccurate relationship Fig.5.2.Theperiod*lunrinosity primarydistancedctermination methodsavailahle.
S upernov ac 97 96
' l ' l r c c o s n r o lo g icndl ist;r n ccl:r tlr ltr
fch.5
S ec.5.?
Strictlyspcaking.(5.10.1 is only valid lirl younucr,l)opulationI Cepheidvariablcs,known as classicalCcpheids.Oldcr, ructaldclrcicnt,Populationll Cepheidsare referredto as W rnagnitude relationVirginisstars,ancltlresclollorvtlreslightll,nroclillcdporiod-absolute sltip. M" = - 1. 9- 2. 8 logl'
(5.il)
A third type of relatcdvariablcslar is the llll l,ylae stars.'fhese can bc thouglttof as 'Ihey pulsatcr'vithpcrioclsbctween0.25 to I day and havea mean short-pcriodCepheids. in the absolutcnragnitude ofabout 0.8. Iloth classes ofCeplreidhaveabsolutenragnitudes range-l to -7 anclpulsationperiodsin the rangc2 to 100days(seeFig.5.2). RR Lyrae rvithin globular clustersand are sometimesreferred starssccrr to be fbund preclonrinarrtly to as 'clustcrvariables'. The only thing which stopsus using Cepheidvariablesexclusivelyto gaugedistanceis the technologyavailableto us. As bigger and bettcr telescopesare being built, however, so thc rangeat rvhich Ccphcidscan bc discernedincreases.
{u E2 ) v ot (s tr J c o $
or, o
5.5 01 'rItiR P Rt M A|TY I NDI CA' |' O RS Novac arc thought to be close binary star systemsin rvhich one of the componentsis a rvhite drvarf star. l'lre othcr componentis a giant star rvhich has grown so large that the gravityof the white dwarf can strip off its outerlaycrsof hydrogen.'fhisgasspiralsdown onto the white dwarland buildsup on its surfacc.Whensufficientmaterialbuildsup, the gravity of the white dwarf can causethermonuclcardetonationof the hydrogen,resulting in a hugc brighteningol'the systcnr,observedas a nova. On tlreoreticalgroundsit is thoughtthat betrveenten and forty novae occur within the Milky Way every year. Only two or three of these are observedfrom Earth, however, becauscthe othersare obscuredby thc vastquantitiesofinterstellardust and gasrvhichare locatedwitlrin our Calaxy.Novae appearto be fairly standardoutburstsand can be charactcrised by a generic light curve. 'l-lreprincipal leaturesappearto be a very rapid rise in brightnessby eight to ten nragnitudes.After a short pause,the briglrtnessrises againby a lcw magnitudes and thenbeginsto lade(seeFig. 5.3). 'l'ypically,the peakabsoluternagnitudeof a nova is -8, and a reasonablvpreciseempirical relationshipexistsbetrveenthe peak absolutcuragnitude,M", and the tirne taken for thc novato declineby thrcenlagnitudes, t:
Mu =-ll+2logt
(s.l 2)
This relationshipis what allows novaeto be usedas standardcandlesand have their distancernodulicalculated. Other prinrary indicatorsincludenralchingthc spcctraltypesofstars in distantgalaxies rvitlr thosc in our own Calaxy. Sanrplinga rarrgeof starsfor their spectraltypes can allow thc construction diagranrfor the distantgalaxy.The main seqof a I lertzsprung-Russell ucncc rvill be presentbut at dimnrcr magnitudesthan tlre correspondingdiagram for our Cialaxy.By analysingthis diffcrcncc,a lurninosityclistanceto tlre galaxy can be determined.
10
70 60 50 +u 40 30 3u 20 zn day s ) 10 (i n of i nterv al s Ti me from max i mum
patternsof outburst The observedlight curve Fie. 5.3. Novae generallyfollow rather similar analysisof manyothernovalight curves o r,uiirti."l *iitr ii, ."r.,""".n u?-"r"a i'r,?.*i"r" ".distance' and luminosity to calculate
t' t t t t t t t t
5.6 SECONDARYINDICATORS whichrelyon beingcaliarethoseobjectsandmethods indicators distance Thesecondary clusteris determglobular a to distance ifihe bratedby a primaryi"oi""t"i. r.i "*ampl", i nedbyexam inat io|lof anRRLyr aest ar , apr im ar yindicat or , t hewholeglobu|ar c|ust er canthenbe usedasasecondar ydist anceindicat or . Thiswou|dinvot vecom par ingit s distantgalaxy' pr"p.ni"t with a globularclusteiaroundan evenmore nebulaewhicharepro- emission regions H n are inJicators airtun"" other secondary of theHcremisluminosity The nebula. ducedby starformationr"gioni*"6 astheorion candles,or their standard into objects tliese transform to sionline at 656 nm canbe"usej rulers' canbe usedto makethemstandard diameters
i
5.7 SUPERNOVAE
t t
sobrightthattheyarevisibleon all cclestialscalcs' arecelestialcatastrophes, supernovae i .e.fromclosebyt oa|m ost t helim it so|t heobser vableUniver se. Theyar e, t her ef or c, havc (seeFig' 5'4)' Two typesof supemova veryimportantJi,iunt" indicators potentially beeni den t if ied. TypeI super novaear et hought t ooccur inst ellar syst em sof sim ilar co
L L j
I
'll 1l t1
1r I
Itr
9li
- l ' h cc o s r n o lo g icadl isl:r n cc la r klcr
l ch.5
llgttratlonto the oneswhichcausen.v;rc. Ir.rthesecascs.theaccretingwhite dwart-collects so rruch nratcriarthat it uncrcrgocs gravitational coilapse.-fhis producesan almightysteil_ ar explosion,ripping the renrainsof the white dwarf to pieces,which we observeas the supcrnova"r'hesesupernovaecan be rurther subdividedinto three categories. ofthese, orlly supernovaetype Ia arc really useful lbr distancecletermination becausethe other two
1l ll 1i 1 I
l ,( I
Sec.5.8l
The Tully-Fisher relationship 99
types,b and c, display irregularitiesin their light curvesand spectra.They are also fainter and rarer. The reasonthat these supernovaehave a sharply defined peak absolutemagnitude is becausethe mass limit for gravitational collapse is sharply defined. It is a quantity in astrophysicsknown as the Chandrasekharlimit and is defined by the value 1.4 solar masses.Beyond this limit, the atomic structureof matterbreaksdown and objectsbecome compactedballs of neutrons.As this collapseproceeds,nuclear reactionsoccur because of the vast amounts of energy liberated by the process.Thus, every supemova type Ia has beenprecipitatedby the collapseof a white dwarf of mass 1.4 times that of the Sun. Typically, a supernovatype Ia reachesa peak absolutemagnitudeof -19, the rise to maximum proceedingat a rate of 0.25 to 0.5 magnitudesper day. After a week or so at maximum brightness,the decline in brightnessbegins.This occursat a rate of one magnitude per week to start with, but soon slows down to just one magnitude every ten weeks. As well as providing excellent standard candles,supernovaecan be used as standard rulers.The explosionproducesan expandingenvelopeofluminous, gaseousmatter which can be studied spectroscopicallyto determine its expansionvelocity from the Doppler shift of its spectral lines. The angular expansionof the supemova remnant can also be measuredand trigonometryemployedto give a distance. A 1996 result from the Hubble SpaceTelescopehas boostedconfidencein the use of supernovaela as secondaryindicatorsof distance.A team of astronomers,led by Allan SandageofCarnegie Observatories,usedthe superiorresolutionofthe HST to identify a number of Cepheid variable stars in the galaxy NGC 4639. They chose this particular galaxy, which is locatedin the Virgo cluster,becausein 1990 a supemovaof type la was observedthere. The Cepheid variable starsyielded a distanceof some 78 million light years,which is in good agreementwith the distancecalculatedfrom the supemova. The secondtype ofsupernova occurswhen massivestarsuse up their supply ofnuclear fuel and collapse.In the heartsof starsgreaterthan eight times the mass of the Sun, the nuclearfurnacesare so intensethat all ofthe chemicalelementsup to iron can be synthesized. ln the smaller massstarsthis processlargely finishes once helium has been transmuted into carbon. Iron is a very stable element which is very difficult to fuse, and it builds up as an inert core in the centre of the star. When it reachesthe Chandrasekhar limit, the atomic structureof the iron breaksdown and the star collapses.Just as in a type I, this causesa supemovaexplosion. Although thesetype II supernovaecan be used to calculatedistancesthere is a much bigger spread in their peak luminosities.This is bccausethe massof the progenitorstar is usually unknown and henceestimationmust come into play.
5.8 THE TULLY-FISHER RELATIONSHIP
*ll
l ' i g . 5 . 4 . . Su p cn r ocxp va lo sio n in th c.g r la xyN( ;C 4 7 25.In thc tow erphotograph. takenon 2 ' r a n u a r y | 9 4 | ,th csu p cr n o va ( a n o wctr ) iscr e a r r 'vi si brc,rvhi i .'i ,,,rr,.upp.,ptrotograph,takenon I 0 May I 940.it is invisiblc.(photograph ,"pro,1u."a pulonlar Mount Observatorv. ) "uur,"..rinil
This is a rather novel approach to distancedeterminationwhich links two observable propertiesofthe galaxy in question.The first property is the apparentmagnitudeofthe galaxy.This property is obviously dependentupon the distanceto the galaxy, and its measurementcan be made at optical wavelengthsor in the infrared.The latter is often better becausethe extinction in the light causedby the intergalacticmedium is not so great.
L 100 'l'hccosrnologicnl distnnccladrlcr
lch. 5
S ec.5.9l
' l ' c rti arY i ndi c ators and grav i tati onal l ens es l 0l
Sccondly,a way to calculatethegalaxy'sintrinsicltrrrrinosity mustbe found.This is where thc secondobservationcomes inlo play. Using racliotelescopesthe galaxy is observed with the intentionof detectingits intelstellarmediurn.This is observedby measuringthe 2l-crl enrissionline of molecular hydrogen. As the galaxy rotates,so tlre hydrogen clouds'cmissionsare Dopplershifted.This createsa broadeningofthe line becausethe variousrnotionsof the individual cloudsare in many diiferent directions.Thus, the aim of tlris measurementis to determinejust how broad the line has becomebecauseof the rotation of the galaxy.This allows an estinlateof the galaxy's massto be made,which in tum allows a figure for the intrinsic luminosity of the galaxy to be calculated.Some measure of the galaxy'sinclinationto our line of sight must also be madeso that a correctionfactor can be applied.Once the value for the luminosityis calculated,the luminosity distanceof the galaxycan be determined. 5.9 TER'TIARY INDICATORS AND GRAVITATIONAL
LENSES
This final type ofdistance indicatorrelieson comparisonofthe global propertiesofgalaxies, one of which will have had its distancedeterminedby a secondaryindicator.For example,the largestgalaxy in a clusternray be used as a standardruler. This assumesthat the lalgestgalaxy in a more distant clusterwill be of equal extent and thus both can be directly compared.As well as using whole galaxiesas standardrulers,the brightestgalaxics in clusterscan be usedas standardcandles.once again,similar typesof assumptionarc neededto lacilitatethe useofthis ntethod. Anothel tertiary indicator is the lurninosityclassificationof spiral galaxiesby the appearanceof their spiral arms. A class I object will have the brightest,most regular and rvell-definedstructureto its spiral arms,whereasa class V object will be conrpletelythe opposite.As wg-:rhallsee later in this chapter,the applicabilityof some spiral galaxiesas standardcandleshas beencalled into question. Finally, one of the most prornisingnew distancedeterminationmethodsrelies on the monitoring of gravitationallenses.Theseare fascinatingobjects in which the irnageof a distantquasarhasbeendistortedbecauseit has interactedwith the gravitationalfield ofan interveninggalaxy.According to the quantumtheory, a photon,travelling at the speedof light, will display the propertyof rnonrentum.Thus, in someway or anotherit behavesas if it possessesa mass and should tlrereforebe influencedby a gravitational field. This shouldnot be a surprisereally,.because of Einstein'sequation(1.2) which he derivedas part of his special theory of relativity. In fact, the bcnding of light in the presenceof a gravitationalfield was provento be exactly as Einstein'sgeneralrelativity predicted,during the total solareclipseof 1917.During this eventastronomers measuredthe precise positionsofstars closeto the Sun and found that they had indeedshiftedtheir positionsby the amount predictedif the Sun's glavitational field was altering the paths of their ph oto ns. Thereare a numberof exarnplesof doublequasarswhich,as well as being physically closc togcther,also show exactlythc samespectrum.'fhe first of thesewas lbund in 1979 by a team of astronomersled by D. walsh. The reasonfor multiple inragesof thc same cluasaris that somewhere,betwecnus and it, is an intcrveninggalaxy. In some casesthe galaxy is so faint that it cannoteven be seen.Instead,its existenceis intimatedby the fact
ul arex :tpl t-l l l l :i :1:i t"^l Fi g 5.5 .Thi s i nrageofthc ri c hgal ax v c l us tc rA bc l l 22l S i s as pec tacrays passing throtrgh dencctslight lt;'il ;iihi; ruiriu. .urp^.t .lu_stc; Thegravitarionat tcnsirrg. lcnsing thc bcyond far lic .thc proccssmagnifics.il;hi;;;';J;i.,'rrs rhat imagcsof obiects ir. wcb' arethc distortedimagcsof clustcr.'l hc thln arcs',pr"nO-*'o" thc picttllc likc-a spideis (Photograph-reproll::{9o,yn"tv iluster' the than i*"v iittt-iutrt'"t s-io ;;;;ir*i i"i".i"t University,andNASA"/Space Cambridge of w. Crouch,universityoiNew soutttwut"l. R. Ellis, Institute.) Science TelescoPe
L
t t t t t t t t t t t t
a multiplequasarimage.The numberof imagesandthe relative that it hasconstructed alignmentbetweenus (theobuponthe precision^ofthe U.igttn"r, ofthem is dependent then arein prefectalignment three quasar. Ifall distant the and seriers;,thelensinggalaxy alignment If the ring'' ii" quuro,imug"*Illbe distonedintoa ring,knownasan'Einstein galaxy(seeFig' 5'5)' p.rr." a nu*b"r of distortedimageswill sunoundthelensing i, is to thinkof thc formed are ""'i images multiple The bestway in whichto understandwhy the Unithrough radially wavefrontswhichpropagate quasaremittin! tigtt in spherical verse' A ta cer t aindist anceonit sjour neyt hr oughspace, par t of t hewavef r ont ent er st to wavesin waterslowingdownwhen field of a galaxy.In a way analogous gravitational ofa gravitational in thepresence down slow photons the so watei, shallow theyencounter movingthrough wavefront quasar In thecaseofthe n.tC 1a,viewedby outsideobserversi. .r.l"gutu*v,theclosertothegalacticcentreitpasses,thedeeperintothegravitationa|we will becomedefornled' it will travelandthe stoweiit will become.ihus, the wavefront galaxyhavingbecn the of extremities the through travelled have which *i,h ,ho.. parts directedfromtheiroriginalpaths' A sthewavef r ont |eavest heinf luenceof t hegalaxyit isno|onger pr opagat lng|na total l yradialm anner . lnst ead, par t sof it havea€om ponent of m ot ionwlr ichhasbeen ofthe wavefront segments fieid ofthe galaxy,andthiscauses causedby thegravitational hitsotrr segment each as and, Earth the from to fold over.when thewavefrontis observed
102 'l'hccosrnologicul
[Ch.5
eycs/detcclors, so a dilforcntirnagcof'the quasal.ispcrceived.The imageslie in slightly dil-ferentclircctionsbccausethe individualwavefrontshit us at slightly differentanglesand our brainsextrapolatcwhat we havejust seento lie in a directior-r which is perpendicular to the wavcfront (seeFig. 5.6).
lm age
*
Ouasar
*
l m age B
t(
l m age C
and the Malmquist bias Problems in distance determination
Sec.5.l0l
103
obviouslythefoldingofthewavefrontmeansthatdifferentsectionsarriveatslightly each ba monitoredand the time taken for differenttimes.tf a changelJ;q;;;.an i magetoresp ondt ot r , is"nung", t hedist ancebet weent hewavef r ontpropersegm ent scanbe system's of thelensing Thiscanttrenuecoririn.a *i,t otherestimates calculated. to boththe galaxyandthe lensedquasar' to obtaindistances G-i" it "J.t this methodsiiit requir"san esiimateto be madeaboutcertainproperties, Although important potentially a therefore is tt candleo.u rtunjurarulertechnique. is nota standard distanceobtainedby the morestandardmethods' corroborating onefor AND THE MALMQUIST 5.10 PROBLEMSIN DISTANCEDETERMINATION BIAS when estimatingthe distanceto celestial*/*"tl; Thereare manyproblemsto consider Thezeropoint er r or isam ist akem adeint hedet er m inat ionof t hedist ancet andoapr lm ar y distanceladderthroughuseof secondary indicator.This error is propagatedup the thentertiaryindicators. A c tual behav i our Magni tude Thes e obi ec ts are not detected
W av efr ont fol ds i n on i ts el f
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Obser ver sees an image pr ojected at r ight angl es fr om each wavefront portion
Fig. 5.6. The principle ofa gravitational lcns s),stenr.shorving the origin ofthe nrultiple irnages causedlry thc distortion iil thc quasar'srvave front.
D i s tanc e A tl argerand Fi e.5 .?.TheMal nl qui s tbi as l s ac ommondi s torti oni n-theus eofsthe tandardc andl es fainter population because reduces candles laiser distancesthe number "'b;;;;;"t;nt luminositvdistances' calculated the "f in oi.t.rtion ,ir",r"... rni, ;:ffi;;;;;;;il;i".','Jr.. ^
104 l'lrecosntological rlistnncc latldr:r
lch. 5
'l'hc cxtinction suffbrcdby standat.cl candlcsin ealaxieswill alsocauseillaccuracies to be prcscntin the calcrrlatcd distanoe. l'.xtinctionr.r,illoccurbecause of the irrterstellar rnatter r'vithinthe galaxycontainingthe ob.iect.It rvill also be causedby intergalactic matter and interstellarmatterwithin the Milky way.'l'hose objectswhich are viervedat high galacticlatitudes, i.e.out of the planeoFtheMilky way, will sufrerlessfrornthis problern, althoughthey will still be subjectto extinction from intergalacticmatter and dust within theirhostgalaxies. Even if extillction rvere non-cxistentthere rn,oulclstill be no such thine as a oerl-ect starrdard candle.Althoughthis chapterquotesscveralpeakabsolutemagniiudesfor various different celestialob.lects,tlreseare orrly avcragemagnihrdes.Each and every one of thern is capableof possessinga value for its absoluterrragnitucle which can vary liorn this nreatrvalue. This rangeol valrresis known as thc clispersion.In more and rnore distant galaxicsit will be easierand easielto detecttlrosestandardcandleswhich have luminosities towardsthe high end ofthe intrinsicdispersion.Tlris, obviously,causeserrorsto creep into the distancedeternrirration. Being able to dctect only the brightestobjects in distant galaxies- the Malnrquistbias- can leadto the distanceofthese objectsbeing underestintate d(se eF ig. 5. 7) .
5.I1 CALI BRATI NG TI { E I I EDSI { I F' T SC A I , E As we haveseenin chapterl, all galaxiesand othcr extragalacticobjects,apart from lhose in the Local Group, are subjectedto the expansionofthe Universe.This ciuses a redshift to be inrpartedupon the spectraofthese objects.It hasbeenestablishedthat, in sorneway, the distarrceof the galaxy is linked to its redshift.'l-heHubble law (1.4), proposesthat this linking is simply a linear relationship.Thus, a galaxy which exhibitstwice ihe redshift of anotheris twice as far away.In order to calibratetlrc relationship,a constantis needed;the I'lubbleconstant.The value ofthis is calculatedby rneasuringthe distanceto a galaxy by one of the rnethodsdescribedabovc and then eqrratingthis with its redshift measurement. Although this soundsvcry easyin principle, in lrracticeit is far from clear cut. Errors and approxitnationshave crept into the cosnrologicalclistanceladder so that the value ofthe Hubble constantis currentlyuncertainby a factor oftwo. The generalconsensusofastronomical wisdom p.lacesthe value of the Hubble constantat somewherebetween50 and 100km/s/Mpc. It is interestingto note that rvhendetermiuingtlre Hubble constant,astronomersseem to fall into one of two canrps.The rivahy beganin I 976 at an internationalcolloquium on 'Redshilland the Expansionofthe Universe'.Gelardde vaucouleurspresented a value for the Flubbleconstantof approxinrately50 knr/s/Mpc,whilst G.A. Tammannand Allan sandagcpresentedthe result of their combineclstudy which was approximately100 km/s/Mpc. Interestinglyenouglr,the passageof tu,entyyearshas done little to narrow the gap betweenthesetwo opposingestinrates, which havebecomeknown as the .lons scale' and thc 'shorlscale'. The reasolilbr thesenanresis as {bllows. The I lubble constant,with its peculiardimensions of kilometresper secondper nlegaparsec,rvill actually simplify to a value which possesses the dirnensionsof inversetime (s-'). Thus, if the reciprocalof the I{ubble con_ stantis taken,a time is obtained.As ivill be shorvrrin chapter9, this tinre is aitually an
Sec.5.lll
Crlibratingthe redshiftscale 105
conupper estimatefor the age o[ the tjnivcrsc and is called the Hubble time. A Hubble the siantof 50 krn/s/Mpc gives a I'lubbletinre of approximately20 billion years.Doubling Hubble to the reference Hubble constanthalvei tlris time to l0 billion years.It is therefore scale'. time that leads to high estimatesof the ttubble constantbeing termed the 'short Similarly, low estimatesare collectivelytermed the 'long scale'' An interestingpoint to note about those rival astronomerswho estimatethe Hubble constantis that,lnmany instances,they can analyseexactly the same observationaldata but still arrive at these different estimates.The only real difference has been in the assumptions they have made about the validity of the data and the way in which they have estimatedits inherenterrors. Short scale estimatespresenta real problem for cosmology becausetheir associatedHubble time is less than the estimatedage of the oldest stars in globular clusters. Many astronomersfeel comfortable using a value for the Hubble constant of about 7S km/s/Mpc. They often feel that becausesome working methods inherently provide high estimatesof the Hubble constantand, likewise, that some others provide low estimates, that a statistical averagebetween the two is necessary. Other astronOmers,however, remain finnly rooted in either the long or short scale camps becauseof a deep conviction that the other method is incorrect' The biggestproblem in calibratingthe redshift scaleis that we are observinga moving object from a moving platform. lmagine a galaxy coming under scrutiny from an astronomeron Earth. As well as the cosmologicalredshift impartedon the galaxy in question line by the expansionofspace, any motion ofthe Earth or the galaxy along the observer's cosmological the diminish or enhance will either which oi sight will causea Doppler shift redshift. Considerthe Earth.Not only is it rotatingbut it is also in orbit aroundthe Sun. The Sun is in orbit around the centreof the Galaxy and the Galaxy is in orbit around the centreo[ gravmassof the Local Group, The Local Group itself is being influencedto move by the to angle precise right at a is ity of the largest galaxy clusters around it. Unless the Galaxy introduced' will be redshift its in change som€ is moving, Earth the direction in which the cosmic miso astronomersare hardly in an ideal situation (see Fig. l.l0)' Luckily, the moEarth's the of all crowave backgroundradiation comesto our aid. The combination a dipoas background microwave ofthe our observations tions through spaceshowsup in milar anisotropy causedby the Doppler effect. In other words, the frequency of the an crowaves is increasedslightly in the overall direction of the Earth's motion' Thus, background, microwave cosmic to the estimate of the Earth's true velocity, with reference can be calculated. It is far harder to determinethe peculiar motion of the galaxy being studied' Not all regionsof spaceare expandingin accordancewith the Hubble flow. Certain placesin our Universecontain so much matterthat they createa gravitationalfield which is sufficiently strongto resistthe expansionofspace. Theseplacesare known as clusters,or the slightly is in smalGrgroups,of galaxies.Within thescassociations,eachof the individual galaxies to are said galaxies where cluster the of orbit around the centre of mass.Near the centre galaxindividual the possessed by velocities well, the gravitational be deep in the cluster's perfectly ies can be large - somitimes enough to significantly alter their redshifts. A constituent its of redshifts if the sphericatclusfir will actually look like a skewedellipse galaxiesare plottedon a graph (seeFig. 5.8).
t t t t t t t t t t t t
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A.lso,sntallerclustcrsarc movcdbv thegravitvof lalgerol1cs,a phenolltenon known as strcalnitlg.'l'hese, oftcn largc,rrrotionshavconly lcally cometo light in recentyearsand arc a significantheadachcfcrrcosnrologists. In chapter3 the scaleupon which the cosmologicalprinciplecould be applicdwas statedto bc hundredsof nrillionsof light years.On anythinglessthan this scalethe distributionof nratterin the Universeis unevenand Irunpy.'I'lrus,lcssdenseregionsrvill bc attractedh1,thegravityofoverly densepartsand stlcanringwill occur'. Only largescalenrappingpro.jects suchasthoscrvhichintendto usemultiplefibre optic sl)cctrorncters - for examplethe 2' field at the Anglo-Australian Telescopeor the SLOAN l)igitill Sky Survey- will makeheadwayin mappingthe three-dimensional distributionof f,,nlaxicsthroughoutthe Universe.Once a map of the cosmoshas been obtaineda better I'cr:linglor the largescalestreamingmotionswill be forthcomingtoo. At tlrc tirnc of writing, the nrost interestingproject concernedwith the cosmological tlistnnccladderis takingplaceusingthe HubbleSpaceTelescope. A key projecthas,as its tlrc lask of refiningthc accuracyof the tlubble constantto within l0 per cent of its 11onl, itclttitlvitlttc.-['othis enda teamof overtwentyintcrnational astronomers hasbeensurveyirrggalnxicsin both the Virgo clustcr and the Fornaxcluster.Both clustersare at approxinrirlclyllrc sarnedistancebut in diffcrentdirections.Virgo is a very large clusterand Itcttccthc rcdshift distortionssuff-ercdby its constitucntsare potentiallylarge. Fornax,on lhc othcr hand,is much more compactand shoulddisplayredshiftswhich are in better itgrccnlclltbetweenthe individual galaxies.The otheradvantage ofstudyingthe hvo clusters in parallclis that,sirrcethey are in differentpartsofrhe sky,hencedifferentregionsofthe IJnivcrsc.largescalestreanringrnotionsfelt by onc may not necessarilyaffect the other. 'l'hc invcstigatingtearr has been deriving valucs of the l-tubbleconstantrvhich fall in tltc rangcof 68 to 78 krn/s/Mpc.Bcforethis chapteflcavesthe readerwith the impression thata conscnsus is linally beingreachcd,it is well rvorthnotingthat anotherindependent invcstigation,undertakenby astronomcrsusingthe I'lubblespace Telescopeand reported .justtwo n'ronthsprior to the abovestudy,resultedin a derivedvalue ofjust 57 km/s/Mpc. 'I'lrccorrtr'oversy ragcson. 5.I2 IS 1 'I I E REDSI I I F' I ' CO SM O LO G I CA L ? Ottr ntoclcrnview of the cosrlos dependscrucially on one bold assumption:that the redshilt displaycdby distantcelestialobjectsis causedpredominantly by the expansionofthe lJnivcrsc.'lhis chaptcrhas alreadydiscussed the confusioncausedby the motion ofthe galaxy through its parentcluster,rvlrich impartsan additionalDoppler shift on its radiation. Sorncastrononlcrs believethat theremay be an entirelynew mechanismwhich can ciltlscil rcdshifl. Although lheseastronomersare in a ninority at present,that single fact irlorrccirnlrolbc uscdto dismisstheir theories. 'l'lrctlrcstionof whetheror not the redshift is solclydependentupon the cosmological r:xpnnsiorr ol'space,restswith eitherprovingor disprovingthe Hubblelaw (equation1.4). 'l'hcrcis a ntountingbody of evidenceagainstthis sitnplelinearrelationship, which must bc cxltllincd within the franreworkof the conventional theoryor it will eventuallytopple ctrtlcnt bcliclls.To sotncit hasalreadydonethis,ancltheyarealreadyworking on altcrnalivcs to lhc cxpandingUniversenroclel.
Is the reds hi ft c os mol ogi c al ? 107
S ec.5. l 2l
l n a l r a t t em p tto i l l u str a te th e p r o b l e r r r sw ]ti ch sti l l fa ce th e H u b b l e i a n p'flies r o p o nine the n tso fa n describea few of the most well-known expandingUniverse,illi, ,."ii"ri*ill that, althoughthere are a number of astronomers cosmic ointment,.It is *o,ti *.ntioning whicli castdoubt upon the expandingUniwho have worked on our"*uiion, uno ti-'.ori", He is a Arp's name which continually arises' verse and Big Bang theories,it is Halton is no this that stressed be must it viewpoint, but tirelessdissenterfrom tne'ionventional o n e . m a n c ru sa d e w h i ch i sb e i n g r e p o r te
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havebeenidentified:M32, Mi3, NGC 205 ancr Ncc l g5, all of which are redshiftecrwith respectto the Andrornedagaraxy.It shourdbe notedherethat the Andromedagaraxyitself shows a blueshift' This is becauseit is being gravitationally attractedtoward"sthe Milky way. Thus, when we talk about the companlo"ngaraxies being redshiftedwith respectto it, we actually meanthat they are lessblulshiftedl lfthese com-panions are in orbit around the central galaxy, we would expect some to be brueshiftedln relation to it. The only conventionalexpranationfor the observationthat they are not blueshiftedis that the galax_ ies surroundingthe Andromeda.garaxy_are ail movini in their respectiveorbits away from us' This would be a rargecoincidencebut certainry riot an outrageousone. The samepar_ tem ofdiscrepant redshifts-areobservedto repeat, however,in other garaxysystems,notably for the companiongalaxiesto Mg l. The leadingadvocateofthis resurt,Halton Arp, hasgone further. He has even incruded all galaxiessmallerthan the dominantone from tile clusterin the analysis.His work on the Local Group and the M8r group certainly appears to show that the smaller garaxiesin thesegroupsdisprayrargerredshiftsthan t-hedominant garaxyof the group.
Sec.5.| 2l
Is the redshift cosmological?
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l'akenat facevalue,thisresultwouldseemto indicatethata proportionofthe redshift too, thatthe Hubbletype ma\ ofa galaxyis dependent uponits size.Thereis evidence, of spiralgalaxiessplit thcrrr alsoinfluencea galaxy'sredshift.The Hubbleclassihcation into threesubgroups. They wereclassedaccordingto the sizetheir nucleiappearedto br' andhow tight their spiral armswerewound.Of the threetypes,the Sc galaxieswere th(' generations ol oneswith the smallestnucleiandthe mostlooselywoundarms.Successive astronomers havemadea new distinctionwithin this group:that of Sc I galaxies.Thcsr' are galaxieswhich areundeniablySc in nature,but havespiral armswhich arenarrowcr andbetterdefined. The problemwith thesegalaxiesis that, if their lineardiametersare calculated,bascrl upon their angulardiametersand their redshiftdistances,they becomelargerand largcr with increasingredshift.It wouldappearthatif redshiftis a totally reliabledistanceindicl tor thenthe Sc I galaxiesat earlierepochswerebiggerthanthe cunentexamples.In fact the problemcan be so severethat, if the redshiftdistanceof Sc I galaxy NGC 309 i' correct,thenit totally dwarfsthe Sb galaxyM8l (seeFig. 5.10).Conversely,basedupol examplesin the presentday Universe,the generalrule is that Sb galaxiesare largerthar, Sc I galaxies. In an attemptto corroboratethe redshiftdistancesof Sc I galaxies,Halton Arp an,' David Block usedthe Tully-Fisherrelationship,presented earlierin this chapter,to calcrr latethedistances to a representative sampleofSc andSc I galaxies. In the caseofthe S, galaxies, bothdistance determination methods werein goodagreement. The Sc I galaxi,' wereanotherstory.TheTully-Fisherdistances l, weresmallerthantheredshiftdistanccs llr' up to 100millionlightyears!As a final pieceof evidence, theastronomers calculated rateat which supernovae shouldbe observedin NGC 309, if it is indeedat its redshil distanceand henceits calculatedgargantuansize,Basedupon supemovarates in lot:" galaxies,NGC 309 shoulddisplayone ofthese celestialcatastrophes everythreeyear: That is simplynot observed,andthe mysteryof the Sc I galaxiescontinues. Perhapsthe explanationis somehowtied up with a documentedbut largely ignor<', observationwhich hasits originsin | 9l l. W.W. Campbellnoticedthatyoung,high ma' stars appearedto have higher redshifts than were expected.This is known as tlr K-Trumpler effect and hasbeenconfirmedby subsequent observationsin more reccr' decades with moresophisticated equipment.An explanationfor it, however,hasnot bc, forthcoming. Ever sincethe discoveryof quasars,which will be discussedin moredetail in the lirl owing chapter,their naturehasbeendebated.As far astheir part in the battleto provc , disprovethe Hubbleexpansionis concerned, everythingrestson their redshift.HaltonA, conducted a surveyofmanypeculiargalaxiesanddiscovered thata numberofthem ayl earto showconnections betweenobjectswith very differentredshifts. Arp's imageof NGC 43l9 andMarkarian205(seeFig. 5.I I in coloursectionbetwc' pagesI 14 and I I 5) may be the most importantcosmologicalimageof the century,or rankingeventhe celebrated HubbleDeepField! The imageshowsthatthedisturbedspir galaxyNGC 4319 is apparentlyconnectedto the quasar-likeobject Markarian205 b1 luminousbridgeof matter.The conflictoccursbecausea spectrumtakenby DanielWct' man showedthat the recessional velocityof the quasar,basedupon its redshift,rr 2 I ,000km/s,asexpected for a quasar. The galaxy,however,only possesses a recessior velocityof I ,700km/s.Againthis is asexpected, buthow canthetwo thenbejoinedl''
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Fig 5 9 The Andronreda caraxv,M3 r, is the ncarcstspirargaraxyto us. stuaics of its satelite galaxiesshorvthat at ofihem-n.sscssa.rerativery rrrg.i-rEJrrtin."nrponentthan thc parent galaxy.This is curious.bccausc ihc garaxies arc l;;; orbiraroundMJ I anrJshourd thereforcdispraya sprca
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Sec.5.l3l
Other cosmological theories
III
bridge of material?Currently,there is no solution to this problem. It hangslike the sword of Damoclesover the Hubble law. Strangerstill is that nobody appearsto be working on follow-up investigations.Surely the reportedbridge is a prime candidatefor imaging with the superioroptics of the Hubble SpaceTelescope. There are other reported links betweengalaxiesand quasars.Some astronomersalso claim that quasarsappearto be found aroundgalaxiesmore often than statisticsclaim they should. At presentthe debateon this is ongoing and so far inconclusive.Some feel that gravitationallensingby starsin the outer reachesofgalaxies may account for a brightening ofdistant, faint quasars.Scepticsdo not feel there are enoughfaint quasars!Statistics can also be usedto show that, ifthey are assumedto be chancealignments,far too many pairs of quasarswith different redshifts are observed,based upon the total number of quasarsknown to exist. Some take this to mean that the quasarpairs must be physically associated,henceat the samedistance,and that their different redshiftscannotbe used as good indicatorsofthat distance. There is also evidencethat perhapsthe redshiftsofgalaxies are not a smoothly continuous distribution as is indicatedby the Hubble law. Data championedby William Tifft of the University of Arizona has shown signs that redshiftscan exist only at certain values. This is very like the energy conditionswhich have to be satisfiedby electronsin atomic orbits and has becomeknown as the quantisedredshifthypothesis.lt is not to be confused with the phenomenonof periodic redshift which is shown in data taken from pencil beam surveys.In these, a tiny area of sky is studied to great depth so that the distribution of galaxiescan be seenfrom their spreadofredshifts. lt has beenfound that galaxiesfall into redshift groups approximately separatedby 400 million light years of virtually empty void and superclusterstructureof space!This has been ascribedto the three-dirnensional the Universeat large.The periodic natureofthe redshift correspondsto the survey piercing the galaxy-filled front and back walls of the voids. There is still a lot which needsto be understoodbefore astronomerscan say that the Hubble flow has been proved beyond doubt. Although the Big Bang is still the theory of choice, it is important that the seriousstudentof cosmology should be aware that other theoriesexist.
N 1
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l ch.5
5.I3 OTHER COSMOLOGICAL THEORIES To finish offour section on scepticismofthe currently acceptedmodel rve shall briefly discusstwo competingcosmologicaltheories.The first is known as chronometriccosmology and was proposedby I.E. Segalof the Massachusetts Instituteof Technology.It posits a non-expandingUniverse,which will be discussedin more detail in chapter9. Chronometric cosmologypredictsa quadraticequationfor redshift versusdistancesimilar to the 1925 equationwhich K. Lundmark suggestedcould explain the apparentvelocity, v, displayed by galaxiesat a distance,d: v = A + H d + Bd 2 ljig 5 l0 ll'thescl-typegalaxvN(ic 309 is at its rctlshilidistanccrr rsoneo{.thelargestgalaxics rn tlrc l,niverse.ri wouldcomorcrcly
( 5 r.3 )
whereA and B are constantsand H is the traditionalHubble constant.Segaland a collaborator, J.F. Nicoll, showed that the change in magnitude with redshift displayed by the IRAS galaxies(seethe next chapter)was betterfittedwith a Lundmarkrelationship(5.13) t h a nt h e l l u b b l e l a w ( 1 .4 ) .
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It is the assertionof clrronometriccosmologythat the Universeis curved.A fundamental constantrepresentsthe curvationfactor in the sameway that the speedof light delineatesthe relativistic regime and the Planck constant defines the quantum realm. This new constant is a length of | 60 million parsecs* 25 per cent. Light is redshifted becauseit is travelling through a curved spacetime continuum, and the further away the galaxy, the longer distancethe light has had to travel and so the more redshifted it will be. Hence, the redshiftcan'still be usedto measuredistance,but using equation(5. I 3) insteadof ( I .a). Plasmac6*nology is even more removed from the Big Bang theory. Instead of gravity being the dominant force in the Universe, the plasma enthusiastspostulate that it is the electromagneticforce which is dominant. A plasrna is a gas which is usually in a completely ionised state at high temperature. It can also be a partially ionised gas at a much lower temperafure.A good analogy to a plasma is that of a metal at room temperafure. In a metal, conducting electronsare free to wander around the fixed lattice of atomic nuclei. In a plasma,the situationwith the conductingelectronsis the sameand the atomic nuclei are also free to move about. Thus, thanksto the mobility of its electrons,a plasma is an excellentconductorof electricity.When it interactswith a magneticfield, large quantities ofthese electronsspiral aroundthe field lines,causinga currentto flow. Theseare known as Birkeland currents after the Norwegian scientist Kristian Birkeland, who performed a lot of the researchinto plasmasupon which the plasma cosmological theory is based. Birkeland currents flowing between Jupiter and its moon Io were discovered by the Voyager spaceprobe in 1979. In 1985the first galacticBirkeland cunents were discovered by FarhadYusef-Zadehand his collaborators whilst using the Very Large Array radio telescopeto observenearthe centreofour Galaxy.The Birkeland currentthey discovered is approximately 120 light years long but only 3 light years wide. It is composedof a plethora of narrow filaments and is associatedwith a magnetic field one hundred times the strengthpreviouslythoughtpossibleon sucha largescale. Using this as their starting point, plasma cosmologistshave shown that two typical interacting galactic Birkeland currents can give off energy which is almost equivalent in power to the radio galaxies (discussedin the next chapter). This may be significant becausethejets in radio galaxiesare luminousdue to synchrotronradiationwhich is caused by electronsspiralling aroundmagneticfield lines, i.e. synchrotronradiation is given out every time a Birkeland curent flows. If two plasma clouds are simulated to interact with one another,double radio lobes are produced which look remarkably like radio lobes from activegalaxies. The cosmic microwave backgroundalso has a plasma explanation as computed by William Peterand Eric Lerner. They looked at rvhathappensto the radiation releasedby the plasmaclouds in randomdirectionsthroughoutthe Universe.Their resultsshow that, underthe right conditions,which may or may not be possiblein the Universeat large,the radiation would possessa black body spectrum apparently coming from a thermal source of just below 3 K. This is a preity good description of the cosmic microwave background! Any plasmamust havepropertieswhich differ from regionto region.Theseregionsare separatedby transition zones.Some of the bolder plasma cosmologistsare preparedto think that theseregionscan extendto larger and largerscalesrPerhapsthey are even the reasonwhy the Universeis honeycornbedwith srrperclusters aroundgiant voids"
Sec.5"I 3l
Other cosmotogicaltheories
I l3
which In the plasmaview of the Universe,redshiftsare a resultof the wolf effect lower a much to down light of emitted the frequency occursin plasmacloudsand'drags' not will these but 'l"hus, redshifts, will exhibit galaxies at naturall/. be would levelthanit taking plasma reactions the about ofdistance:ratheriheywill provideclues be indicators to havemanaged AlreadyWolf andhis colleagues placein thegataxyunderobservation. appThe source! a stationary by produced 0.07, of a redshift with iines simulateo*y'g"n run for roachlooksvlry promisingandcouldgive cosmologicalredshifttheoriesa distinct theirmoneyin the comingYears!
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l i i g. 5.l l ..l -h e q u a s a r-l i k c g a l a x y N 4 a rk a ri a n2 0 5 . w h i c h l i c s . i u s t b c l o rv t h c d i s rrrp t c ds l t i ra l gai ax y N ( i ( 4 -l l 9 i n t h i s i n ra g co b t a i n c d b y t h c a d d i t i o n o f C -C [ ) l i a mc s t a k c n a t t h c K i t t I )t a k National Obscrvalory 4-nletre tclcscopc Nole thc apparent straight. lunrinOUSc()lrncclr()nbc 'l'hc isophotesrvhich bcst show thc'bridg,c' betrvcenthc t\\1) ol)'ccts afc twccn thc trvo galaxies c pl our c d r e 6 i ri t h i s p i c t rrre . f h i s f a s c i n a t i n gi n ra g ew o u l d ro c k t h c f o u n d a t i t n o l t h c l l i g . l l a n g theor y . i l 'v e ri l i c t l . h c c a u s ct h c t rv o o b j e c t sp o s s c s sra d rc a l l yd i i l e re n t re d s h i f t sa n d h c n c c s h o u l d joincd ex i s t at dr a n ra t i c a l l y ri i f l e re n t d i s t a n c c s . p re c l u d i n g t h e p o s s i b i l rt l ' o f t h c i r h c rn g ( l ) hotogr a p t rre p n rd u c c d c o u rt c s y o l -l l a l l o n A r| . f ro n t t h e c o v c ro f h i s b o rt k Q t ro rs o r. r, I l c d s h rf t s jSA ) ttnd ( onr nt | t r. y i a s . p rrb l rs l rc di n 1 9 8 7 b y h t t c rs t c l l a rMc d i a , l l c rk c l e y . C a l i f o rn i r, .t
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Iit t t t t i l ri g 7 l t.'l hcIluhble I) ccplr icltl ( lll) lr ) ,slr o*nhcr c.till r r r dor v ni nhi s tor y as oneol 'thc tnor c i l n l x)rl a n t inr agcsol ilr oticr ncosr r r r logr .Altlxr r r ghtllc c i l 1i r ci nr agec ov c r s onl y a ti n1,ar c aol ' th c sky l /.lOth the ( liillnctcrol' lhc lir r ll N4or m( aboul 2i 'l i ' ( ) l 'l he l l D F i s s hor v nher c ) . i t r c pr c scn tsa n a r r ( ) w' kcyholc vicr v all tlr c \\' ill to lhe visiblc h,'r i z or rol 'the l J ni v c r s c .l t i s a s nr ps hol ol llrc I lnivcrsc cxtcndirl!: li(nr tltc pr(:\cnt dav [o n]osl ol thc way back to its crealion Scvcral httndrcd ncvcr-bclirrc-sccrrgalaxics arc visible in tlrc irrragc.Ilesides thc classical spiral arrtl cl l i p l i ca l galaxies.thcr c is a bcuiltlcr inu var icty ol' othc r 1:r l ar l ,s hapc s l ) etai l ed anal v s i sol 'tl l c i n ra g ch a s still to be pcr lir r r ncd.blr t r s a qclcr al r ulc r,l 'l l r r r nr h,the r eddc r the ob.j c c t.thc nr or c (l i sti rn l i t i s ( Photogr nphr cpr oduccdcor r r tcsvofl{ ohol W i l l i ar ns ,thc l l ubbl c D c epl i c l d'l c r r nr . a n d N A S A,/Spacc' lelescopc licicncc Ir str tutc.)
'Ielescopeas part ol'thc Fig. 7.9 T'hesepeculiargalaxieswerc irnagetlby the Hubblespacc rvas whenthc (Jnivcrsc seen are that they far away arc sThey McditimDecp.Survcy. thiee-ycar struca fruciionol. its presentage.Thc Meiiurn I)ccpSurveyhasrevealeda bizarrevarict) of 'l bluc in c.lour ltc whicharc irregilarin shapeandremarkably turcsin ihcsedistantBalaxies. objccts.. blu. regionsindicatethat vigorousslar lirrrnationhas recentlytakenplacc in thcsc galaxicslike our own Milky Way,but havefhdcdand,scll'rvhichincc lhr oulrunrberedlarge courtcsyofRichardGrifliths,the Mcdium l)ccp by roday.(t'hoUrgrapirCpruxlucc<J clesrructed ScicnceInstitute) Tclcscope Survev'l catl. andNASA/Sfracc
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Active and IRAS galaxies l;ig 8 2.(a).'fhcsc furr sky nricr,ivavc maps ploilcd in garactic co-ordrnatcswith the pranc of ottr.(ialaxy.runnitrg.horizrlrtallyacrosstlrc nritkllc. arrrllenlred on lhe Cialacticccntrc - sborv varialions in thc cllbctivc tcnrncrflturc of thc cosrnic ,rricroware background ,o,tiotiun-:i:ii" rl e aslr r cm cntswer c m adc ilr lr r ft:cdi|l' cr cntwavc r c ,gr r r s 1r t. s i ano,gobttr ) , i " r r " " ,r i i r " r " ,r t (lctcctorclranncls(A antr rl). h'rrrc ( (-)smic llact;rrri'n
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So lar the majority of this book hastalked about normal galaxies.Chapter I irrtrocluccdthc subsetofgalaxies known as active galaxies,and this chapterwill expandconsiderablyon the subject.As a broad average,about one galaxy in every ten is activc. 'l'his activity originatesin the core ofthe galaxyin question,and can be eitherdirectlyobscrvcdirr llrr centralregionsof'the galaxyor inferredto take placethere.Sometimes. as in thc cascol rarliogalaxics,the effectsof the activitynrayonly be visiblemuch furthcr away fiorn tlrr' centralregionsof the galaxy.ln most cases,however,the activity is causcdby plrysicirl processesother than the radiationofenergv from stars. 'fhe study ofactive galaxieshas beenproceedingfor the last fifty years,with an interrsc flurry ofactivity over the lastthreedecadessincethe discoveryofquasars.Many researclr astronomersnow investigatetheseexotic objectsto determinetheir nature.Active galaxies are often bright landmarksof the far distant Universe,and provide some of the nrosl efficient probes into earlier epochsofthe Universe. 6.I SEYFERT GALAXIES
lrig lt 2 (b) ll thc diporar arrisr)lropysho$r rn I:rg. li 2(a) (abovc) ls srbtracled riorn thc (.oril: litll sky microrvavcntaps.nntl thc cli-cctsofour (;irtn.r' u*'t,,tcn i,rk) consrderation.the rcnraini tl g ntaps.,olr vlticlt.onccxantple is shur vn hcr e. ,ti ,'pr av ttuc i i r ai i tr r sIn thc l c m pc r atur col .l hc crsrnic microrvavc backgr.rrnd ar rhc rc'er oI l parl irr 't oo.00o. rvas thc fiist dctcction .f 'l.hi, l h c'r ccds ol' lar gc- scar cslr ucr r r r cin r r r cear r y tir r i r ,r r s c ( l r nage r epr oduc c dc our tc s yor .N ns A (krddard Spacc Irliglrt Ccntcr.)
The Seyfertgalaxieswere first discoveredby Carl Seyfertin 1943.He had beenusing tlrc Mount Wilson Observatoryredshiftsurveyand had distinguished six galaxieswhich
I l6
A c t i v e a n d I R A S g a la xie s
l ch.6
dil'ferencesl'retweentlrenrbecarneobvious.The spectrallines, for instance,rverenol unifirrnrly broad. ln 1974, Khachikian and Weedmanploposeda slight modilication to the Seyfertclassificationscheme.Theseactivegalaxiesrvottldnow be classifiedaccordingto tlrcrvidthof their emissionlines. lrad noticeda bifurcation in the types of spectralline rvhich I)1'this stage,astrol.romers rvcrepossiblein celestialobjects,and lradtermedthenr'permitted'and'forbidden'lines. -l"henanresderive totally from the easewitlr which thesespectrallines can be reproduced under laboratoryconditionson Earth.The forbidden lines are thosetransitionswhich are easily accornplishedonly in the highly rarefied environmentof space.For example, a spectralline in the greenpart oftlre optical spectrumrvasobservedin an emissionnebula and, thinking it derived from a new elenrent,it rvas rranred'nebulium'. Later it was reaoxygen(OIll) which can only be lisedthat it wasactuallya spectralline of doubly-ionized producedunderthe nrostextremelyrareficdconditions. Khachikianand Weednrannoticedin their studiesof Seyfertgalaxies,that sonteexamples of tlreseactive galaxiesdisplayeddifferencesbctweenthe widths of the perrnitted lines and thc forbidden lines. Seyf'ert'l'ype ls, as tlrey called them, had perrnittedline rvidthswhich indicatedDoppler velocitiesof between I and 10,000krn/s. In other rvords, tlre clouds of gas producingtheseenrissionlines werc swirling around in the nucleusat theselargevelocities.The forbidden lines only shorveclvelocitiesofapproxirnately 1,000 knr/s.In the Sey\t type 2 galaxies,both pernrittedand forbiddenlines displayedrvidths which indicatedv'elocities up to 1,000kn/s (seeFig. 6. l). An irnrncdiateidea which can spring out of this is that perhapsthe broad lines - those rvhich indicatevelocitiesof over I ,000 krrr/s- and the narrow lines - thosewhich indicate velocitiesol'bclow 1,000kn/s - are generatedin clifferentpartsofthe activegalactic nucleus(AGN). This initiallyallowedastronon'rers to talk confidentlyaboutBroad Line llcgions (llLIts) and Narrow l-ine llegions (NLRs) rvitlroutreally having a clue about the physicalcharacteristics o1'suchplaccs!As we shallgo on to discusslater in this chapter, tlris is no longertrue, as astronon'lers have now developcdan excellentworking model for thc central engihe of an active galaxy which provides a very satisffing explanationfor wlratcausesthe distinctregions. Once again,in recentyearstechnologyhasnecessi{ated the modification ofthe Seyfert classificationscheme.Detailedstudy hasslrownsonreolthe Type 2 Seyfertgalaxieshave their narrow lines superimposedon nrucli fainter, broaderbases;almost as if the BLR is there but not easyfor us to see.Thrce nervsub-classifications are cunently in use,based upon the appearance ofthe hydrogenlincs in the galaxy'sspectrum.A SeyfertType 1.5 is .l.8 a narrow line Seyfertwhich lrasbroad basesto its hydrogenlines. SeyfertType has a distinctly broadbaseto its FIo emissionline but a fainter broad baseto its FIB line. Carrying this distinctionone step further,Seyfert l.9s have a broad Hcr basebut no Hp base. So, insteadof the rigid differencebetrveenthe two typesof Seyfert,a gradualblurring or nrergingof the types has becorneobvious lvith increasirrglysubtle observationaltechniques.This is perhapsour first cluc that all typcso1'Scyfertgalaxiesare intrinsicallythe sanre,andthat it is the way in whichwc perceivetherrrthatcausesthe difference.This idea rvill be pursuedlater in this chaptcl rvhenrve look at unification schemesfor active galaxics.
Rrdio galaxies
Scc.6.2l
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(b) Seyfert2-galaxyMarkarian Fig 6.1.Opticalspectraof (a) SeyfertI galaxyNGC 3?7' and Nebulaeand Active Galuies, o!Gaseous o.,liropi1,ri", ort",il..r.l r., iiiz. iliip"o 1989.) Books, Science UniversitY
6.2 RADIO GALAXIES
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suchas stars,alwaystail offto inby therma|sources, The black.bodycurvespossessed behaveanythinglike our own stars *t. other if tnir, top of On cludesomerajio emission. radio alsoproducenon-thermal suchasharesandprominences Sun,surfacephenomena enri ssi on.E venso, t her adior adiat ioner nit t edbyanor m a|gat axyisr at her low. Cer t ain (moreusually wavelengths otherobjectsin the Universeare copiousemittersat radio spectrum)' electromagnetic the of end low-energy this to referring when calledfrequencies galaxy' ofactive andcertaintypes r"rnuni, ofsupernovae Theseareiheexpanding by the radioengineerand amateurastSo calledradiogalaxieswerefirst discovered Jansky,who was the first to detect Karl of work the ronomerGrote Reber.He had read
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ra(liowitvcsliotl space. Alllrouglr.lirnsky,wlrrr\\/its\vorkillgunderthc auspicesof Uell I-atrotatorics, had tttadctlris firscirrntirrg discovcry.his superiolsaske<J hirn to nroveonto olhcr work and his pionccrirrgratlir.rastrononrywas abandoned. Reberread of Jansky's rvorkand reasottcd thatiflhc crtrissiorr rvasblack-bodyin nature,it shouldbe rnorcintense at highcrli-cqucncics. Ilo tlrcrefbrc sct aboutbuildirrsa l0-metreparabolicdish which hc operatc
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rvhcrea is the spectralindex, varying betrveen-0.5 and -3 for radio galaxies.The more ncgativcthe number,the 'steeper'the spectrunris saidto be. The steeperthe spectrunr,the rarerthe higher energyphotonsofradio becorne,and so the radio galaxy is lesspowerful than a counterpartwhich has a'flatter' spectrum(sec Fig. 6.2). As technologyhas irnprovcd,so havethe classifications and sub-classificatigns which can bc appliedto radiogalaxies.In goncral,lrowcvcr', the first and most obviousclistinctiorr rvhichcan be madc is whcthcrcrrnot the radio cmissionis lobe donrinatcdor corc dorninated. In (hccaseof a lobeclominatccl rircliosource,crrrission corneslrorntwo giganticrcgions rvhichlic syntntetrically ott citltcrsitlcolthe hostealaxy.Somctirnes they are 'conlected'
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Fig 6.2.Flatandsteeppowerspectraarenamedaccordingtotherelativeamountsofhighe olhighand equalamounts galaxies rvhichproduce roughly Those active radiation. tolo* "n"rgy objects. radiation areknownas'flat spectrum' lowenergy to the central galaxy by jets of radio emission which make it obvious that the activity driving the phenomenonoriginatesin the galaxy's nucleus.In termsofobservationalcharacteristics,these lobes are usually extendedby many arc minutes on either side of thc central galaxy. When the distancesto these galaxies are taken into account, the actual linear dimensionsofthe lobes can be calculated.lnvariably they are enorrnous,typically extendingfor hundredsof thousandsof parsecs.ln some cases,they are millions of parsecs in length. These radio lobes are the largestsingle objects in the Universe' being so gigantic that they often spanthe entire diameterofa galaxy cluster. Lobe dominatedradio galaxiescan be sub-classifiedaccording to the flux density at 178 MHz. This distinction was first shown by Cambridge astronomersBarnard Fanaroffand Julia Riley. Radio galaxiesare now grouped accordingto their Fanaroff-Riley (FIt) classes.FRI sourcesare the lower luminosity radio galaxies.Their flux density at lTtl MI-lz is typicallybelow 5x lO" Wll'lz. 't hcir lobesappearto be very extendcdbut cluilc faint at their outer extremities,with the steepestspectrabeing displayedin these laint regions.The lobesareconncctedto the ccntralopticalgalaxyby smoothlycontinuousjcls. FRll radio galaxies,on the other hand,are the most powerlul sourcesof radiation.'llrc part of their lobe spectrais found in their innerregions,whilst the extremiticsarc steepest
r' 120 Activennd IIIAS galaxics
[Ch.(r
-l'hcjetsarc rrsuallylesscorrrparable oftcnctlgc-brightcncd. in brightness to the lobesthan tlreyare in FRI sources,and henceappearfainterlhanthe lobes.In actuality,both thejets and the lobes are significantlymorc luminous than their FRI counterparts.T'he "ietsare oftennot syrnmetrical in FRIIs.Instead,one sidervill usuallybe far brighterthanthe other, or the sourcewill be totallyone-sided, with the.ietlccdingone lobebeingtotally invisible. The core dominatedradio galaxiesdo not display thesehuge lobes of radio emission. but sonlc do possesssingle-sidedjet structures.Tlresejetscan extendover distancesofa few kiloparsecs.The radio spectraofthese sourcesare usually almostflat and extend into the millimctre/submillimetre regionof the electronragnetic spectrum,i.e.to frequencies in excessof300 GHz. 6.3 QUASARS The great interestwhich follorvedthe discoveryof the radio galaxiesencouragedthe newly burgeoningfield of radio astronomyto attcnrptits first sky survey.This was collated at Cambridgeby Martin Rylc, F. GrahamSrrrithand Bruce Elsmore in 1950. lt was called the First CarnbridgeCatalogue,and containedfifty northernhemisphereradicr sources.Eachobject was namedlC lirllowed by tht: source'scataloguenumber.Five years later,thc SecondCambridgeCataloguewas publisheclwith almost2,000 sources!As radio astronornycontinuedto beconremore and more sophisticatedit was realisedthat much of the 2C cataloguehad resultedfrom overzealoussourceplotting, and so in 1962 the third catalogue was issued which contained only a quarter of the previous ::jrj;1"','"" As tlris chapterhaspreviouslyrecounted,many ofthese sourceswere discoveredto be extendedobjectswhich fell into two categories:either they were supernovaremnantsor tlrey were radio galaxies.A certainnumberofobjects were not extendedand appearedto be point sourcesof radio emission.It is slightly rnisleadingto term theseobjects 'point sources'becausethe beamwidths ofthose early telescopeswere so large than any object smaller than severalarc minutes in extent was considereda point source.Nevertheless, thesepoint sourceobjectswere intriguing;they were relatively strong radio sourcesand ripe for further investigation. The strength of the emission and the compact nature of the sourcesled many to believe that they were nearby 'radio stars' within our own Galaxy. The distributionofsourcesthroughoutthe sk7 was wrong forthis to be the answer.Instead of being confinedto the Milky Way, the sourceswere dotted more or less isotropically acrossthe sky. This indicatedto some that the sourcesmust be extragalacticin origin. Otherscontinuedto arguethat, statistically,the isotropywas not that significant. The only way to solve this puzzlewas to detennineexactpositionsfor the point sources and then seeif any optical object could be found and studied.With the data available,the positionswere so inaccuratethat when correlatedrvith optical plates,any one ofa hundred visible objectscould havebeenthe'opticalcounterpart.In an effort to refin_e the positional accuracyofthese point sources,the nervtechniqueol'radio interferometryrvasemployed. Jodrell Bank astronomersshowedthat 3C 48 was indeeda point source,and that the radio emissionwas confinedto an areaof the sky which was lessthan one arc secondin diameter. Astronomersat the Califomia Instituteof Tcchnology also began investigatingthis object in orderto refine its position. Eventually it was identified with a l6th magnitude
Sec.6.3l
Qu a sn r s l 2 l
blue stellar object which was surroundedby somefaint nebulosity.The identificatiottwas made by Allan Sandageusing a photographicplate taken using the 5-metre (200-inclr) Hale telescopeon Mount Palomar.Immediately,further investigationswere ttndertakctt The object was studied photometricalty,and its spectralcolours were ftruntl to bc vcry peculiar indeed;quite unlike anythingobservedin a star before. The next step was to study the star spectroscopically.When this was achicvcdtlre ntystery ofwhat this object was took anotherdeeptwist. The spectrumcontainedbroad cntission lines. This was a featurewhich had not been seenin starsbefore. When astrononlers tried to determinewhich spectral lines were produced by which chemical element thcy came up againstanotherbrick walMt seemedas if none of tbe patternsmatchedup with anythingthey had ever known before.Sojust what were theseobjectswhich appearedlikc starsbut displayednone ofthe characteristicsofany known celestialobject? Investigationsof 3C 48 led many to believe that what had been discoveredwere radio stars. The story continues, however, with the work of cyril Hazard, the English astronomerwho led the first successfuldiscoveryofthe true natureofthese objects' llazard was working in Sydney,Australia,using a radio interferometer.He calculatedthat, of thc
Fig. 6.3.'I'hebrightestquasar,3c 273 (alsoshorvnin colouron lhe coverofthis book), is a sttong 4-nlctrctclcscopc of Virgo.'l his Kitt PeakNationalObscrvatory ,nJiosour." in theconstellation jet. wc photograph showsthevisiblepaftof this | 3th nagnitudeobject,includingthepronrincnt outshincsthc starsin the undcrlying i.. o"ly ihc point-likcactivenuclcus,which dramatically .host' galaxy.'l-hisquasarmay radifltc100tirncsmorelight thanthe brightestordinarygalaxy, courtesyof and itijet nr"y r"ir,,r" 150.000light ycars in length.(Photographreprodttcccl NO^O/Kitt PeakNationalObsewatory.)
t t t t t t t t t t t t t
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conrpactladio sourccsirr thc Carntrritlsc cataloguc,i(:.273 (see F'ig.6.3) i.vouldbc occttltedby tlrc Moon.'l'hisrvoukloccurnot.iustoncebrrtthreetintesin 1962.If he could o bscrveth cs c oc c ult at ions lt c,c ouk lpinpoint t he p o s i t i o no f 3 C 2 7 3 b y t r a c i n g w l r c n t h e radioenrissionwas blockcdout by the Moon. The rrewpositionenabledlrazardto use a Mount Palomaropticalplate.broughtto Australia by l{udolph Minkowski, to identify 3C 273 as a l3th nragnitudeobject rvhich resembleda star.This informationwas comrnunicatedto Mount Palomar,where in December1962 Maartin Schmidttook an optical spectrumol'the source.It displayedtlresamebroadernissionlinesas 3C 48 and in sinrilarly intractablepatterns.Schrnidtwas stubbornin his efforts to understandthis spectrum, but he eventuallyrecognisedthe Balrnerlinesof hydrogen.The only remainingpuzzlewas that they wcre nowherenear wherc tlrey rvcre expectcdto be in the spectrum.They had becnsevcrelyredshifted.l'aking this extraordinaryresultat facevalue,Schmidtcalculated a distanceto the object using the Hubble law with a constantof 50 km/s/Mpc. lt rvasan cxtraordinarilylarge948 Mpc. calculating3c 273's lurninosity,it was found that it is about50 timesmore lurninousthan eventhe brightestgalaxies- 5 million million times the luminosityof our sun! Thus,quasarswerenot stellarobjectsat all. Insteadthey were thc brightestform of active galaxy known, and existedat extremedistances.Becauseof thcir appcarancethey becarleknown as 'quasi-stellarracliosources',a namesubsequently shortened to'quasars'. The broad emissionlines in quasarssuggestDoppler velocitiesof up to 10,000 knr/s. In rnanycases,the spectraare suspiciouslysimilar to thoseof SeyfertType I s. Despitethe lact that quasarswere originally discovereddue to their strongradio emission,subsequent rvork at optical wq'elengthsto identi! theseobjectshas shown that the vast majority of thenr,about 90 per bent,are, in fact, radio quiet. Thesewere initially termedeSOs (quasistellarobjects),althoughthis sub-classification seemsto have fallen fronr common usage, and both radio loud and quiet varietiesare currentlyreferredto as quasars.Ifany qualification is needed,it will usuallybe explicitly statedthat the quasarhas a radio loud comporrcntin its spectrum. 'l'he optical properties quasars of are, in generaltcnns, so similar to those of Seyfert 'Iype ls that the dividing line betweenthe two has becomeextremelyblurred.For institnce,the lowestluminosityquasarsare lesspowerful than the highestluminositySeyfert 'l'ype ls. A rather arbitrary, but workable, distinction has been the segregationof these rrbjcctby their redshifts.Literally anythingbelow a redshiftof 0.1 is termeda seyfert rll laxy Type I , and anything betweenthe redshiftsof 0. I and 5 is ternreda quasar,regardlcssof thcir intrinsicluminosities. .lustas the only distinguishing featureof a Seyfertgalaxy is the overlyingluminous ccrrtralnucleus,it has always been assunredthat quasarsare the super-brightnuclei of othcrwisenornralgalaxies.[his theorywas recentlyconfirmedby the Hubble space -lelescopcin a sct of observations conductedby John Bahcall(lnstituteof Advancedstudy, l)rinccton)and Mike Disney (tJniversityof wales). 'l he resultsshow that quasarscan rcsidcin pcrf'cctlyundisturbcd, nolmal galaxieswhich can be eitherspiralor ellipticalin slrape.Approximatelyhalf of thequasarsstudied,horvcvcr,werefoundto existin mclging syslcms,which more closelymatchesastrononters'cxpcclations (seeFig.6.4). -fhc ncw t'csultsarc tantalisingand provocative.'l'hcy prove lhat the causeofquasar activity nray bc lcssobviousthanpreviouslythought.bccauseit can bc found in sucha wide varictyof ralaxy typcs.
S ec.6.41
Bfazers
123
canbescenin_theseimagesobtainedwith thc I lubblc andtheirhostgataxies Fig 6.4.Six quasars PC 0052+251which can be seento be in a normalspiral Sp'acelelescope.'l'opIeft is quasa'r 'l'heotherfour galaxy.Belowrhis is quasarpitL g0g which residesin a normalellipticalgaluy. top rightiquasar03I 6-346. l0l2+008, PG centre, bott.m IRAS04505-2958, ccnrrc; ltop fiuasars courtesy.ofJohn (lmagesreproduccd bottonrright; lRAsl32l8+0552)areall in galaxymergers. and Ilahcall,insiitute for AdvancedStu4y, Princeton,Mike Disney, Universityof Wales, ScienceInstitute) Telescope NASA/Space
6.4 BI,AZARS The final distinctionwe shall make in our surveyof active galaxiesis of the group which has becomeknown genericallyas blazars.ln 1941,a celestialobject in the constellation Lacertawas discoveredand classifiedas a variable star by H. van Schewick. ln accordof the ance with convention it was named BL Lacertae.The'star' returnedto the centre radio a strong to be was discovered it astronomicalcommunity's attentionin 1968 when InObservatory' River Vermillion Illinois' of the University at sourceby a surveymade vestigatingfurther, it was discoveredthat Ill, l-acertaedid not have very mrtch in contmon thc with a star at all. lts spectrumdid not display the expectedstellar absorptionlines or how is. that distribution energy the spectral of A study more unusualemissionlines. much power is being given out at the cliflbrentwavelengths- revealedthat theseobjccts had very little in common with starsbut sharedrnostof the propertiesof the then recently classified[]1. l.ac obicctsas a quasars.'t'hus.in an act ol laith. astronomers cliscoverecl
['
124 Acliveand lllAS gll:rries
tCh.(r
tlcw typc of activc galaxy.n s tcrchniques havc irrproved,so emissionlines lravebeen lbund in a slnall nunrberof llt, l.ac obiecfs.'l-lrciridentificationhas proved that these objectsare indeedextragalacticand have maxinrurnluminositieswhich overlao rvith the rninimrrrnlor quasars. BI- l,ac objectsare highly variable in nature,lading from brilliance before returningto pronrinence,on irregulartinre scalesrvlrichcan sonretimesbe measuredin days. The objectsarealsohighlypolarised, which indicates that rheradiationis beingproducedby high velocity electronsspirallingaroundrnagneticfield linesto give out synchrotronradiation. A subsetof quasars,known as OVVs (optically violent variables)were noted to trave certain propertiesin common rvith the BL Lacs. Namely, they both display highly poIarisedradiationand are very variable.Similaritiesin the spectralenergy<listribution,too, has led astronomersto concatenatethe two groups and amalgamatethe narnesBL Lac and quasarinto'blazar'.The oVV cornponent ofthe blazarsextendsthe top end ofthe lunrinosity rangeinto a broad overlapwith the more generalquasars.
The c entral engi ne 125
Sec.6.5l
accretiondiscsurrounds the blackhole
;
6.5 THE CENTRAL BNGINE The questionofjust what could possiblyprovide so much energyfor the activegalaxiesto radiate into spacewas a natural one wlrich sprangto the minds of the astronomerswho studiedthesefascinatingobjects.The early 1960srvasa time ofgreat speculationabout theseobjects' power houses.As a broad generalisation,they existed at younger epochs, i.e. greaterredshifts.This single fact led many to speculatethat the causeof this excess radiationwas a massivebout of star lbrrnation.Calaxiesin the presentday Universehave nuclei populatedwith old stars;fornrationhas long since ceasedand is now confined to some irregularand peculiargalaxiesand the spiral arms of certaingalaxies.Although, as we shall see in our discussionof starburstgalaxies,this theory cannotbe completelydisrnissed,it wassuperseded by another'astronornical child ofthe '60s'. In the sameway that active galaxiesand quasarssuddenlybecameelevatedin importance,because ofthe advancesin tcchnologyduringthe 1960s,so did black holes.prior to that decade,they were reallyjust confinedto the scientificcuriositybox. Ceneralrelativity seemedto be the only way in which to study thesetheoreticalconundrums.In | 969, however, Donald Lynden Bell from carnblidge proposedthat a quasarcould, in fact, be powered very efficiently if it possesseda black hole at its core. Any object, such as a star, which strayedtou closewould be ripped to shredsby the tidal forcesofthe black hole. The energy which can be liberatedby an object falling into a black hole is enormous.It is actually the Inost efficient energy productionnrethodin the universe, converting42 per cent ofthe object's massinto energy. 'fhe black holes found in actiVegalaxies have beentermed supermassiveblack holes, in order to distinguishthem frorn their smallercousinswhich are thought to be produced in supernova explosions. Supermasiivc black holescancontainover 100million tirnesthe tnassof the Sun and be no largerthan2 AU in diamctcr.In other words,tlre centralengines of the brightestobjectsin the Universemay be no bigger than the diameterof the E,arth's orbit! This size estimateis backedup by observationswhich measurethe variability of the radiation output from the active galactic nucleus.'l he radiation observedcoming fronr activegalaxiesobviouslycannotbc conringdirectli,from the black hole. Insteadit is
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ofan engine thatthecentral blackhole.lt ispossible ofanaccreting diagram Fig.6.5.Schematic blackhole.As theblackholedevoursthe starsandgasclouds, aciivegalaxyis an acCreting aregivenoffby theswirlinggas, of radiation intense amounts
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thought to come from a disc of gaseousmaterial which is spiralling down into the black hole. Someactive galaxieshave beenmeasuredto vary on the time scaleof a day or so. In order to compensatefor any areasofthe accretionwhich are decreasingin brightnessas other areasare rising, it is assumedthat a changein the output ofthe sourcecorresponds to the whole emitting region having brightened.This brighteningmust propagateacross the disc at a velocity which cannotexceedthe speedoflight. So, taking thesetwo conser-
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va tiv(:itj is t t t lll) liot t slir ; t lt : tv' ir lr r c ; lr ,rl: olnbi t r i r xt lrr , 'r rrrv i t hl l r er a t co f v a r i a t t i l i t yt.h e r r r a x i lrtun rsiz col- t lt cc r nit lir r g, r c r ior rlr r r r : bc ; t no s r c r r l e r t h a tnh e d i s t a n c ei t r v o r r l ct a l k el i g h t t o tt'avclitt l s inglcr lt r y . ' llr ist lis lr r ncis c abor rth t r r l i ; r r l c t c r o ft h c S o l a rS 1 , s t c nrrv. h i c hi s t h e cxl)cclc(lsizcol'tlrclt:<'rcliorr tliscirrounda supclrnassive blackhole. l-hc accrctiontlisc:firrnrslirr csscrrlially the sanrcreasontlratwaterspiralsdown plugholes.lt is thc rotationof thc liarth rvhiclrcarrscsbath watcr to spiral downrvards. The nrassof the black lrolc is so {rrcatthat it crc'atcsan incrediblydeep gravity rvell in the cenn'cof'thegalaxy(lhc cosnricplrruholc). As rrralcrial fallsdown the gravitywell it is still movins in its orbit aroundthc ccntreof the galaxy(which probablycorresponds to the positionof.the black lrole).As the gaseousrnatcrialorbitsthe black hole it rvill interact with othor [ibuds in sirnilarbut clil-fcrently oricntatedorbits,and eventuallvit will settle into an accretiondisc bccauscol'thc energyit has lost in the collisiorrs.'fhe gas in the accretiondisc is hcatedto incanclcscence by thc:sheeringforcesand friction in the disc. This causesit to give oI'fcvcn tnoreradiationin lhc forrnof X-rays.because the gasparticlesarc hcated1otcmperaturcs irrcrcessof l0'l.: (seeFig.6.5). Using this nrodcl,thc broad lirreregiottcarrthcn be explainedquite naturallyas the re-radiatcd entissionfi'onrthe s*'ir'lirrggasclouds'"r4rich areyct to settleinto the accretion disc.'l'hedetailsof the tuodclarc Ihr lrorn sirnplc,however.1'hegasrvhichradiatesfrom thenarrowIineregiorrexislsnruchfurtherout, at n distanceof somewhere betweenl0 and 100parsecsfrotn the blackhole.whcrethc radialionand kineticenergyare lessintense. In our previousdescriptionsof'lhe differentt],pesof activegalaxy,sornedisplayed broadlinesand othorsonly narrowlines.So the rlrrcstion ofwhat causesthe activegalaxy to be a broadline galaxyor a narrowline galaxyntrrstbe considered next. 6.6 UNIFI CATI O N SCI I EM I iS In I 9 85 one of the ntostintportnr'to bservations r;ontributing to our modernknorvledgeof active galaxiesrvas nrade:I{obcrto Antonucci and Joe Miller observedthe Seyfert2 galaxyNGC 1068 in polarisedlieht. lnsteadol'rrarrowlines they sarvbroad lines; the galaxydid havea B[,[{ btrl it corrlr.l rrollrc scur irr ditect light. In chapter2 it was stated that one mechanismby.,vhichlislrt can becoirrcl,,rlarisedis rvhenit is scatteredoff dust clouds.ln someway, the llLR lcgion of N(iC l{)(,flis hiddenliom our directline of sight, but smallquantitiesol'light frorrrit arescattcrecl irrtoour directionby dustclouds. The broadline regionntustbc surroundcdll,a torusofdusty tnaterial,about I parsec in diantcter,which from ccrlainpointsof vierv hlocksour directviervof the centralregions (sce Fig. 6.6). 'I"hecdgesof this torus rnrrsrbe opticallythin enough,however,to allorvlight to scatterout in our clircction.The nrrrrol line regionthen cxistsbeyondthis torus.Corroborativeevidencetlral Scyfertgalaxicsrnayall be intrinsicallythe sametype of ob.fecthas conte fronr NG(-' 4 l-5I, wlrich hus been observedat different epochsto changeits observational properlicsfrorntlratol ir SeyfertI to a 1.8and back again.per(onls hascarrscrl hapsprecession ol'a non-unif'()n)l this.Whcn the toruspartiallyblocked our view. the broad lirresalnrostdisappearecl arrtlit was obscrvedas a'l'ype 1.8. lt then returncdto its broadlinc statrrsrvhcnthc rrbscur;ttion passedby. lf rveextendthis idcaol'unificatiott t
light a krrusofdttst.-800 shows N(iC4261.1'hisinlage coreoftheactive Irig.6.6.'l'he Balax) 100nlillion localcd. oflhe galaxy, blackholeat tlle.centre a supcr-nraisivc y"-urc o.ro..,fuelliug Astronomcrshavecalculatc(lthatlhc iighty.orr6istantirirhcdirectionofthcconstcllationVirgo withina olthe discis 1.2hilliontimesthemassofour Sun,conccntralc(l o6jeciat thccentre of l ' courtcsy (Photograph reproduccd notmuchlargerlhanourSolarSystem. reiionof space lnstitulc Science ) andNASA"/Space'felescope University, I.lopkins Jbhns Fe'rrarese, quasarsand Seyfert ls. As we have stated,one ofthe basic classificalioncritcria is llrt ofthe object'sredshift.Thus,perhapsthesetypesofactive galaxl' artificialconsideration are indeedintrinsically the sametype ofobject and overzealousclassificationhas blirltlcrl us to the fact. The only differencebetrveenthesetypes ofobject is whetheror not yotr carr see over the obscuringtorus and into the BLR to the power of the radiation being givcrr out by the centralengine, R a d i o l o u d va r i e ti e so fa cti ve g a l a xvca n a l so b e o r g a n i se d i n to a u n i fi e d se q u e nl tr ce' 'l of radi,r characteristics the of One poirrt in this scheme. radio loud quasarsare our starting measttrcrl. with jets ol rnaterial.From the high polarisations louctAGN is their association the.jetsmust be almostcertainly{'unnclledout of the AGN by magneticfielcls.A qtras;rr displaysbroad line emission,anclso ottr viervinganglemust be well arvayfrom lhe lot tr"
1 2 8 A c t i v e a n d IRAS g a la xie s
fch. 6
If the anglebecomes steepenough,however,our view of the broadline regionwiil be obscuredby thejet emission.This is the situationwhich is proposed for bfazars.Astronomers areliterallyblindedby thelightbecause theyarelooiing straightalongthejet,s symmetry axis.Hence,emission linesareincrediblydifficultto dJtect.iilting our tineot sightin theotherdirectionwill eventually leadus to losesightof the broailine region because it is obscuredby thetorus.In thiscase,the activegali'xywilt appea.io ue a raaio galaxy(seeFig. 6.7).
Sec.6,7l
IRASgalrxi€3
i
If we wantto extendthe ideasof unificationwe haveto considera way in which radio loud and radio quiet galaxiescan be broughttogether.This is a muchmore difficult job, and many astronomerii hre of the opinion that this is a fundamentaldifferencebesuspicionis thatthe majorityof radioquict tweenactivegalaxies.A curiousobservational activegalaxiesappearto be hostedby spiralgalaxies.Conversely,the observationalim' withinelliptical pression givenby studiesof radioloudgalaxiesis thattheyareembedded galaxieswhich are often disturbedin one way or another.This is by no meansproven, however.
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6.7 IRAS GALAXIES Our discussionso far hasbeenaboutthetraditionalactivegalaxies.Recently,astronomers havebeenwonderingjust how thesefit in with the so-callednormalgalaxieswe see duringthe 1980salsobroughtanother aroundus in thepresentepoch.New investigations classof galaxyto light. The so-calledIRAS galaxieshavecauseda re-appraisalof thc plethoraofgalaxiesandthe interrelations, aswe shallsee. IRAS is the acronymof the Infra-RedAstronomicalSatellitewhich was launchedin 1983.It revolutionisedinfiared astronomyby being the first instrumentto perform an betweenl2 micrometresand 100mialmostall-sky(95 per cent)surveyat wavelengths crometres.Duringthe mission,which lastedfor just undera year,IRAS detectedapproximately250,000infraredsourcesscatteredthroughoutthe Universe.ln the yearsthat followed,most of thosesourceswere identifiedwith objects,particularlystarswithin our own Galaxy. The beamsizeusedby IRAS was2 arcminutesin size,andso anythingwhichappeared smallerthanthis wasclassifiedasa point source.Obviously,all of the starsdetectedcamc from thepointsourcecatalogue. Of theremainingpoint sourcesa significantnumberwere correlatedwith extemalgalaxies.Furtherinvestigationshowedthat theywerecompletely normalspiralgalaxieswhichhadbeendetectedby IRAS. In somecasesthe infraredradiation is fifty timesmoreluminousthanthe opticalemission.This was instantlyfascinating the wavelengths selectedfor IRAS to studywerepurposelychosenbecausestars because emit relativelylittle radiationat this longwardendof thewaveband. of between temperatures Stellarsourcesradiateblack-bodycurveswith characteristic of 60 to 100micrometres 3,000K and20,000K. Peakradiationbetweenthe wavelengths black-bodytemperature of between25 to 100K. Thus,thegreater requiresa characteristic part of the emissionperceivedin this rangewaspresumedto be comingfrom dustwithin the detectedgalaxieswhich had beenheatedby starlightfrom youngstars.A surprising resultwasthata smallfractionof the spiralgalaxiesdetectedby IRAS werefoundto have luminositieswhich rivalled the quasars!Their spectra,however,were not similar to the activegalaxiesat all. Instead,they resembledthe spectrumdisplayedby an HII regionan emissionnebulawhich signifiesthe sight of star formation.Other IRAS-detected galaxieswere slightly more modestand favouredluminositieswhich were comparable with Seyferts.In fact, furtherstudieshaveshownthat the numberof IRAS galaxies actuallyfar outweighsthe numberof Seyferlgalaxiesdetectedin the Universe. As is alwaysthe way in astronomywhena newclassof celestialobjectis discovered,a Somethoughtthat the numberofdifferent theoriessprangup to explainthe phenomenon.
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IRAS galaxics,as thcy lrccanrcknown,wereqrrasars in which the activegalactionucleus was crtsltroudedirr dust. Otlrcls f'clt that they were galaxiesin which an incredibly active bout ofstar formationwas taking place.Thesegalaxiesare known as .starburst'galaxies. As previouslystatcd,stars in the presentday Universeare only .naturally' created in the spiral anns ol'spiral galaxiesarrdin certainl.ormsof inegulai galaxy. in both these cases,star forrnationtakcsplaceat a regular,stcadypace.stellar masies.un uury between 0.05lirnesthe massof'theSunand 60 timesthe rnassof the Sun.The smallerthe mass,the more populousthc numbers.IJigh rnassstarsare incredibly bright, with luminosities in excessof 10,000timesthatof the Sun. In other situations,starscan be 'forced' to develop in galactic collisions. when trvo galaxicsmergeit is ratherlike the interlinkingof fingers.Althoughstars do not collide witlr each other * becausethc spacesbetweentlrcnr are so great - the giant nrolecular clouds do merge. The increaseddensity results in an abnormally large fraction of the merged clouds collapsing gravitationally to become stars. This is the starburst phenomenon and, although it is a common event in interactinggalaxy systems,it is by no meansconfinedto them. The galaxy M82 in ursa Major is a good eximple of a starburst
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S e c . 6.8 l
Are IRAS galaxies active galaxies?
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occurringin a relativelyclose-bygalaxy(seeFig. 6.8).Althoughthegalaxyis disturbed is notcertainin thiscase.Onepossibilityis theexactcauseofthe starburst in appearance, thatthe galaxyhasbeentidally disruptedby thenearbyspiralgalaxyM8l . 6.8 ARE IRAS GALAXIES ACTIVE GALAXIES?
is onewhichneedsanswcrquestion, 'areIRAS galaxieiactivegalaxies?' Theperplexing ing if we areto gainan insightinto galaxyevolution.Certainly,IRAS galaxiesare not normal,butwhenwe usetheword 'active'in thiscontextwhatwe arereallyaskingis 'arc At present,the IRAS theypoweredby a blackholeaccretingmassfrom its surroundings?' to be interacting, Althoughsomehavebeenobserved galaxies arethoughtto be starbursts. shouldhc andwhy starbursts a significantproportionofthem areisolatedfield galaxies, Whateverthe precist' systems is not y€t understood. takingplacein thesenon-interacting explanationfor the reasonbehindthe burstof starformation,the singlemostobviousfact is thatthe starburstis hiddenfrom directview by a surroundingcocoonofdust' Theyourrlr clusterat thecentreofthe galaxymustcontainmanyhotyoungstars.Theseerrrit starburst spectrum. Observ' predominantly in theblueandultravioletregionof theelectromagnetic The atomicgasspectraof theselllAS ationsclearlyshowa lack of thesewavelengths. gataxiesalsosupportsthe factthatthehighestenergyphotonsaremoppedup beforeexcil thegalaxic'; ing thegasintohighlyionisedstates.Insteadof highenergy'blue' emission, displayexcessiveamountsof 'red' which, in collaborationwith the other phenomenorr listed above,is entirely consistentwith the ultravioletphotonsbeing absorbedby dust A similarprocessactuallytakcs which thenre-emitthe radiationat infraredwavelength$. placeon the Earthwherebythe groundis heatedall day by the high energyphotonsol this energyas longerwavelength radiationfrom the Sun.At night,the groundre-radiates photonsofinfrared. So, if IRAS galaxiesdo not haveblackholecores,whatmakesthemso fundamentall.v differentfrom activegalaxies?In orderto beginto answerthat questionwe are going to examineour basic assumption:that activegalaxiesand IRAS galaxiesare poweredb1' of an activegalacticnrr" originallybecamesuspicious Astronomers differentmechanisms. clei interpretationbecause,as we havementioned,the spectralenergydistributionantl emissionline spectralookedso different.They resembled,more strongly,the speclraol star-formingH II regionsfrom within our own Galaxy. led by RobertoTerlevichof the Universityof Cambridgebc A groupof astronomers In gantowonderaboutapropertyofquasarswhichwasseldomthoughtofassignifica fact, it is a.resultwhich hascosmologicalsignificanceandshowshow usefultheseactivr' galaxiesarefor probingthe earlyUniverse.'Inthe spectrumof manyquasarsareemissiorr I In chapter4 we describedhow the Big Bangcauset lineswhicharedueto heavyelements. theUniverseto be filled with atomicmatter,thepredominantfractionof whichwashydroof the chemicallithiurrr genandvirtuallyall of theremainshelium.Tiny, traceelements havebeenformedin thecentresol werealsoformed.All of the otherchemicalelements starsandreleasedbackinto spaceat theendofthe stars'lives.Theseheavyelements- thc 'metals'astheyarecalled- arepresetin the spectrumof eventhe youngestquasars.-l'h,' for the linesto be so strong,largenumbersofstars musthavr conclusionis inescapable: it. Morethanthat. livedanddiedin thequasarbeforetheepochat whichwe areobserving
1 3 2 A c t i v c a n d IRAS g a la xie s
l ch.6
many ofthese starsmust havebeenofthe high massvarietywhich explodeas supernovae. Chapter5 describedhow supernovaeare so briglrt that they can be seenacrossmost ofthe visible universe,so why can we not seethesesupernovaeexploding? euasars have been found all the way out to redshiftsof 5 or more which, dependingupon the choice of Hubble constant,correspondsto a Universalage of.iust I billion to 2 billion years.That leaves precious little time for the largely isotropic universeof 300,000 years to l.ragmentand gravitationallycollapseinto galaxies- as we shall discussin the next chapter- let alone havegenerationsofhigh massstarslive and die. Terlevichand his co-workersbeganto run simulationsto try to discoverwhat the observational propertiesof such a bout of early star formationwould be. His conclusionshark back to the earliertheoriesaboutactivegalaxiesand the fact that they may be poweredby starbursts.He especiallyconsideredhis calculationfor what happenstowards the end of the starburstcluster's lives, when the massivestarsbegin to explode as supernovae.The modern version of the starburstmodel can actually be split into four distinct phasesof activity. In the first, which lastsfor approximately3 million years,the centralregion of the forming galaxy becomesan intenselybright emissionnebula; similar to but on a much largerscalethan the emissionnebulaein our Galaxy. This has happenedbecausethe starburst has causedthousandsupon thousandsofstars to form with a range ofall possible masses. In the secondphaseofactivity, the rnostmassiveofthe stars- thoseofbetween 40 and 60 solar masses- becomewolf--Rayetstars.Theseare very hot starswhich shinebetween 100 thousandand I million times as brightly as the sun and producean incredibly large amountof dust in their outer atmospheres.One of the characteristics of a Wolf-Rayet star is that it shedsthe outer layersof its atmosphereby expellinga sheil ofhydrogen. According to calculationsattachedto this model,the galaxy will now begin to resemblea Seyfert Type 2 with nanow hydrogen enrission lines becausethe hydrogen envelopes are only expandingslowly. The third phaseof activity beginswhen the cluster is between4 million and 8 million years old. The massivestarsnow explode as supernovae.Although theseexplosionsare titanic,they are relatively few in numberand the galaxy retainsits seyfert Type 2 appearance.The centralregionsare seededwith the heavy elements.The expandingsupernova shock waves also create the low level radio emissiondetectedfrom radio quiet AGN. Finally, the fourth and most dramaticphaseof activity beginswhen the cluster is over g million yearsold: as time hasgoneby so the lessermassstarshave begunto reachthe ends oftheir lives. By aboutthis stagein the cluster'sevolution,starsofbetween 8 and 25 solar mass€sare beginningto explode as supernovae.There are many more ofthese starsthan thereare largerones,and the effect ofthe explosionson the nucleusofthe galaxybecomes very noticeable.with the violently ejectedgas flying all over the nucleus,the emission lines become Doppler broadenedand begin to resernbleSeyfert I or quasar line spectra. This type of activity, once it begins,ib calculatedto last about 50 million years. This starburstmodel is applicableonly to thoseAGN which are radio quiet, but this is a staggering99 in every 100. Even then, many astronomershave trouble acceptingthat this type of activity can persistfor long enough and generatethe kinds of luminosities displayedby the most powerful quasars.one of the rnostinteresting,and totally independent, observationswhich increaseconfidencein starburstswas reportedby Alex Fil-
Sec.6.9l
The evolutionof activegalaxies | 33
of the superippenkoof the Universityof Californiaat Berkeley.His opticalobservations novawhich explodedin the spiralgalaxyNGC 4615 duringMay 1987producedsome line profiles.He ascribedthe profilesas beingpeculiardue to the dustyenvunexpected ironmentin whichthe staractuallyexploded,but he wenton to saythat ifthe supernova hadtakenplacein thecentralregionofthe galaxyit couldeasilyhavebeenmisclassified modelis a big mistake;it must asa Seyfertnucleus. Obviouslythen,to ignorethestarburst ofgalaxy types.The abun' in explainingthe grandcornucopia havea ptacesomewhere danceof heavyelementsin quasars,the ubiquitousnatureof the IRAS galaxies,eventhe simplefact that galaxieshavestarsin them,point to starformationandstarburstsasbeing of intensecosmologicalinterest.For instance,we still do not know when,in the life of a galaxy,the first starsform, havebegunto regardsomeof With furtherstudy,an increasingnumberof astronomers of starburstactivityandactive IRAS galaxiesas beinga combination the ultraluminous galacticnuclei. 324 IRAS galaxiesare classedas ultraluminousbecausethey have farStudyof theseobjectshasrewhichexceedl0r2solarluminosities. infraredluminosities vealedthat all showevidenceof interactionandmerging.Althoughthis is boundto causc maintainthat,whenthe emissionat differentwavcan intensestarburst,manyastronomers Somc lengthsis compared, the'colour'ofthegalaxyis moreAGN-likethanstarburst-like. studiesof the ultraluminousIRAS galaxiesArp220 and Markarian231 havealso shown intenselycompactinfraredemissionsourceswhighareprobablytoo smallto be starbursts. are beginningto realisethat activeand The continualstudy meansthat astronomers other peculiargalaxiesare perhapsnot as simpleas was once thought.There are now severalresearchgroupswho postulatethatthecentralengineofan activegalaxyis a black hole surroundedby an accretiondisc, a BLR, a dusty torus and a NLR which is then surroundedby a starburst!As well as the htropreviouslymentionedultraluminousIRAS of its specCertaincharacteristics galaxies, IRAS Fl0214+4725is an excellentexample. trum indicatethat it is a starburst,whilst othersstronglypoint towardsa black hole.The objecthasbeensimulatedby David Clementsof the Universityof Oxford usingoneof the by a starburst'models. hybrid 'dust-enshrouded blackholesurrounded 6.9 THE EVOLUTION OF ACTIVE GALAXIES The importanceofactive galaxiesin the studyofthe youngerUniversecannotbe overstated.Eventhe HubbleSpaceTelescopestrugglesto seegalaxiesat redshiftsgreaterthan oddl, whilst quasarsburnbrilliantly at redshiftsof 5 andmore.A peculiarobservational ity of quasarsis thattheir densityappearsto peakat aboutredshift2. This oddity wasfirst pointedout by GeoffreyBurbidgein 1967,but it is not knownwhetherthis peakis realor the effectofour cunentselectioncriterionand stateoftechnology.Ifit is actuallya real peakit could be interpretedas being strongevidencefor the evolutionarynatureofthe Universeasprovedby the changesin the objectsit contains. Astronomersarecurrentlygrapplingwith the basicproblemof how the IRAS galaxies andthe activegalaxiesarerelatedto the normalgalaxies,Justwhendoesa normalgalaxy becomenormal?Are somegalaxiesbornnormalandothersbornactive,or do all normal galaxiesgo throughan activestageaspart oftheir evolution?Candormantactivecoresbe turnedon again?
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In ordcr to answcrthcscquestionswe have to take one more step towards the edge of the Univcrseand.journcyinto the astronomicarlvirderness where garaxiesform.
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'fo our advantage in this questis lhe factthat the galaxiesare groupedinto clusters whichprescntus with ready-made laboratorysamplesat differentredshifts.As a brief aside,it is irnportant to remember duringthesediscussions thatthe redshiftscaleis not actuallya linearone,so eventhoughredshift0.1 soundsverycloseby it actuallyencompasses a colossal volumeofspace(seeFig.7.1). To drawan analogywith starclusters: thesecomein two distincttypes,openclusters andglobularclusters.Both containstars,yet arevery differentfrom oneanotherin terms ofage,evolutionary historyandposition,in our overallunderstanding ofthe cosmos. All of thesethingshavebeendiscovered simplyby takingthat first stepandclassi0ingthe starclustersby their morphology. Similarlywith galaxies,as we shallseelaterin this chapter, theirpasthistories canbe inferreddepending uponwhetherthesystemis spiralor elliptical. with this in mind,the classification of a galaxycluster,baseduponits shapeand its content,may be the first steptowardsunderstanding how it, andthe galaxieswithin it, formed.In the 1950stwo astronomers beganto compileindependent catalogues of galaxy clusters. GeorgeAbelltookashisdefinitionofa clusteronly thebrightestanddensest of aggregates, whilst Fritz zwicky set aboutdefiningeveryconglomeration no matterhow smallor how sparse.ln the end,Abell's catalogue ofrich clusters,publishedin 195g, contained 2,712members, whilstZwicky'smorecomprehensive catalogue listed9,134 galaxyclustersandwaspublishedoveran eight-year periodfrom 1960to 196g.In the courseof their efforts,both astronomers realisedthat galaxyclusterscan be classified according to theirappearance. Abellthoughthisbifurcated intoregularandirregularclusters,whilst zwicky felt that a bettersystemwasto classif accordingto the densitiesof galaxies, i.e.compact, mediumor openclusters. Virtuallyconcurrent with theseworks,william Morganwasstudyingthe contentsof galaxyclusters.He determined thata clustertypecouldbe definedaccordingto which I-lubble typeof galaxywaspredominant. His initialworkallowedhim to definerworypes of cluster.The virgo clustertype,namedaftertheprototype,is onein whichthe majority of galaxiesarespirals.only a few of the very brightestmembersof a Virgo-typectuster are ellipticalsor'Jenticular galaxies.The brightestgalaxiesin a Virgo-typeclusterare concentrated towardsthe centralregionsofthe cluster.Morgan'ssecondtypetook as its prototypetheComacluster.In exanrples ofthese,ellipticalsandlenticulars predominate amongthe brighterclustermembers. Whatfew spiralstherearetendto be confinedto the muchdimmerclustermembers.Accordingto his studies,the majorityof nearbyclusters wereof theComatype. Morgancontinued hisworkon definingtheclusters by examination of thegalaxies they contained. In 1964he showed,with thehelpof rhomasMatthewsandMaartinschmidt, that a relativelycommonfeaturein someclustersis the presence of one exceptionally large,luminous galaxyat thecentreofthe cluster.Theyareso largeanddiffuse,however, that despitetheir relativelylarge luminositythey actuallydisplaya low surface brightness. TheseweretermedcD galaxies where'D' denotes diffuse. The.c' wasusedto indicatetheluminousnatureof theobject,in thesamewaythatthis letterwassometimes usedasa spectroscopic designation for superluminous stars.Manysimplyremember it as standingfor'clusterdominating'galaxy.By continuing to analysethe ubiquityof these types,Morganandhisnewco-worker, LauraBautz,introduceda classificationscheme
schemcfor gelaxyclusters 137 The Rood-Sastryclassification
Sec.7.21
galaxofbright clusterdominating or absence whichrelieduponthepresence for clusters a galaxy resembling giant galaxy binary or a cD of a single ies.A type I clusterconsisted dumbbell.Type ll clustersaredominatedby two or threebright galaxies'whilst a type lll hasno particularlydominantgalaxy.
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Fig, 7.1. As studied by Hubble and Humason,the redshift of a galaxy appearsto. b-elinearly pr6portionalto its distance.This diagramshowsthe relationshipbetwcenrcdshiRand distance.
7.2 TH.EROOD-SASTRY CLASSIFICATION SCHEME FOR GALAXY CLUSTERS
Two differentmethodsof classiffingclustershadthereforebeendevised:the morphological systemsof Abell and Zwicky and the contentscriteria usedby Morgan and Bautz. Whatwasneededwasan interpolationbetweenthetwo to seewhetherclustermorphology influencedclustercontents.This work wasperformedby HerbertJ. RoodandGummuluru Rood in 1971.In an attemptto reconcilethe two approaches Sastry,andwaspresented of the the brightestl0 to 20 membersof the andSastryanalysedthe spatialarrangement typeofgalaxy.By so doing,theycouldidentiff six typesof clusterandthe predominant cluster(seeFig.7.2). by a singlelargecD galaxy,a slightlysmallerandless A cD clusteris onedominated of the luminousD galaxyor a giantellipticalgalaxy.Whateverthe preciseclassification
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ccntt'algalirxy,itt orrlcr lirl tlrcclustclto lre of this t1,peits centralgalaxymustbe at least threetintcsbiggclthirrrits rtcarcs( rival.-l-hleesub-groups arealsopossiblebaseduponthe exactar)r)cararcc.r'thc cr) gal.xy. A cD" galaxyis onewhich hasa satellitegalaxy visible within its Iaint.outercrrvcr.pcolstirrs.A cD,,garaxyhas a peculiarfeature]suchas a jcr or a tail or a skcwcd or c'verope.A cb'galaxy dispiaysrnultiprenuclei,arthough caremustbc takenlo'ucrcus lnakesurctltattlreobservation hasnot beenthe iesult ofother foregroundgalaxicsgcttingin thc way. 'l'ltenrembers of a cD clusteraremainlyellipticalsand lenticulars. A B type clustcris donrinatcdby a pair of garaxies,both of which are at reastone magnitudebrighter than any othe' cluster member.They must also be separatedby less than ten times tlre diarnetero| eithergalaxy.In trrecase of the subgroup,Bo, they are joined togctherby a lurrrirrous bridge of nraterialor even sharea .on..on envelopeof stars. l'his latter situatio. gives rise to the clurnbell-shapecl galaxies noted in the Bautz--Morganclassification scheme. The tlrird type of clusteris thc c type, or core-halocluster.'l-his corlsistsof several bright galaxiesofany type which constitutethe core. 1'hey are then surroundedby many more faintergalaxieswhich nrakeup the halo. L galaxyclustersare sinrilarto the c lype exceptthat instcad ofthe bright galaxies beingconfinedto a core,they arespreadout in a line.The faintergalaxiesarJsometimes found to Iie within exterrsions of theselines,whilst in other examptesttreysimple surround the brightgalaxies.A subgroupis denotedL", rvhichmeans thaithe bright galaxieslie in an arc ratherthan a straightline. F type clustersappearflattenedor elongatedon the sky. Theseclustersare not dominated by any bright galaxies,however,and the crustermembers are predominantlyspirar and lenticulargalaxies. The final classificationin the l(ood-sastryschemeis the I type (irregular)cruster. Theseare not dominatedby any galaxy,and appearinegularly spreadacrossthe sky with no centralconcentration. In examplesof this kind alnrosteverysingleclustermember is a
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n-
Sec.7.21
for galaxyclusters I 39 classification scheme The Rood-Sastry
spiral galaxy. Subgroupsare I" for a clusterwhich containssub-groupingof galaxics throughoutits volume, and I, for clustersrvhich show no concentrationswhatsoever. Having identified these six different types of galaxy cluster, the first tbing to noticc about them is that the morphology affects the content.For example,cluster types B and cD are predominantlycomposedof ellipticals,whilst I and F clusterscontain mainly spirals. C and L clustersappearto be intermediatein galaxy populationbetweenthe two other pairs.The differencein galaxy type also meansthat clusterscontaindifferent stellar populations. Ellipticals - and thereforethe clustersin which they predominate- contain old stars,whilst spiral-richclustersare populatedby young stars.Is this a clue that perhapsa cluster's type signifies its age? If we assumefor a moment that I and F clustersare thc youngestand that B and cD clustersare the oldest,then it would thereforeseem logical to place them in an evolutionarysequence. This evolutionarypicturehas beenbroadly substantiatedby both observationand thc
1 4 0 T h e f o r m a tio n o f g a la xie s
lch. 7
alwaysfound at, or very closeto, lhe centreofmass ofclusters, are thoughtto have grorvn to such huge-sizesbecausethey have repeatedlycannibalisedsmaller galaxies.In fact, thoseexampldsof the multiple nuclei cD galaxieswould appearto have beencaughtin the devouringprocess! So are irregular,clumpy spiral-richclustersrcally youngerthan the denser,ellipticalrich collections?Although it is true that clustersat higher redshifts appearto contain a larger proportion ofspiral galaxies,the availableevidencewould, in fact, appearto disavow this simple interpretation.Clusterformation, rather like galaxy formation, is something we haveyet to conclusivelyobserve.In fact, one of the questionsthat we will go on to consideris whetherclustersformed first and then fragmentedinto individual galaxies, or whetherfully formed galaxieslateraggregatedinto clusters.Whateverthe preciseformation scenario,it would appearthat the majority of a cluster's aggregationof mass has taken placeby a redshiftof 5. In other words, galaxy clusterformation takesplace within a few billion yearsof the Universe'sbirth. So if the clustersare all approximatelythe same age,then the Rood-Sastryclassificationmust also be a pointer to the initial conditionsof the cluster. This is becausethe other factor which we have stated has the most eflect on the dynamicalevolutionof a clusteris its density.The greaterthe concentrationof matter, the higherthe likelihood ofgalaxy interactionsand hencethe fasterthe clusterwill evolve into a cD or B type. So insteadof indicatingthe ageofthe cluster,its Rood-Sastrytype can actuallybe used to infer somethingthat, cosmologicallyspeaking,is far more important.We can gaugethe initial density of that region of space.Thus, the three-dimensionaldistribution of galaxy clusterscan show us the architectureof the cosmosat a time when the Universewas less than one sixth of its presentage.
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7.3 THE LYMAN-a FOREST The spectrum of the hydrogen atom was investigated by American physicist Theodore Lyman in the first two decadesof this century. Specifically,what he was investigating were those electron transitions which ended or originated at the first energy level. The brightest of these became known as the l.yman-cr line, which occurs at a wavelength of 122 nm in the ultraviolet. The value of the Lyman-a line soon became apparent after the discovery of quasars.Their great redshifts mearrthat the light we receive from them at visible wavelengthshas usually originated in the ultraviolet region of the spectrum.The Lyman-c emissionline will be visible in the optical part of the spectrumfor any quasar witharedshiftgreaterthanl.?.Observationsofthesespectrasoonrevealedanotherinteresting phenomenon.Shortward of the (usually) large Lyman-a emission line is a plethora of absorptionlines. This forest of lines cannotbe due to absorptionin the quasaritself, becausethey are all Lyman-o absorptionlines spreadacrossa rangeofsuccessivelylower redshifts.Instead,it is thoughtthat this absorptionoriginatesin interveningclouds ofhydrogen gas which exist along the line ofsight betweenus and the quasarin question(see Fig. 7.3). This being the case,the Lyman-o,forest in a spectrumcan be a very sensitive indicatorofthe distributionofhydrogen gas in the direction ofthe quasar.It can be used to determinethe redshiftsat which thesecloudsexist and. in certaincaseswhere the lines are well defined, it can be used to estimatesome of the cloud's properties;its mass,for instance.The ozone layer of the Earth limits us to observationsof the Lyman-o lines
1
The Lyman-crforest 14|
Sec.7.3l
Posltions of hYdtogan cloudg h8ve b€en Inferrod from the aoacirs ol both quasats'
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(bt in Fie. 7.3. The optical spcctrumof a quasarmay show a largenumberof absorptionlines r".n,itiion linis. In thisspectiumofthe quasarPKS2126-l58 (a) canbe seendozensof the "a.6ition narrow ausorptionlines attributed to the Lymrn-d, line of atomic hydrogen,comprising :'ly.un-" forlst'. Tlreseare causedby multiple cloudsofintergalactic hydrogenlying-alongthe fin'. J,Gf,t bitr'ccn the qu'sar and the oblerver. (Adaptedfiom Audouzc,J., and lsrael, G., lincs Canbridie Atlasol Astroiomy,CambridgeUniversity Prcss.,1988.)(b) The absorption appearstirng out airossthe spictrum becausethc cloudsareall at diffe.entdistances.
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wlticll origirlllcritt clouclsat rctlshilissrrrallcrtlrlrr 1.7, becauseanythingwith a shorter wavclcngthrvill bc absorbcrl.l'he upperlinril oftheseobservations is obviouslydictated by tlrc distanccs of tlrc individualquasarsbeirrsstudied. Analysissuggcststhat a hydrogencloud bccornesmore nrassivewith increasingredshili, presumablybccauselessofit hasbeensubsumed into starsand galaxies.The enrichmcntof the intcrgalactic ntediunrwitlr heavyelerncnts is somethingwhich appearsto have happenedearly. As rnentionedin chapter6. quasarsat high redshiftsshow lines due to ntetalsin their spectra.Other ntetalabsoqrtionlines in spectraindicatethat at leasra generationofstarshaslived and died in the youngtJniverse. This raisesan interestingideain which someastronomers believe. Traditionally,starsare split into two generationsknown as PopulationI and population It. A PopulationIl star is one which evolved rvhenthe universe was young. lt has a low metal contentand is now very old - usually around l0 billion years. A population I star is any star which has fornred subsequentto thc enrichmentof the Universe with metals fronr the dead PopulationIl stars.Sotneastronomersfavour the formation of a primordial populationofstars which appearedvery soonalier the decouplingofmatter und -fhcsehavebeendubbedl)opulationill starsanclwould "n.rgy. be compoiedof virtuallynothing but hydrogenand heliurn. Someofthe high redshiftLyman-o.lines havebeenobservedto have associatedcarbon lcatures.This would appearto favour an interpretationin which a generationofstars has lived and died in the early [Jniverseand has seededspacewith heavierelements.Another possibleexplanationis that the Lyman-crcloudsthemselvesare presentin star-bearing galaxies.corroborating this view is the fact thzrtsome of the Lyman-o lines display the characteristics of being producedby rotatingcloudsofgas, which might possiblybe spiral galaxydiscsin the processoffornration. At redshiftsof lessthan I.7, directobservations haveshownthatmostof the gaswhich wils once strewnthroughoutintergalacticspacehas now beenconfinedto large spherical lral.s aroundgalaxies.Thesehaloslie within a radiusof 40 kpc from the galaxynucleus. 'l lrc (Jniverschas therelorechangedfrom its ncarly homogeneousform, as indicatedby llrc trticrowavebackgroundradiation,into a very unevenlydistributedcollectionof mass (llitllxics and clusters)which is homogeneous only on very largescales(seechapter3). 'l'lrcschalos ofgaseousrnaterialappearto be alrnosttotally independentofthe properties ol'tlrc galaxicsthey surround.The only weak dependence is on the massof the galaxy. 'l his would secmto be ratherclear evidencethat the halo is producedby infalling gas lirllrorthan outflow fi'om thc galaxy itself. This infalling matter may be the final stagesof pillaxylbrmationitselfand be an essential ingrctlientin keepinga galaxyfuelledwith star Iirrrningrnaterial.
7.4 'I-IIE EVOLUTION OF GALAXIES sooncror later,despitcall thc constraints and tlrcories,the only way oftruly understandirrg galaxy formation is to observe it. In orlcr to clo this, astronomersmust peer ever dccpeririti the cosmos,searchinglor ever-fairrlcr objects.As theyhavedonelhis, so it has bccomeobviousthat the appearance ofgalaxicschangesrvith redshift.ln 1960,Rudolph
Sec.7.4l
The evolution of galaxies
I 43
Minkowski crowned his astronomicalcareerwith a discovery made on his last night observing with the 200-inch telescope at Mount Palomar. He discovered the most distant galaxy then known. It was the optical counterpart of the radio galaxy 3C 295, and possesseda redshift of 0.46. Although this is not large by today's standards- radio galaxies are now known out to redshiftsof 4.25 * when comparedto the Coma cluster at redshift 0.023 and Herculesat redshift0.036, it was a massiveleap outwards. The most obvious feature of 3C 295 was that it was very red in colour. This is not too surprising, as elliptical galaxies, on the whole, contain old stars ofspectral types G and K. These stars are yellowish-red in colour and so the galaxies which contain them arc yellowish-red in colour. 3C 295 had had its spectmm redshifted by 46 per cent and so harl transformed most of its yellow light into red light as well. With little blue light to bc redshifted into the yellow part of the spectrumthe galaxy ended up looking very red. Over a decade later, when astronomershad discovered a sufticient number ofgalaxies at this kind ofredshift to be able to distinguish individual clusters, they began to apply corrections to the spectra,in order to compensatefor the cosmological redshift. To their surprisc many of thesedistantgalaxies,including the ellipticals,showedup to be rather bluer lharr expected.Even the clustercontaining3C295 was shown to contain an abundanceofbltrc galaxies.It appearedthat theseelliptical systemswere not as old as those in the prescnlday cosmos. Some were obviously being caught in their final acts of star formation as signified by the blue light from young, massive stars. Sincethen,the study ofhigh redshiftclustersofgalaxies has continuedto advancewitlr the inventionofnew technologies.Ofthe availableimagestoday, the best have beentakcn by the Hubble Space Telescope. Ground-basedobservations are hampered by the atmosphere; the angular size of distant galaxies is so small that atmospheric effects wash oul any detail. The only analysispossiblehas beenphotometricand spectroscopic. The first tantalisingimagesto be returnedby the orbiting telescopewere of the clusters CL 0939+4713in Ursa Major and CL 0024+1654 in Pisces.Both clustershave redshifts of 0.4, which correspondsto a look-back time of about 5 billion years, if we assumefor the momentthat the Universehas an age of l4 billion years.The imagesof the two clustcrs containedseveral hundred galaxy imagesand were inspectedby Alan Dressler and his co-workers.They discoveredthat the morphologiesof these galaxies were identifiablc with the Hubble classificationsseenin galaxiesin the presentday Universe. This was at once a significant and surprising result. It meant that the galaxieswhich populated tlre Universewhen it was two thirds of its presentage were highly developedobjects.1'hcrc were differences,however, which were every bit as significant as the similarities. l'hc clusterCL 0939+4713containsmany more spiral galaxiesthan clustersof today (see Fig. 7.4). Not only that, but the spirals were nearly all peculiar in some way or another.'l'h(: question of what was producing the peculiaritiesremains slightly perplexing. At first it seemedlikely that the galaxieswere still forming, but closer inspectionof the imageshas led to the conclusionthat the density of the cluster is probably pulling them apart. Ccr' tainly, some mechanism is responsible for the depletion of spiral galaxies in the dense clusters during our presentepoch, and gravitational interaction would scettr one of the best candidates. The only other possible mechanismis that hot gas in thc clusterhas strippedthe star-forminggas from the spiralsas they havetravelled aroundtht: cluster.
:-1
144 'l'he formrtion of galaxics
lch. 7
Sec.7.41
Theevolutionofgnlrxies 145
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llt l:ig. 7.4.ThedistantgalaxyclusterCL 0939+4713is locatedin UrsaMajor at a distance of about 5 b illio n lig h t ye a r s.It co n ta in ssp ir a lg a l axi esrvhrchl ook a l i ttl e l essdi sti nctthan thos€ in the present-day Universe,but the ellipticalgalaxiesare virtually identical.(Photograph reproduced andNASA,/Space Telescope Science courtesyofAlan Dressler, CarnegieInstitution, Institute.)
The resultsalsoshowedthattlie galaxiesin Dressler's two distantclusters weremuch bluerthanthoseof today.In otherwords,starformationwasa muchmoreprevalentactivity 5 billionyearsago.ln theclusters examined, thebluegalaxieswerealmostinvariably thepeculiarspiralgalaxies. UsingtheHST, RichardEllis anda teamof UK astronomers probedanotherclusterat a redshiftof0.3, anddiscovered thatmostofthe bluegalaxies thereweredisturbed whichwereeitherin theprocessof mergingor showedthe systems distinctive signsof interaction. On thewhole,theEllisclustercontained fewerspiralsthan the first two. This,combinedwith its olderage,suggests that it hashad moretime to dynamically evolvethanthefirsttwo. More surprises werein storewhenthe HST identifiedevenmoredistantclusters.Mark Dickinsonidentifieda clustersurrounding theradiogalaxy3C 324at a redshiftof 1.2 (seeFig. 7.5). This time, the clusteris representative of the Universewhen it was aboutonethirdofits present age.In thisstudy,hardlyanyofthe galaxies wererecognisableaspresentdayspirals,althoughsomeresembled edge-ondiscs.Apart from an abundance of disturbedandmerginggalaxiesandfragments of galaxieswhichwere strewnaboutthe clusters, thebiggestsurprisewasfindingmatureellipticalgalaxies. Analysisofthese objectsrevealedthat they wereessentiallythe sameas their counterpartsin the modernUniverse. Theycontained old, maturestarsanddisplayedno hint of ongoingstarformation.
all.d,istanceof9 Fig. 7.5. This galaxyclusterin Serpens,aroundthepeculisrgalaxy3C a2l.li:l biiiion light y;ars and containsspiial galaxieswhich bearvcry littlerescmblTg:-1" g:lt-?:T""u (Phorogaph a"y cou"nteipatt..The elliptical gi'laxies. however, arc rcmarkably similar. Scicncc ,.ir"Ju".O'.ourtesy of Mark Dickinson, STScl, and NASA/Spacc Tclcscope Institute.)
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TeleAt the time of writing, the most distantclusterdiscoveredby the Hubblespace Locatedat a ,.of. i, in sculptorandlies in front of the quasare0000-263(seeFig. 7.6). yearsafterthe reasniftof 3.3, ihe clusteris seenas it existedonly t.5 billion to 3 billion present galaxy of types the between distinction the distance, sig Bung,At ihis incredible increasbecomes (about14 individualmembershaveso far beenidentified) in it . ofa "tirt"r Oneinterestinggalaxy,however,appearsto displaythe characteristics ingly blurred. yet on consfraints tightest provide the will it confirmed miture elliptical. If this resultls gd*vr"n"ution(seeFig.7.1)'Fortheel|ipticaltobematureitmusthavecondensed takesat leastone f,o,o tt. intergalacticmeaium,a processwhich accordingto theory popsubsequent any ofstars; firstpopulation its billion years.Ilmust thenhavegenerated the only to leave exploded stars mass its high and ciased ulationbeforestar formation wh-ilstnot impossible' its redshift, by indicated as cluster, the of age The stars. red older (after first allowing leavessucha short time for the galaxyto evolve as we observeit have astronomers some that to decouple) Universe ihe years for approximately300,000 galary formationwas process of the that indication an it as view Others becomenervous! gravitationalcollapse, not a slowone.As soonasthe Universewascapabteofundergoing
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P rotogal ax y c andi dates 147
feature appearedlike an incredibly distant l,yman-crsystem.Subsequentspectralobservations of the quasar revealedthat light wai not only being blocked by hydrogen but by other elementstoo. Metal absorptionwas found in the spectrumat the sameredshift as the hydrogen.This instantlysuggestedthat the hydrogenwas not simply an inert cloud ofgas, but that it was just beginningto show the effectsof star formation. Perhapsit really is a protogalaxy.An analysisof the strengthsof the spectrallines by Limin Lu and co-workers of Caltech, shows that the chemical content of the protogalaxysuggeststhat stars havc only beenforming for a few tens of millions of years- a baby in galaxy ternrs! 'l'he optical identificationof this object remainselusive,however.Following thesctantalising glirnpsesinto the spectrumof the quasar,astronomerswanted to try to obtain irn actual image of this protogalaxy.The absorptionlines were like seeing its shadow: norv astronomerswantedto look it straightin the face. A picture taken by the Keck lO-metrc telescopeon Mauna Kea did indeed revcal a faint, diffuse object,two arc secondsaway lrom BR 1202-07.It looks superficiallysirnilar to the young galaxy near the quasarQ0000-263 in Sculptor.An initial analysisshowcd it to possessthe correct wavelength dependence,but successiveobservations have cast
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Fig.7.6.ThemostdistanrgalaxVch5tl rm1qeg.99 far by rheHubbleSpaceTelescope is located In sculptor'and lics at a distance.of aboutl1 billion ligit years.rne inoiviouaijal'o*i"r'in *,is crustcraredifficurtto distinguish. butsorneof thc vi.sibt"-t;ng"ntsappear rikeryto become spiral galaxies. Onceagain.howcver.thc ejlipticalsarevcry sinrilar to rtieirprcseni-Oal] npp.u*,r.". (Photograph reproduccdcourtcsyr)t.lluccio Macchcti,.tSrySfS.t. iV","" Cl,""jir_. 'l'clcscopc NASA/Space Scicnccl;rstitutc) ^",f
7.5 PROI'OGALAXY CANDIDATI'S one of the most interestingobjectsin the image around e0000 -263is agaraxyseenvery closeto the quasar.It is rerniniscent of an objectrvlrichmay be the moidistanr nascent galaxy cver observed.1'he quest for protogaraxies is one of the hardesttasks in modern astronomy.It is a blurry definition at best. In steilar astrophysicsa protostarcan be defined as any young sterrarobject which hasyet to begin rusingrryorogeninto iretiumat irs centre when doesa protogaraxybeconrea galaxy?when it beginstJsnine with starlight, perhaps.what then distingLrishes a cloud of hy,rrog.n gas from a protogaraxy?Despite thescvagariesofternrinorogy,one thing is certain:piotogalaxies must be faint. .fhis, conr_ binedrviththeirexpectecr grcatdistanccs, makeslhc.rrr very ditficurtto observe. of trrc quasarI)ri. 1202-07,rry a tcarr of astronomers rcd by Sandro ^.obscrvations D'odo'ico, revealedan intercstingl'cature.'fhe qrrasar's spectrumposscssed an absorp_ tion line at 654'5 nm' the propertiesof rvhichsirgilcsted that there is a nrassivecloud of h yd rog enat a r eds lr if tof 4. 311."l' hc quas a r i t s " t t 'e x i s t s a t a r e d s h i l - to f 4 . 6 9 . T h i s
l;ig. 7.7.(ialaxysnapshots throughtirnc.( onrparingthe variousgalaxiesin Figurcs7.4. 7.5 and 7 6 allorvsastronorners to run an evolutionarysequence, in orderto dclerminchorv galaxics evolvethroughtime. (Photograph reproduccd courtesyof A. Dressler(CamegieInstitutionsof Washington),M. Dickinson(STScl),D Macchetto(ESA/STScI),M. Giavalisco(S'l-Scland NASA"/Space Telescope ScienceInstitutc. )
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doubton its idcrrtilicatiort rvith tlrr:absorbirrg An infrareclinragetakerrrvith 1r'rrtogalaxy. the Univcrsityof Ilalvaii's2.2 nrctt'ctclescoprc rilrorvs it to possess the sanreredshiftas IIR 1202-07,and a l.lublllc Spat;e-['elescopeiurrgc of the objects suggeststhat the 'protogalaxy'wasacluallyno{llingnroretharrir r:loudof gas,sub-galacticin size,illurninatedby the nearbygalaxy.So rvltereis the trr.reprotogalaxy?lt rnustbe there somervhere becauseof the absorpl.iotr lincs in tlte cluasar's spcclrunl.Astronomersnrrrstsirnplylook harder. Searclres lbr protogalaxics can alsotaketlro lbrnrof searchingat specificr.vavelengths. Fol cxatnple,a protogalaxyrvhichis fornringits llrst generationof starsrnustbe heavily Iadenrvith hydrogengas. 'l'hc srrperrnassive stars.,vouldionisethe gas and make it glorv, andthe galaxywoLrldtakeott the appearance of a lnassiveemissionnebula.If this were to occur itr an objectat the distalrceofthe quasars, the light fi'ornthe ionisedgas rvouldbe redshiftedinto the ttearirtfiarcrlportionofthc clcctronragnetic spectrunr. llsing this rationale,MatthewA. Malkan and colleaguesidcnrificda potentialprotogalaxyon the Sextalls l,eo border.lt is at a rctlslri{'t of 2.5, so is lrot as far away and difficult to study as somcol'theotherprotogalactic candidates, and it displaysthe hallnrarksofa younggalaxy systemby havingexcessive lrydrogcnand nitrogcncrnissiorrs. Astrononrers arc anxiously awaitingits more delailccls1.lectroscopic study_ 1-hedeepestever view of thc ljniversehas also beensuppliedby the t-lubbleSpace Telescope(seeFig.7.8 in the coloursectionbetrveen pagesI l4 and I l5). Known as the Flubble Deep Field it rvastakcn try the orbiting telescopebetween l8 and 2g Decenrber 1995,as it peeredat a tiny'keyhole'areao1'rlrctJrriversejust abovethe plough/BigDipper star pattern.lt is a conrpositeirnageol 342 separateexposuresof this same field of vierv and has been irnageprocessedto revcal incrr:diblyfaint galaxiesof about apparent magnitude30 (4 billion tinrcslaitttcrthanhurrarrscanseewith the nakedeye).'I'heirnage containsat least 1,500galaxies(recentestimalesplace the figure over the 2,000 mark) at variousstagesoftheir evolution,antl nrayprovc 10be the RosettaStoneofgalactic astronomy. Many astronomytearnsaroundthe globe ar^enow working on the complex analysis which will makesenseof the data in this irnage.One of the first tasksis to deterrninervhich galaxiesin the imageare nearbyand which are far a*'ay. spectroscopyofall 2,000 objects using curent technologyis not possible,and sr.rastronomelsare having to rely for assistanceon the photometricdata responsiblefor nrakirrgthe colour image. Assumingthat the mnre clistanta galaxy is, the redderits colour will be becauseof the redshiftand the faintel'it rvill be, a tearrrofastronontersled by Kennetl'tl,anzettaissearching part ofthe irnagefor distantgalaxies.They have found six galaxiesrvhich appearedin the near-infraredplates but rvlrich failed to shorv up on the shorter r.vavelengthimages. This is a strong clue that they are distantobjectsrvhich have beenseveiely redshifted.In fact, they appearto lie at redshiftsf-al in excc-ssof 5, beatingthe recorclset by the most distantquasars.The resultsare,as yet, unconfirnredbut the infraredcamerarvfiichwill be fittedto the HubbleSpaceTelcscopeduring 1997rvill enableastrononrers to look at these distantgalaxiesin unprccedcrrtcd tletail. 7 .6 FAINT BI , UE G AI , AXI I iS Wh ilst ga lax yf t r r t t r at ionis t r ar lilior r lllyI hor r i r l r1l o h a v et a k e l p l a c e i r r d i s t t r r rrtc a l r ; s , som0astrononlcrs havc trrrncrlllr,:irattcntiorrto ,.liqlrtlyclo:;orrcgionsu,itlrthr:lropethat
Sec.7.61
Fai nt bl ue gal ax i es l 4tt
answersmay also be found there.One reasonfor this is that the adventof sensitivedclcrrl' ors and telescopeshas not only allowetl us to probe further into the Universe but has itl:itr given us the ability to make much nlore complete surveysof our more immediatc strrl oundings.The Medium Deep survey on the Hubble space Telescopeusesthe wirlc Field/PianetaryCamera2 to take a photographofthe sky wheneverone ofthe llubblc's other instrumentsis observing.In this way, a random survey of the sky is made possiblt: ()rrt and does not interferewith the more specific observationsthat the HST has to makc. of about fifty random snapshotsa grand total of tens of thousar$sof galaxieswere idcrtti fied. Of theie a very large number were faint, blue and in:ef VAr in shape(see Fig, ?.() irr /objects detail showed thirl in the colour section).Follow-up observationsto image these faint blue galaxies,as they were termed, are probably the most ubiquitoustype of galaxy in the Universe.There are so many of them, in fact, that if our eyeswere sensitivecnotrglr we would be able to detect a faint, blue backgroundglow from them acrossthe wllolc night sky. They seem to predominatebetweendistancesof 3 billion and 8 billion ligltt years,Uut are incredibly scarcein the tJniversetoday. Obviously the star formation whitrlr or, perhaps,the galaxics iistinguishedthem in their earlyexistencehasbeenextinguished themselveshave been subsumedor dissipatedby interactionswith others. Another form of galaxy which has come to the forefront of astronomcrs'attcntionsirr the past ten years has been the low surfacebrightnessgalaxies(LSBs). A lew far-sightctl astronomershave cautionedagainstassumingthat galaxiesonly take the forms secn in lllc presentday Universe. For instance,in the 1930s FritzZwicky suggestedthat thc cnsilv observablegalaxiesmay only be a sub-setof the total population.Halton Arp also ntatlc it similar comment in the 1960s,when he assertedthat the galaxieswhich were known lo exist actuatlydisplayeda very narrow rangeofproperties and that, perhaps,otherswith ir rnuchwider parameterbasewere out there,awaiting discovery.In 1986,worltl renowncrl David Malin noticed that as he usedphotographicamplification nrclhastrophotographer ods on his image plates he could detect faint galaxies"everywhere"' Analysis of onc ol theseblobs by chris Impey and Greg Bothun showedthat it was about 700 million light yearsaway and about six times the diameterof the Milky Way! Its masswas about twcnly times that of the Milky Way, and unquestionablyMalin l, as it was called, was the largcsl spiral galaxy so far discoveredin the Universe (seeFig.7.l0). Why then was it so laittt'i Itjust did not seemto want to form stars.It containedso few starsthat ifit were replacc(l at the position of the Andromeda galaxy, 2.2 million light years distant, it would hc llrc width of 40 full Moons, yet we would hardly notice it was there. Its lack of stars is srr pronouncedthat it would only glow at a feeble2 per cent brighter than the sky. A survey undertakenin l99l by Impey and co-workers revealed 500 previously tttt known low surfacebrightnessgalaxiesin an equatorialstrip of the sky. All the galaxi*; discoveredwere within the distancerange of 200 million to 400 million light years. Srt many were there,in fact, that if this trend is continuedthroughoutthe Universe,the galaxv by 100 per cent! contentofthe cosmosmay have been underestimated ofa low surfacebrightnessgalaxy,UGC 6614,show conclusivcly Radioobservations thatthe galaxycontainsa vastamountofgas but, for somereason,it is not condensingirrlo stars.Theoreticalcalculationshavc shown that a low density gas disc may be stabl(: againstthe kind of fluctuationswhich lead to gravitationalcollapse and star formatiorr' Certainly, as far as gataxy formation goes,the denserthe initial cloud the fasterthe collapsewill proceed,so perhapslow surlacebrightnessgalaxiesare simple galaxieswhiclr
;l
;
1 50 'l ltc t ir r r nr liorol r g; r llr r ies
[ C h .7
havclitkcttltlllcll lt)lrllctlo ltrlrr llrarrlhc olhofsl)ccause they originatcrll.rornlower clclslty 8 asc lot t ds ll s o.lhc y olli: r ' llr cLr t r it lLr c p o l t u n i t yt o s t u d ya g a l a x yi r r{h e p r o c e s so f op fo rrtrittir t r r . lf l,SI) galaxicsarc itttlt'c
S e c . 7 . 71
The as tronomi c alw i l dernes s l 5l
1 . 7 T H E ASTR ON OM IC AL WIL D ER N ESS T'he vast majority of the available evidencepoints to galaxy clustersforming before thc Universereachedan ageof 2 billion or 3 billion years.Speakingin termsof redshifts,thc most active region ofgalaxy and clusterformation thereforetook place betrveenredshills of 5 and 1,000. We have calledthis the'astronomicalwilderness'because we havc no direct observationaldata from this epoch of Universal history. In this realm we lrave to rely almost solely on theory. Remarkably,we can make progressand constrainour idcas about galaxy formation by simply consideringa few elementaryfacts about the Univcrsc: aroundus. ln chapter4 we introducedthe notion of the scalefactor of the Universe,R(t), which is an arbitrary measureof the size of the Universe and changeswith time. t. lf we takc ir known wavelength,1,, to be our scale factor, the ratio of this to its currently obscrvcrl rvavelength,l"o,gives us the factor by which the Universehas expandedsincc the timc ol the radiation'srelease.The redshiftequation(3.6) alsocontainsthis ratio so we can cirsily equatcthe redshift,z, with the expansionfactorof the Universe: 1
| + z,= i-9-
.,
1
'-1
;ll ;r' i
t.:' i
'
r,.' "'
tl:, t"'
i f'
'L ,
l i tg T- l 0 l hc discr tvcr yl) lr tcs ( ) l' lhe lor v sur licc hr r gl r l r r c s gal s ax y l r l nl i l | ( ar r o\\c ( l ) .'l hc l c l l Itattd inlage is-lltc ttnProcessctlplalc. \\'hilst lhc rir:lrt,lr;rrrrliriagc iras hccrl collrnsl crrhnurc,l t,l shrrv that Malirr I is ir lorv srrrrirccbriglrtncssgillJ\\ (t,hotographsnradc hy l)avitl NIalin lionr p l i rtcstaken with thc ( lK Scltnr idttclcscopc.Ar ig l tr _Ar r r tr r r l i an- Obs c r v ar or y .t
( 1. t ,
The quantity l+z is known as the spectralratio, and translatesdirectly into the expansiorr factorof the Universe.In otherwords, radiation from objects which possessa cosmological redshift of I originatedat a tinre rvhenthe Universewas halfits prescntsize, becarrst: the spectralratio is 2. llwe acceptthe common-sense assumptionthat, in order for a galaxy to form, thcrc must be enoughspaceto accoulmodate it, then we can set a maximum rcdshiftat whiclr galaxy fonnation can start.The averagediameterofa galaxy is about 20 kpc, and so for il galaxy to be able to form there must have beenat least20 kpc betweenthe protogalaxics At srnallerdistancesthan this, the galaxiescan no longer retain their identity as separatc objects. If we assumethat on averagethe distancebetweengalaxies in the present[.lnivcrse is about I Mpc, then we can use theseto representour scale factor measurenrcn(. Doing this meansthat individual galaxiescould not have formed before redshift 5(t. l,arger structuressuch as clusterswould have to emergeeven later.This does not mcan l() saythat the fluctuationsin density,which eventuallybecomeindividualgalaxiesand clusters, were not presentat earliertimes in the Universe.All we are assertingis that tlrc individual galaxiescannothaveemergedin their presentform until the Universewas larg(l enoughto accommodatethem. 'l'his assertionforcesus to considerthe morphologyof the fluctuationswhich grew irrto galaxiesand larger structures.For the moment we will not concernourselveswith thc physicalmechanisms responsible for the creationof the fluctuations;insteadwe shallsirrr. ply acceptthat they exist and chart their progressin the decoupledUniverse. We can be reasonablycertain from both theory and observationthat the collapse ol galactic structuresoccurred on all levels simultaneously.Thus, as stars are forming, so galaxiesare condensingand clustersare aggregating. There are subtletieswhich will bc discussedin the next chapterthat lcad to two different formation scenarios.Broarlll, speaking,however,evolutionof Universalstructureproceedson many lcvels.As rvehavt'
t:
ii {f. :i ;
1 5 2 T h e fo r m a tio n o f g a ln xie s
lch.7
seenthroughoutthis book, thc Universeappcarsto have begun in a nearly homogeneous state.Fluctuationsfrom homogeneitycan be chartedby consideringhorv the density,p, at eachpoint in the Universe,x. deviatesfiom the averagedensityofthe Universe,po: 6p(x) = o(*)- oo
(7.2)
A dimensionlessquantity known as the density contrast,6(x), can then be defined and usedto tracethe growth ofthe fluctuations.
u(-)=#
MV2
R2
(7.4)
whereG=6.672xI 0-rrNm2/kg, M ii themassof thevolumeelementunderconsideration, V is a measure of therandommotionsin thegaswhichareresisting thecollapse, andR is theradiusof thefluctuation. Usinga hydrodynarnic treatment of theproblem,themassat whichcollapseis unavoidable canbe derived.lt is namedthe Jeansmass,M,, afterthe distinguished astrophysicist JamesJeansrvhofirstderivedit: MJ
4l --/tl
3t
- t3 lnvt I
Voojn
expand.Therefore,in the region of fluctuations,the Universal expansionis slower tharl Iessdenseareas. Whilst in the linear growth regime, this slowing down is almost imperceptiblcat lir So much so in fact, that the diameterof the co-moving volume element,l"n,which cottl:rl the fluctuationcontinuesto grow at the rate ofUniversal expansion.Thus, its lincar tlirrl eter, l, at any redshift epoch can be given by
lsc=t+, (7.3)
whilst the collapseproceedsas a scale-independent process,the growth is said to be linear.This is a very slow processat first, fbr a rrumberof reasons.The first is that the initial fluctuationsare very small in size, as will be seenin the next chapter.The secondreason is that the expansionof the Universe acts to inhibit the condensationof the fluctuation. Condensationwill also be inhibitedby the internalpressureof the matter,which acts like a gas, in the fluctuation. If it were not for the expansionof the Universe, the growth would proceedat exponentialratesand there would be no linear growth phase. To determinethe masslimit which defineswhether or not a fluctuation will collapse gravitationallyrequiresa considerationofthe kinetic energyofthe gas presentin the fluctuation.This kinetic energyis producedby the expansionof the Universeand the intemal gas pressure,so by equatingthis with the gravitationalpotential of the fluctuation the criterion for collapsecan be quantified.If the kinetic energy is greaterthan the gravitational potential,then the fluctuationwill not grow. Insteadit will dissipateby behaving like a sound wave in the denseearly Universe.The borderlineoccllrs when both kinetic and potentialenergiesare equal. GM2
wil
S e c . 7.7 l
(7.s)
(t'
l As the fluctuation approachesthe non-lineargrowth phase,it finally accumulatesenorrr mass to be able to resist the expansionof space.At this point, the material conlairr' within the fluctuation begins to condense.The point at which the flrtctuationatt;ri enough gravitational potential to resist the Universal expansionand begin collapsirrl' known as the point of tumaround.This criterion for gravitationalcollapseusesmassiri defining quantity, and becauseit is impracticalto deal with all scalesof fluctuatiotr:r once,tliey are usually divided up by masstoo. 106solarmassesdefinesa fluctuationwlrr will becomea dwarf galaxy/globularstar cluster, l0rr solar massesdefines a galaxy' lr definesa galaxy clusterand I Orasolar massesdefinesa supercluster. Different fluctuationscalesreachtheirnon-lineargrowth phaseat different points irr I history ofthe Universe. ln the absenceofreal data, these turning points are dcfirrc,l arbitrarily setting 6(x)=1. The point at which the growth of most fluctuationsis tltorr, to have become non-linear occurred somewherebetweenthe redshifts of 100 to 5(t. though, in the presentday Universe, galactic structureson scalesof greaterthan tl ltl show evidencethat they are still in a linear growth phase.Hence, the formation ol'l;'' scaleUniversal structuremay not yet be complete. As soon as the non-linear phase is entered,the objects begin the headlong coll;,1 which leadsto the protogalaxiesand other objectsdiscussedin the earlier sectionso{ t chapter.The detailsof galaxy formation are still very unclear,however.The first irrrl'' ant questionwe have to try to answeris the order of formation. Did the galaxiesforrtr I and then aggregateinto clusters, or did the various large scale structures emerge first later fragmentinto individual galaxies? The origin of the primordial fluctuationsmust also be addressed.Where did thcy r , from, how were they formed, what was their behaviour during the very early llrrir' before the decouplingof matter and energy?In order to answerthesequestions,llrc , observationalevidenceavailableto guide us comesfrom the very edge ofthe obscrv, Universe itself. Locked up in the cosmic microwave background radiation ffay lrl answersto thesetantalisingquestions.
t
t t t t t I
t t t
;
This equationalso includesa densityternr,p. As soon as this massis achievedby a fluctuation, the region is destinedto experiencegravitationalcollapse.In the linear phaseofits growth, a fluctuationstill does not contain {he massnecessaryto prevent it from experiencingthe expansionof the Universe.lf one imaginesthat the rate at which the Universe expandsis governedby the densityofspace at eachpoint throughoutits volume, then 6(x) can be usedto detenninethe local velocity ofexpansion.The greater6(x), the more work the Universehas to do to overcomethe gravitationalpotentialat that point before it can
L L rl
,,7 tl
1 1 arl
'1 ''l ''l
;l''l "l ''l ''l
1 1
The glow from the edge Although the actual formation of galaxies is tantalisinglyjust beyond our observational reach,the fluctuationswhich eventuallybecamegalaxiesand clustersare availableto us. This data is accessibleto us thanks to our studiesof the cosmic microwave backgrounrl radiation.The photonswhich composethat radiationpresenta view, as far back as wc cirr possiblyobserve,using conventionaltechnology.Our joumey has finally brought us to llr(: faint glow which marks the edgeof the Universe. The redshift is approximately1,000from our point of view, and shows us the Univcrsc just 300,000 years after the Big Bang. 'the maelstromfrom which the radiation was scl free had cooled to about 3,000K - almost cold, consideringthat the temperatureof {hc Universe,at lessthat a secondin age had beenmany millions of K. As we observeit norv, it is a frigid 2.7 K. Chapter 3 describedthe cosmic microwave background as appearing like a thernral sourceofradiation. Having establishedthis as an observationalfact, and thereforeusing it as a constraintin our model of the Big Bang, chapter4 describedthe evolution oithc Universeup to the point at which the backgroundwas released.We will now concentratc upon the ways in which the background's spectrum deviates from its black-body characteristics and discussthe consequencesof these deviations in our larger picture of horv structure emerged in the Universe. 8.I THE COSMIC MICROWAVE BACKGROUND DIPOLE There are many potential sourcesof anisotropy in the cosmic microwave backgrourrrl (CMBR). If the Universeis not subjectto a largely homogeneousexpansionthen the variation in the Fiubbleconstant,along different lines of sight, will conespondto differencc:; in the temperatureof the microwave background.In this non-isotropicview of the lJni verse, less dense lines of sight will expand faster and the CMBR will appearmore retl shifted, making them look cooler. Overly dense regions will only expand slowly, arrtl. hence will appear hotter becausethey are not so redshifted.Although the equationsol generalrelativity allow all mannerof anisotropicexpansionmodels,by the cosmologicirl principle we assumethat the Universe is isotropicand so the CMBR is not subject,in anr significantmanner,to this form of fluctuation.As explainedin chapter3, whilst therc arr'
f" 156 Th.slor rromthccdse
lcfi 8
I
Ripprdh rn..6nk nt,*.F
,-.r.,
b.ckgrouldri?
t
lodl deviationsfrom isot.opylh6c ar€ cxpeole(l1oavemeeon h. s6le of rhe UniveB. ThcrEfor, ihe onty adt.r cxphnarior for lhb motim i! that rh€ Lo.al Group ha3bccn I asa who'e d sinc€ ilrc d€coupling. The only phy3lcd m..h.nbn which could possibly rccElent l lr dE Univ€rsecortains largescale magnctic fields, such as tlose postutaredby rhe movc a clurrd of grtaxies i! rlrat of $aviq. For rhi! to occur, dle Univcn. ha! io hc i P |as m aco s mo | o g i e s d i s c u 3 s i n c h a p 1er5,thcnthcsew i | l al terl heba.kgroundradi ati onas| i nhonog$eoWonr dat ivclyl, 'gcscale. . chapcr 3di! cu$i'poht d@ncludcd
. I L
well.As weareconsiderins only Big Banscosmologies in derailin rhh book,however, ourdis.ulsionsof masnetically inducedanisotopies$ill prcced no f nhd. Thetwo fonnsof anisotropy thatw will corsidcrin det il ar€rhos' whicharepro-
a II
rhati*irnoecncitier existoirscalcsofup to md ov.r lm mi[ion light rrffs. I rn ctraprcrs i|lc conc€p!of srcdnint motiorsw& lnrrod$cd.Thesee larg€s.rlc. I tut*y nowsot mrtcriil (q/pic.lly gat;iar rnd dle inbrglla.ric mcdium)which!r. h I duc . dby t h e m o v e fe n to fo u ro b s e rv i n g P I' tfo.mmd$o5€w hi char€prducedbyi nhFIm.ti .ontcco* or *gniit "li'i"r - "t t 'oot m or ancalbycoI r ccnt r lt iof m gg. llour m og6nei| i e s i n l h .m a tte rc o n te n to fth eU ni vcrse.Ttc5i mp| €actofobseN ati onha!| bcA | gd' cti cneighbour hoo4r '€nor m ouconccr r . t ionof d|t cr h'! b. . l'dut d{|or shownthat inhomogeneities .er."i"tr*t""' exisrd m.ny c6mic $ales,tom saldies ro cludcr- iup(i-"* .!rr. q*!j,-",-h"l''s g 0.n0. of rh! Hubbl€ cxp.nsion in | clusleBandvoids we wouldexpectth. concentrations ard nrcfacrionsofmancr fiom Hlbbb fld i! subractd ftomth€ individualsalarwhen thc Jur bcat ngion ofspacc. I which thesestructurcsspmogto hav€|.ft an imprint sm*t6r. on thc mic|wav€ backi"r, *otio*-it b€ s.tn thrt grlaxi.s ar! sts 6mingtowud! dl. grrt rttractor. | grcund: ltihoush dft""oappiorchis promising,lhcrt k not yct agrccordtbctrcar thevelocity
L
I T Anisotmpi6sinthecdmicmicrowaveback8rundorquantifedbyth€mliooftheh|a*i'"aro.mcr'aBRm6;ur.mentandrlFdirctlonofth€8r€at't!rctor'ca|cu|ntc
d.viation, AT, to tl'e averagetempcr*ur€ of d'e radiation,T:
|
ar r
-
(E.', I i
Th€ most obvious onisolroPy to show up in th€ microwave backsround i, ! dipolo
ftom sn aming morion .rrdi6. It is importrnr to r!|Irl.mbcl dut dlc C]!'BR dipot. m..s
ffi:'n::lsH'trffifli:sffi#LT'#J#i"ff"1$s:i I L
close-bynat€rirl.
exist(asprovedby the CMBR dipole)meanstltlt. The fact thattheseinhomogeneities at somotcvcl, thcrc lhould be ih. f$!it imprinr! otthc dcnlity difl€r€no.r on thc micro.
I aniso,,opywhichoc,uBat;'arn+.ooi.e*'.inginlil";:;';il*;i'ff ilJ"Hifrff:-illif"f":'if"T1tJiiT"fi:i'iiil'"';:f;iiiI mov€mdt rllatirt lo thc CMDR, lh.n lhc isotropy is caiEed by rhe Doppl.r cfiect. We thm floctu.rioN which ll.rc Lug. oobctin with.
would appearto be nroving at360*20 km/s in the direction of Leo's border with Crater. This is a slightly puzzlingresult becauseobservationshave clearly shown $ar crcaflysno*rt that rn€ the Sun is su, rs
hvelling aroondtle cenrrcofrhe Milky Waywirh a vctocityofaboutZ0 kn^, but in almosttheopposilcdir.ctionfromlco! ihus, it mustbettp movencntoflhe enrre ofthc
I
I i !
nr". .*ity lxphin€d
"* -*tt
T E2 RIPPLf,SIN TI{E C(NMIC MICROWAVEBACKGROUND
ctldv whi.h is .a$ing lh. anisotrcpyin ih. CMBR. As iilr a3thc velociti.! *! havc Th€ brcakthroughin tho scarch for lh€ pcfttrbltionr rvftlch werc thc s..dr of todny's i thc| " m.tu." quo1edare quos ' thare ynor a rcyer n orclatrv$rrc ty € tr€ l a ti v i sso tiw candso[tcansi yaddtl ' cm'tfal !odirhc scovcr| fal " " .. iot ggz'lesA'. 5r t c||it c, t hcco6r ioM ir Blc@undkp|or ! are.mey and cansimptyaddmp| rhcm, !o discovcr sirctrE citnc in | 9q. NASA,3 lllc ibc,rhc Co6r c MisDwav. Brckround Exptorr I c a|ax y m u s tb € mo v i n g a tro u 8 h Iy 6 0 0 k ' vs.R i gorou.5c0| cuta!i ons' 9hi ch| akci nl oac-l (coB E )(!eFi&8. l) hadcoI |cc1oddat ! which, whc'pr os*a. gvct inr llllndllslnl counl the sur'! mo\€m€ around thc Gal.xy and thc calaxy c E I 's nsUmovemcnt v € I n E a r uarourd o ( . | h i n trhc s i h a t t I c b 6j6 k g r u n d rhints i d i l t iihat o n wa sab66ksrcund n i 3 o to p [o nrididion sr n 'l |e r !$was l d l c3 l n 'n Il s.alca rhrn rhc ;n smrlbr ;guk ankoropic thc c€nhe ofmass ofdE LocalGroup, have cotfrmed lhis velocity. Basd upon thc intcrprE-
T L
dipotar anisolropy.-This tinc ih. rnirotropy hn be!.' cicd
|T
by dcm€r thm av€ragc r
I r a|ionoI d e j i c ro 9 a v e b a c k 8 ro U n d \.d i P oIarani sotropy,sLronomerscfnsayw i thconn-:gi onsofl h cUniv. nc. edenscr r gionwit t acgcascr t denc elha l .b * c d u p o n o t,s e m ti o n \fo mE ai h.| heLoc€| Groupo| gaIaxi eskhovi ng:;eauci tw i | l grnvit nt iona||yr cdsh. f t }t €r . di! t iot m o wi$. ar |oc i ty o f6 0 0 } 3 0 k n ' /5 to w a rd s tl E cmtcr/H ydFborderatl 0.5hri ghtascensi on.i * ' .* .rr' .' ,;o.a nisono; i6uene8ur a! of t t F( li5t I ibudof €r int 6Univcis( : The sourceof this velocityhasimportantcosmological consequences. If it wereproI atiheepochofdecoupling.
ducedbyprimordia|vc|ocii,fuctugtionsofthemattcrintheear|yUdvcrselhenthoscl".,li."3.iili..ii.iiiJil""hadbe€nproocsscd!or€mowcdiplc$df v e|oc it i$mu s tl t!v e b .e n m u c h | a rg c ri n tl E past,w i thfcfe.cnc€!ol heco-movi n8f{mci ga| axyeetti n ginr hc*ay. lsar sut iof alldr cim r $i; gm d&cf '|'he$of $c of r €f er en c e ,w h i c h d e s c ri b c s th e e x p ansi onofspaceti mc.InfacrdE yw i | l bcs;bdi nl -nuduod' oo' ' ir "", i. p*"iu|et ot ellif dEpr t cheg; f li8ht 'I di, f klBit ur so[ ac . or dan @ w i th th e s p e tra l m ti o ,l + z a ndso,atthepoi ntoff€de@ upl i ng(FI,000)i si D p| ynoi sci nl he daia'A'iat ist ica|analysi'of t t Eall. skym gpr ! |d|hat 6cpal|. nl
woud hav. bce' approaching,h" spe€a or'!h,r'':;';:#J":;fi:'T&fr''i#
I
ii:'I"i:lx",[T',"S:f;?.llr1ll#l#ffiiili?Ifr#ffJff,T""T'fi:]t
ev idenc c fo rth e s e k i n d s o fm o ti o n i n th e U ni v.Featdecoup| i ng,ThesmaI| scal .are' ' ctaocrvi si onpicnr '. 'som clr accsor m cunder |lng3|r uct ur €r un evidenccforthesekindsofmotionintheUnivcrseatdecoup|ing,ThesmaI|scal.a.o'ctao"r"i"ionpicnr'.'somclracesormcunderVngsrructure*ereun anis o1. o|lop o pi e i essppro rodduucceeddffo fromrc mro88i oi on's o fs f spacew paC eshi hichcoul dbe| raveI| w eIi i n8atcl i n8atcl osctothe;i osetothe:i b|b| c.tnfact,aI'incet ..tnfact,a Pincet onUniv. onUniv. r sit r itybat ybatloonoQ loone}
resions
'
ilil##;:liiiiiiiiid6isi""Jr;h;;ff;";;';.;;;;;.by,i'"
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lch.I
Ripples in the cosmic microwave background
unobs erv abl e
159
obs erv abl e
W i dth of l as t s c atteri ng surface
observer microwave radiation. Thedepthof Fig.8.3.Visiblefluctuation scales in thccosmic background fluctuations. the lastscattering surfaceaffectsthe scaleof the smallest detectable Only those in sizeto thedepthofthesurface will bcdetectable. fluctuations comparable
Fig 8.I Anartist's inlpression ofthecosmicBackgrornrl (coBE),a sarellite Explorer dedicated to thcstudyofthccosnric microrvavc background ridintion, liunched intodarthorbitin tqgq.tts nlcasurcments confirnred thatthespcclrum ofthebackground radiation is indeed characteiistic of a black-body source at anabsorutc tcnrperature of 2.7-K,verifying u ,n"io,p..Ji"ti* nrg Ilang.(tllustrarion reproduced courresy ofNASACodtai
To seethe kemel of what becamea superclusterrequiresa microwavetelescopecapable of' resolvingthe miuowave backgroundinto half-degreeblobs. This is probably the smallest scaleat which we should€xpectto seestructurein the microwavebackground.The perturbations which becarneindividual galaxiesare probably beyond our observationforevcr becauseof the time the Universetook to completethe decouplingof matter and energy. In our previousdiscussionrve have alwaysreferredto this event as ifit took place very suddenly.With referenceto 15 billion years of cosmic history, it probably did, but thc Universedid not go from being completely ionisedto totally neutral ovemight. lnstead it must have happenedover a period of time. This meansthat the surfaceof last scattering, as the place of origin of microwave background is sometimesknown, is a misleading name. Insteadof a two-dimensionalsurface,it must be three-dimensional.Therefore,our' line of sight through this transition region of space must include regions of over- an
160 The glow from thc cdgc
[Ch. g
matterin the Universefollowing this eventrenrainsneutraland tucked up in concentrated lumpssuch as galaxies.There is evidencethat this may not be completelytrue. In the previous chapterwe discussedthe Lyman-crforest and the way chemical elementsin space,along our line of sight to distantquasarsand galaxies,imprint themselves on spectra'From thesespectrait is possibleto determinenot only the elementpresentin spacebut also its ionisationstate.From theseobservations,which stretchbetween rcdshifts of 1.7 and 5, it can be seen that a significant proportion of intergalactic gas is ionised.Although the Universeis still optically transparent,becausewe can see through it, the implicationis that there are a lot of errantelectronsout there,whizzing through the cosmosand colliding with photonsof the cosmic microwave background.This will blur the primordial fluctuationsand, if the electronsare presentin suffrcientlylarge numbers, will actuallyintroducesecondaryfluctuationswhich we are misinterpretingas ancient in origin. Thiils currently known as the sunyaev-Zel'dovich p.o".rr, aftei the two astrorlomerswho studiedit and presentedthe idea that this would affect the spectrumof the microwavebackground,especiallyin the direction ofa rich galaxy cluster.Essentially,it is an inverse-Comptonscatteringprocess(describedin chapter2) in which the interacting electronspossessgreaterkinetic energiesthan the microwave backgroundphotons they are scattering(seeFig. 8.4).
photons scattered by electrons in th e in tergal acti cmedi um
photons unhindered
<:
observer
Sec.8.31
Origin of thc primordirl fluctuations I 6 |
The observationsimply that this ionisationprocessmusthavetakenplacebeforert:tl. is thc forthe reionisation shift 5, duringthe epochof galaxyformation.Onemechanism bclolt: Populationlll starswhich would havecondensed formationof the hypothetical of ultrlr mass.Theywouldhaveproducedlargeamounts galaxieshadtimeto accumulate violetradiationwhichreadilyionisedatoms. whichmayhavebeenmadeto tlr" thesechanges investigate Whilstsomeastronomers datagivesus our firstclucaslo the COBE otherspondertheirorigin.Again, anisotropies, wherethey camefrom. At the point of decouplingthe Universewas approximirtcly 300,000yearsold. This meansthat only areasof space300,000light yearsin diantctct this is thedistancelightcouldhavetravelledin tll;rt because wouldbe causallyconnected lengthof time.A diameterof 300,000light yearsat the distanceof the microwavebachptts to an angulardiameterof lo. The COBEfluctuations ground'semissionconesponds tlrt' timcs seven some a linear diameter to sessan angulardiameterof ?o,corresponding existon scalc:; The factthatfluctuations horizondistanceofthe Universeat decoupling. stronglythat their origin tool: far greaterthanthe horizondistanceat decouplingsuggests Hadthisnot becntlrt' plaJebeforetheepochof inflationat a cosmicageof l0r5 seconds. grown to sucha greatsiz(' coherently could have a fluctuation no way there is case,then to haveevolvcrl regions,outsidethehorizondistance, adjacent Onewouldhaveexpected Whcnan avcragcol'lrll thesametemperature. andthereforenotto possess independently theseindividuallyevolvedareaswastakenby the 7obeamwidth of COUE,thc llttcttrir The factthatthis is not thc caseindiclrl('' tionsshouldhavebeenwashedout completely. beganbeforeinflation.ln chaptcr2. lh' that what becamethe largescalefluctuations andin chaptcr4 it tv;r principle(2.8)wasintroduced, uncertainty conceptofHeisenberg's explainedhow, accordingto this principle,energycouldbe borrowedfrom thc vtlclrrlrrl withitt it' so longas it annihilated into a pair of particles, spontaneously andtransformed tlttirrr high that was so of the Universe theenergydensity Comptontime.At l0-35seconds, Univctr;' the When were occurring. all scales and on levels at all energy tum fluctuations quantumfluctuatiorr' of the GUT force,theseinfinitesimal inflateddueto the separation regionsmanytimesthe sizeof tlr' macroscopic weresuddenlyblownup to encompass whichthenbccnrrr' Universeat that epoch.Much smallerscalefluctuations, observable galaxies,may havebeenformedin a similarway or at a laterepochbefore(or evennflt't thedecoupling. 8.3 ORIGIN OF THE PRIMORDIAL FLUCTUATIONS
cl usterof gal axi es Fig. 8.4. The sunyaev-Zel'dovich processinvolvcsthe scatteringof the cosmicmicrowave backgroundradiationby intcrgalaclicelectrons.'l-hisis partiorlarlyprevalentin clustersof galaxiesin whichhot intraclustcr gasis in a highlyionisedstate.Cireiuiobservations canreveal 'holes' in the cosmicmicrowavebackground whcrcclustergas has scatteredthc background photons.
to occttt,tr' In orderto answerthe questionof whatcausedthe primordialfluctuations haveto delvebackinto thetheorygovemingthe very €arlyUniverse'Chapter4 descrilt'' radiatirrl of thecosmicmicrowavebackground historyup untiltherelease theUniverse's of the earlyUniversecould be modelled,by treatirr' It describedhow the constituents Fromour consideratil' themasan idealfluid,subjectto randommotionsandprocesses. thattheymusthaveinitirrll by COBE,we havededuced scalesdetected of thefluctuation th;' amongcosmologists formedbeforethe epochof inflation.Thereis a deepsuspicion (' the fluctuationswereactuallyPfesentwhenthe Universeleft the Planckeraat an agc fror ' left-overs l O-arseconds.If this is the case,thenthe fluctuationsarealmostcertainly shrr' We and time. space mass, energy, the creation of physical laws and theforgingof the returnto thispointlater.
t t t t t t t t t t t
;l
L L
,,
1I IN
1 6 2 ' l ' h c g lo w fr o r n lh e r :r lg c
1t
It is assunlcd lltitl l'lttclrratitttts occrrrrcdon all sc;rlcs. andso thebestrvayto characterise this kind of beltaviottt' is to rcdtrccr it by Fourierarralysis and treatit as a po.ruer spectrum. The powerspectnrrn dcrsclibqr thc anrplitucle, A, clthe fluctuationwhich takesplaceon a scale,k, at a timc, t. lt hastlrc firrrl:
fi
1 1 1 ll
lr 1r 1r 1r ''11
l ,(k ,t) = A k "
'x
(8.t)
where n is the spectralindex anclrakeson dillcrcnr valrresdepending upon the type of primordialspectrumwc assutne.Although nothing in this equation explicitly statesit shouldbe constantover the entirerangeof k, this is r-rsually assumed. The simpiestpower spectrumcorresponcls to a totally randomdistributionofmatter throughoutspace.This is termeda r.vhite-noise spcctrumanclis characterised bv n=0. In order to investigatethis, let us assumethat the rrrattercontentof the Universe can be split into particlesof equal mass and that thcsc particlesare then distributed randomly throughoutspaceat l0-43seconds.The nurnbercil.particlesis therefore directly proportionalto the mass,M. If the averagenumberof particlesin a volumeelenrent is N, then the exactnumberin any specificelementmay varv bv: <\N= VN (8.2) 'l'his comessimply from the Poisson distributionlbr randomevents.It followsthatat any particularpoint in spacctinre,the rractionalvariationcan be as much as 6N N
JN- I NJ N
(8.3)
which in turnsleadsto a root-mcan-squared varialionin the mass,om: _ l,/
clnr oc N /2
(8.4)
'l'hc lrasic idea is to therrwatch ltorv theseevolve nnd grow through gravitationalinteraction with one another.A white noisespectrum,which we havebegunwith because it is the sirnplestto visualise,unfortunatelyruns into problemsbecausethe fluctuations it causes collapsetoo early. lt actually leadsto a 'chaotic' cosmologyin which the collapsingregions ol'space would play havoc with the isotropy of the microwave background and Iranrper the nucleosynthesis of heliunr. Altcrnatively, if we assumethat fluctuationscan be presentin an otherwise homogetltlottsdistributionof tnasssinrplyby rearrangingliic particleswithin each specificvolume clcntcntwc arrive at a spectrumwhich possesses n-2. This leadsto o ttt cc N
l
lch.8
_)/ /6
(8.5)
'l'hisis ollen knownas the particles-in-boxes spcclrunr, and postulates thatthe sizesofthe boxesshouldbe in the orderof thc horizonscaleal the time duringwhich the fluctuations wclc creatcd.Although tlrereafe some statisticalproblemsfaccd by this approachduring rlrc analysisof when tlrc universc was very young. its main dil.ficultyis ihat it fails to prcdictthegr owt hof f luc t uat ions inthonaJ o iclegalaxicsintimeforustoobserve(oreven cxist in ) thc m -
Sec.8.41
Growth of fluctuationsduring the early Universe | 63
Finally, we turn our attentionto a spectralindex, n=1, known as the Harrispectrum: son-Zel'dovich o^nN- %
( 8. 6)
aseventswhich Havingmetwith failureby tryingto interprettheprimordialfluctuations occuroutsidethe horizondistance this time the fluctuations occurinsidehorizonscales" andthencrossinto an influentialrangeasthe originalhorizongrowswith time at the speed of light. Rememberthat the theorystatesthat the Big Bangtook placenot in one singlc at the sametime.Therefore,at thePlancktime many placeat a singletime but everywhere As the informationof their existence placesin the Universewerenot causallyconnected. propagated outwardsin concentricspheresat the speedof light, however,moreandmore with eachotherthroughthe exchangeof particles.Alregionswereableto communicate fasterthanthespeedoflight and it wasnotexpanding thoughtheUniversewasexpanding, Universe,whichbecameour own,continuedto get biggerantl so thecausallyconnected fronl so fluctuations moreregionsof spacetime, bigger.As it gotbiggerandencompassed outsidecrossedthe horizonandbeganto havean effect.Oneofthe mostinteresting spectrumis that it predictsscale-invariant properties aboutthe Harrison-Zel'dovich fluctuations,which meansthat the amplitudesof the fluctuationsare not correlatc(l with the scalesupon which they occur.This is the type of spectrummost cosmologists assume,basedon the factthat it cangive figureswhich predictthe right levelof' fluctuationsin the cosmicmicrowavebackgroundand can producegalaxyformationon modby inflationarycosmological to be predicted timescales.It alsohappens acceptable els. As for the actual,bottom-linereasonwfiy the fluctuationswere presentin the first place,cosmologists still do not know.Most assumethat it is a leftoverfrom the quantum gravitationalforces,which werein flux duringthe Planckera. Subscriptionto the Harridiffson-Zel'dovichspectrumprovidesanescapefiom providingan explanation,because wouldnot be expected beyondeachother'shorizondistances, erentpartsofthe Universe, a preferredpowerspectrunr anyway.Havingestablished to displaysimilarcharacteristics of their initial cause,the next thing is to determinethe way in of fluctuationsregardless which theygrow. 8.4 GROWT}I OF FLUCTUATIONSDURING THE EARLY UNIVERSE era,gravitywasnot the dominantforcein the Universc. Duringtheradiationdominated causedby photoncollisions.Therefore,any by the pressure Instead,it was superseded fluctuationswhich did occur could not grow throughthe accumulationof more matter, because the radiationpressuresmoothedthemaway. actionof the photonsbecamelessand lcss the smoothing As the Universeexpanded, efficient.In chapter4, we definedthe beginningof the matterdominatedUniverseas was governedby ils beingwhenthe energydensityof space,andhenceits expansion, contentof matterratherthanby its radiation.At this point,gravitybeganto takecontrol beganat aborrt in theUniverse.Eventhoughmatterdomination andshapedthestructures thegrowthofthe strtrcstill restrained 100seconds aftertheBig Bang,radiationpressure
r. 164 'Ihc glow frorn thc edge
[C]h.8
turesquite effectivelyuntil tlre Univcrsereachedan age of 10,000years. Interactionsbetween matter and radiation continued,however, inhibiting the growth of fluctuationsso that the structuresgrew only slowly, until 300,000 years.At this point interactionsbetween tlre radiation and matter ceasedand the cosmic microwave background was released. The preciseway in which a fluctuationgrows before the decouplingof matter and energy dcpendsupon whetherit includesan increasein the densityofradiation, or ifit is just the mattcr contentwhich is affected.Thus, two types of densityperturbationare possible in a Universecontainingmatterand radiation.They affect whetherthe entropyof the early Universevariesfrom place to place or remainsconstantthroughoutspace.Entropy is the measureofa system'sability to undcrgospontaneouschange.It can also be thought ofas a measureof the system'sability to clooutsidervork. lt is thermodynamicallydefined as dQ ClS=j
(8.7)
T
where dS is the changein a system'sentropybascdupon the absorptionof a minute quantity of heatenergy,dQ. The systemitself,throughoutthis reaction,remainsat the temperature,T. An adiabaticfluctuationis one in which both the densityof matter,p,,,,and the density ofradiation, p., are perturbedarvayfrom the averagedensity,Ap, in such a way that the entropy of the perturbedregion remainsconstantwith its surroundings.This condition is met when the matterand radiationperturbationoccursin the following way:
(rp)
4 f^p)
w,=l[t.
(8.8)
The secondtype of perturbation,known as an isothermalfluctuation, occurs when the matteris the only colxponentof the Universeto be perturbed.The fundamentaldifferences betweenthesetwo typesof densityenharrcement are their effectson the spacetimecontinuum. An adiabaticfluctuationaltersthe curvatureof the spacetimecontinuum;an isothermal one doesnot. The type of fluctuationis of concernonly during the radiationdominatedUniverse and the period of time up to the decouplingof nratterand energy.This is becauseit is the action of the radiationwhich dissipatesthe fluctuation,if the fluctuation is not big enough. Following the decoupling,the radiation content of the Universe (observed today as tlre cosmic microwavebackgroundradiation)and matter evolved separately and no longer influencedeaclrother to any great degree.At the point of decoupling, the type of the initial fluctuationsdetermineson rvhatsize galacticstructurewill first emerge. In the caseofadiabatic fluctuatibns,the top-dorvnscenariois proposed,in which the 'fhe reasonfor this is that the fluctuafirst structuresto form are clustersand superclusters. tions attomptto confinean over-density olradiation which then diffusesout. This diffusion processisrcharacterised by the collision of photonswith the 'encasing'matterwhich, in tandem with the external bufteting received b1,the fluctuation, increasesthe kinetic energyof the particlesand smootlresout the flrrcturtion. Only very large fluctuationsare
Sec.8.51
Darkmnttcr165
thetime it takesfor the radiationto difTuscottl capableof survivingthisprocessbecause thc orrll' At the pointof decoupling, ofthem is muchlongerthanthetime to decoupling. l0''solarmassesandttvct' fluctuationscapableofsurvivingaretheoneswhichcontained Computersintttl on thesizeof clustersandabovearethefirst to emerge. Thus,structures intoindivitl fragment and structures ationsshowthatthesethencollapseintopancakeJike nnd lilrr sheets which in structures scal€ large io ual galaxies.This would naturailylead thattlrc galaxy maps from is evidence voids. Whilsithere targe galaxies surround mentsof prcrlictt; lt occur' model the with soilethinglikethis,problems realUniverseis distributed in the cosmicmicrowavcbnck fluctuations andexcessive too muchlargescalestructure groundradiation. Isothermalfluctuationsleadto a bottom-upapproachin which smallerassocinliotts suchn'i suchas galaxies,or evenglobutarclusters,form first. The largerconstructions, instabilitics gravitational from later formed giant gJaxies,clustersani superclusters, lea(lt(l Iuur.Jty the smalleruggr.gui.rof matter.This hierarchicalclusteringwould krol' galaxies of In otherwords,the superclusters clusteringpi[-t. self-similar -shottl{ l;rttttt galaxies' to thc similar look should in turn, similarto theclusteriof galaxieswhich' Universe,althoughthe conceptof hierarchicalclttnlcr of the surrJunding observations in the properticsof gnlnxic't' would appearto be broadly.orr..t, thereare differences llr(' physicalprocos$ci different that indicate differences ih"t. clustersandsuperclust.rr. of.galnxics, scale the 11t" on example, For scales. different on these work at obviousty galaxies'On tltt' dynamicswoutdseemto play an importantrole in the shapingof spiral in abundnttec predicted as that such structure filamentary andabove, scaleofsuperclusters ' present. is also scenarios, by top-down earlier.The contrnslilr Bothmodelsalsosufferfrom the commonproblemmentioned from the lcvel ol different is sd colossally density,betweena galaxyandits surroundings, thanappcnrslrI matter more that collapse, gravitational its to begin the fluctuationneeded to fornt irr Universe be presentneedsto be adde-din oider to causethe structuresin the ol'thc content matter of the estimates time for us to observethem. In other words,our If tlrnl clusters' and galaxies build to models these by required cosmosfall shortof that mattct normal of quantities large are thaithere assuming up by made is deficit -barYonic (neutrons andprotons)whichwe simplycannotsee,thenthe amountsof heliumsynthc sizedin the earlyUniverse(seechapter4) are thrownout of kilter with observatiorl:r thattir is thattheUniverseis morecomplicated conclusion the inescapable Unfortunately, simpleinterplayof baryonicmatterandradiation' gravity ltr Somehowwe want to introduceparticleswhich would give us someextra nec
t
t t t t t t t t t t
L
8.s DARKMATTER
I isin formswhicl' L of theUniverse content of thematter fraction thata substantial Evidence world nowforoverhalfacentury. hasbeengrowing observe directly cannot astronomers t
r-
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arl
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ren()wllcdastl'otlollrcr.lan Oort discovereclthe first evidencethat forms of matter were hiddcrrfi'ornout'vicw wltenhc conducteda studyof stellarmotionsin the vicinity of our Sun.llcmernbering tlratin our solarneighbourhood we areembeddedwithin the outerdisc region of the calaxy, oort discoveredthat most starshave some velocity component out of the planeof the disc.'l'hisperpendicular motionwould be stoppedand eventuallyreversedby the mass of rnaterialin the galactic disc - exactly in the same way as a ball thrown upwards frorn the Earth is slowed by gravity and eventuallypulled back dorvn. This would causean oscillationto be set up, as the starsplungedbaik through the centre ofthc disc and out ofthe otherside.Thus,starsas theyorbit the centreofthe Calaxy also oscillateup and down out ofthe disc.Theseoscillationstakethousands ofyears to complete a single cycle, however,and so are unobservablein a human lifetiml. A study of stellar distancesfronr the galactic plane and the velocitiespossessedby those stars does allow an estimatefor the gravitatingmassin the Galacticdisc. Oort discovered that there had to be more nrassin the solar neighbourhoodthan could be accountedfor by stars alone.The mysterywas partially resolvedwith the adventof radio astronomyin the l950s. Thesenew instrumentsprovedthat interstellarspaceis home to vast quantitiesof dust and gaswhich had not beensuspectedat first. Still, doubtsremainabout whetherthis provides the totality of the hiddenmass. The next piecesof evidencecame from stuclyingthe rotational ratesof stars in other spiral galaxies.By assumingthat the luminousportionsof a galaxytracethe mass distribution, a spiral galaxy should be a classiccaseof a Keplerian orbital system.This is one similar to the solar system which has a centralconcentrationof mass,i.e. the Sun or the galacticnucleus,aroundwhich other,much smaller,bodiesorbit. In the Solar system this resultsin the furthestobjects from the centralbody having the smallestorbitai velocity. Rotationcurvesof galaxies,however,showthatthis is notthe case.Orbital velocities for spiral galaxiesreacha plateauvalue and remain there for the width of the disc. This behaviour is indicativeof the spiral garaxybeing surroundedby a large spherical cloud of mattcr. ln chapter7 we statedthat evidencehas beenfound for large halos ofgas existing aroundexternalgalaxiesbut, in many estimates,the massof gas is smaller than the mass inferredfrom the rotationcurvesand henceanotherdark componentofmatter is suspected to bc present. Extendingour observationsto the scaleofclusters ofgalaxies,we find that the individual velocitiesof galaxieswithin theseclustersshould mean that they-cannotremain to_ gcthcr, if the only masspresentis that which can be seen.The fact that we seeclustersof galaxicsthroughoutthe Universeobviously meansthat theseare stable structures.To be stablethey must containa lot more massthan is obvious.Halos and the suspectedpropensity oltiny, faint dwarf galaxiesmay help to rnakc up this shortfall,but otlier more exotic rnaltercomponentsare still necessary. 8.6 IIOT DARK MATTEIT So what is this exotic forrn of matterwhich we cannotseebut can detectthrough gravity? There are two possibilities.For our first we rvill use a dark matter candidaG which is knownto exist: neutrinos. conventionallyit hasalwaysbeenassumedthatneutrinospossess no nlassand travel at the speedof light. 1-heywere originally postulatedto exist in
Sec.8.61
Hot dark matter l6'i
1930 when energydeficits were discoVeredin certainsub-atomicreactions.Knowing that energy could neither be creatednor destroyed,Pauli, the man responsiblefor espousinl' quantumtheory's exclusionprinciple, proposedthat a new particle was taking part in th{ reactions and carrying offthe excessenergy. Theoretical considerationswere made and it' propertiesdeduced.Neutrinostake part only in reactionswhich involve the weak nucle:r' force. They were shown to be extremely reluctant to take part in reactions. Neutrinos hav, to get incredibly close to atomic nuclei before a reaction can take place, becausethe weal force operates over such a short distance. To a neutrino, the separation between atoms i' so largethat they can literally find an unhinderedstraightpath throughmatter like a huntirrr being walking through a sparselywooded forest. In fact in the spaceof time it has takcl you to read that sentenceand this one, millions havepassedthroughyou, this book anrl tlt, entire planet Earthl Neutrino theorieshave been largely conoborated with the inventior of the neutrino telescope,an enorrnousswimming pool-like device, filled with watcr (rr that catchesone or two neutrinosout ofllr, some other liquid such as tetrachtoroethene countlessbillions which passthrough it! On the subject of a neutrino's mass, all particle physicists could say was that it rvl very, very small and therefore probably 0. Some suspect that is not the case and, if neutrinohas even a minusculemass(somewherebetween| 0 and 30eV is the current cslI mate) then, becausethey populatethe Universe in such vast quantities,they could be th' major constituentof the dark matter in the Universe.Neutrinos are relativistic particlt' which meansthey rush around the Universeat velocitiesvery close to the speedof litrllrt They are therefore termed hot dark matter. They ceasedto take part in the thermal evt'l ution of the rest of the Universe a long time before matter and radiation decoupled. In fat t neutrino decoupling is expected to have taken place at about one second after the lli' Bang. Ever since that time, they have hardly reactedwith matter at all. Their very hilt speed causesthem to resist clumping together and their inherent gravity has a smoothirr effect on the distribution of matter, pulliag apart the density fluctuationswhich occur i' the baryonic matter. The hot dark matter scenarioof galaxy formation is therefore similar in outlinc ar' consequenceto the older adiabatic scenario which led to top-down structure formatit" Whilst the determining properfy of the matter-radiation scenarioswas the type of thc in tial fluctuation,this is not the casein dark mattermodels.Whilst two principle fluctuati' modes are still possible, the overwhelming factor is what type of dark matter is prescrrl ' the Universe. It is this which determinesthe subsequentevolution. In the first typc ' fluctuation,all three of the Universe's components- radiation,matter and dark mattt r are perturbed,This is an adiabaticfluctuation and causesa perturbationin the spacctir, continuum.In the secondtype offluctuation, known as an isocurvaturefluctuatiofl,thc rr energydensityremainsconstantdespitethe densityfluctuation,and so the spacetimec()l tinuum is unaffected.In most cosmologicalmodels today, the more general case ol-ll adiabaticfluctuation is the only one considered. So, hot dark matter leadsto top-down structureformation in which cosmic pancal' condenseto form clusters and galaxies (see Fig. 8.5). In common with thcir nl ter-radiation counterpart,thesemodelsagain run into problemswith their predictions too much large scale structure.Sheetsand voids and filamentsare there, butjust not many and not so big.
| (r8
Thc glow.fronr the edge
Sec.8.71
lcrh.I
Colddarknrnltcr l(tt,
particle.Numeroustheoretical possi unlikehot darkmatterthereis no knowncandidate bilitiesexist,however,andthesearetied intothe evolutionof the Universeat vcry ciuly times.The cold darkmattercandidates arebestthoughtof as cosmicrelics.I)urirrgllrl earlieststagesofthe Universetheyservedtheirpurpose,influenced andhclperl reactions shapeour cosmos.Now, however,theysimplylitterthecosmosanddo very littlc cxcr:pt influencebaryonicmatterwith theirgravity.
t t t t
8.7 COLD DARK MATTER Like theneutrinos, cold darkmatterdecoupled fromthe restof the Universelongbclort' matterandradiationdeparted thermalequilibrium. It beganclumpingtogetherbccausc llrt' colddarkmatterwasslowmovingandunreactive with therestof theUniverse.Whcntlrt' cosmicmicrowavebackground wasreleased andradiationceased to supporlthebaryorrrr pol matter,it couldfall quicklyandefficientlyinto the ready-made sitesof gravitational entialwherethedarkmatterhadclumpedtogether. Thus,cold darkmattcrmodclsfrrlIrrv the bottom-upscenarioof structureformation(seeFig. 8.6). Justwhat constitutes the cold dark matteris a questionwhich hasbcenvcxirrgrrsl ronomers andparticlephysicists for overa decade. In chapter4 our descriptiorr of lhc I t iy' Bangdescribed how theforcesofnaturearethoughtto havebeenunificdat cnrliertirrrr.,. whenthe particlesand radiationwere at greaterenergies. The unificationof lhe wcrrl, nuclearforceandtheelectromagnetic forcehasbeenprovedby high-energy cxpcrlnrfnt,, in particleaccelerators. Thetheorised unificationofthis electroweak forccnndlhe rtronp, nuclearforcehasyet to be shownexperimentally, but manystill believein its vnlirlitv Knownas'grandunification',it is duringthiseraof cosmichistorythatwe explninhorr, baryonsareexpected to form.As a by-product of thisprocess, onecolddarkmattcrclrrrli dateis produced: theaxion. Duringthe adventofquantumandparticlephysicsin the first halfofthis ccntury,tlr( available evidence seemed to suggest thatall theparticlesof naturefollowedthreesirrrpl, (or invariances symmetries astheyareusuallycalled):
/ ,/
,/
C invariance. Particlesand antiparticles obeythe samephysicallaws.C dcnotescharge.
(f)
P invariance. The lawsof physicsare exactlythe sameif the quantumspin statesofthe reactingparticlesarereversed. This is like replacingthe reacting particleswith mirrorimagesof themselves. parity. P denotes
---
6
t
t t t t
T invariance. The lawsof physicsare unchanged if the directionof time is reversed. T denotes time. In 1956theviolationof theseinvariances waspredicted by physicists Tsung-Dao Leearrrl ChenNing Yang.Theirwork indicatedthattheweaknuclearforceviolatedthe P invari ance.This hasbeencorroboratedfor neutrinos,the signatureparticleofthe weak lorcc Neutrinosalwaysdisplayan antiparallel senseof spinin relationto theirmotion,whichir a clearviolationofparitybecause onewouldexpectthereto be equalnumbersofparallcl andantiparallel spinningneutrinos. Worsebventhanthis,neutrinosviolatethe C invari. ancetoo! This is because antineutrinos alwaysdisplayparallelspinvectorsin relationtl
Fig 8 5 ln the top-downmodelol'-structurc fornration.largcobjectscollapseto form ,cosnric pancakcs'.'Ihesethcn fragment,andgalaxies form.
The 'washingout' of smailscarefluctuations occursbecause of the neutrinos,great speed,so,ourotherpossiblecandidates mustbe typesof particrewhichporr.r, ,nu* but arenotrelativistic. To distinguish themtheyoreknnr"nascolddarkmatter.l1nfortunately.
I
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s\ Iiig',tl 6 ln thc boltonl{tp ntodcl ol'slrttctrrrc lbrnratior. snrall ubjccts lirrnr first and arc lollorvcd b y l ar ger and r ar gcr objccr s..r :vcntr r aty thc ttni 'r 'r s c i s r i ted r v i th i r i g.- " r r i ..i i 'r r .r , supcrclustcrs,which arc conglorncrations ol-thc snrallcr,rtlccts. ^
their ntontcntumvcctors-Taken together,however., it rneansthat the weak nuclear force doesdisplaya*rombinccr cp invaliance.In othcr rvords,if the particles of nratterin the Universewere replaccdby anliparriclcs and their spin stateswere reversed.the Universe would still evolvein the sanrcwa1,11,n, ourshas. ln the rnid-1960s,evidcnccenrcrgcdthat thc crccayofparticrescailed kaonstrid not follow cP invariance.rrinaily,as a rist resort, par-ticle physicistsstilr bericvein cpr in_ variancc,especiallysit'tccttlatltcnratical constraints havebolsterecl its possibilitf.In other
S e c . 8.7 l
Cold dark matter
l'7 |
words, for a lJniverseto evolve in the sameway as ours, it would haveto have all particles of matter replacedwith antimatter,their spin statesreversedand, in addition to this, timc would have to flow backwards! So, individually the invariancescan be broken. In the high energy environmentofthc early Universe,so many reactionstook placethat evenstatisticallyimprobableeventstook place in abundance.It would be the perfect place to study theseinvarianceviolations. ln the processof breaking the invariances,C invarianceparticularly, the excessof mattcr over antimattercan be built up. T invariancecan also skew the ratio of baryon creationto baryon destructionin favour of a matter Universe.Some versionsof this baryosynthesis model involve the creationof axions. It is expectedto have a small massbut to be preserrr in such large numbersthat it could contributea considerableamount of massto the tJni verse. Another front-runnins idea concerninsthe nature of the cold dark matter noints to itr, creationeven earlier than baryosynthesis.ln trying to uniff gravity with the grand unilicrl force, theoristsreally need a quantumtheory ofgravity. The first stepshave becn takcrr. however, with theories known as supersymmetrictheories. In these mathematicalcorr structions,the dividing line betweenfermionsand bosonsis removedand they are ablc to change into one another.As a consequence,every boson must have a supersymrrrctrir fermion counterpart.These hypotheticalparticlesare known by taking the original parti cle's nameand addinga prefix or suffix. The prefix 's' is reservedfor the fermion countcr, part of a boson, i.e. a selectron,a squark.The ending of a fermion is changedslightly to 'ino' to define its boson counterpart.Thus, photinos and gravitinos abound. lt is thcsc final two supersymmetriccounterpaftsin which we are primarily interested,because,according to the theory, they are the only two stable ones. We shall concentrateon tlrr photino becauseat leastwe know that photonsexist; gravitonsstill reside in the unprovcn file. The photino is theorisedto have a masssomewherebetween l0 and 100 times that ol a proton. It is therefore a very heavy particle and, as a consequence,slow moving anrl weakly interacting.This has lead to it, and otherslike it, being genericallytermed WIM['s * weakly interactingmassiveparticles. There is, as yet, no evidenceof the existenceof theseWlMPs, but particle accelerator, are being gradually upgradedto bring their energy thresholdswithin grasp. At tlrl time of writing, the Europeanlaboratoryfor particlephysics,CERN, is just embarkingon a searchfor thesehypotheticalparticlesusing its souped-uplarge electron-positroncol lider (LEP2 for short). Physicistsare hopeful that, by recreatingthe conditionswhich alr' forecasted to haveprevaileda mere l0'ro secondsafterthe Big Bang,they may be abtc t,, glirnpsethe supersymmetricparticles(known as sparticlesto their pundits) bcing crcalcrl and decaying. Theoreticalwork on cold dark matterand hot dark matter is now awaiting experirnental verificationand tighterobservational constraints. The proofofa neutrino'smassor tltr' discoveryof a WIMP are both top priority now. Without them,theoriescan be built on top of theories,but this is really like building paperhouses.Unlessthey are firmly rootcd irr observationalevidence,they run the risk ofbeing easily blown away. We defined the edgeofour Universeas being the observationboundarycreatedby lht releaseof the cosmic microwave background,just as the Sun's boundaryis defined by tlrt' releaseof light at the photosphere. With neutrinotelescopes, however,we can pecr into
r 172 '[he glorvfronrthe edge
t-
l ( t h ,8
the very heart ofthe Sun and otrservethe fusionlcactionstaking place ils at core. If rve possessedsufficiently large and sensitiveneutlinotelescopes, then the cosnticneutrino background would alsobecorneavailable. In chapter4 we discussedneutrinodecouplingand statedthat it occurred at about | 0-5 secondsafter the Big Bang. lf a neutrino telescopeof sufficient power were to be constructed,this would offer cosrrtologists a chanceto observethe conditionsof the Universe just 0.00001secondsaftercreationitselflAll orrrthcorieson baryosynthesis, supersymmetry and primordial density fluctuationcoulcl bc severelytested,and our un<Jerstanding would take a massiveleap forwards. As physicistsstrugglewith quantum ideasabout gravity, they m.st arso have an urtimate goal in mind. Successfuilyproving thc cxisrenceof the graviton, presurnablyrvith the constructionof a sufficiently large and scnsitivegraviton telescope, meansthat the i. Universecould be studiedas it existedat the enclofthe planck era, l0 secondsafter the Big Bang. This was the point at which the gravitonsare theorised to have decoupled. Observationalcosmologyis really only just beginningl
I
t I The fate of the Universe
t t t_ t
Manytimesduringthecourseof thisbookreference hasbeenmadeto theageAnrlsizr', ' theobservable Accordingto currentestimates, Universe. theageis anywhcrebetwccrrlt thisbookwe haveused| 5 billion rrr, billion and20 billionyears.Mosttimesthroughout middle-of-the-road estimate. As for the sizeof the observable Universe,this is dircttl linkedto its age;aboutl0 billion to 20 billion light years.Onequantitythntwe hnve1'' Formostof thislror'l to fully consider, however,is themasswhichourUniversecontains. it hasbeentacitlyassumed thatthe matterin theUniverseis the lunrinous mntcrinllirrrr" however,hassltowtttlr,, in starsandgalaxies. Theworkdescribed in thepreviouschapter, to define. lf thcrcnrc vrr theactualcontentof theUniverseis rathermorecomplicated quantities of darkmatter(whetherhot or coldmakesno differenceto this argunrcnl ) llr' ' rr, astronomers arefacedwith thefactthatthebaryonicmattermaynot be thebcstbltttrpr with which to studythe Universe.lt would be the equivalentof an ccologist$lurlyir, humanbeingsand their impact.lf the ccoloy'r Earth'sbiosphereby only considering wereto ignoreall of theotherlivingspecies on theEarthhe couldnot hopeto devcloltll' correctmodel for the way in which our planet'secologyworks,Astronomersto(lay,rl facedwith theprospectthattheyhavebeenstudyingtheUniverseusingthemostrcslricl, ofdatasetsandmissingthe'big picture'.To useanotheranalogy,theyhavebeenpccri' at a city duringthenightandseeingonly thewindowsin which lightsareburning,rlth' thanthe skyscrapers to which thosewindowsbelong.
I
I
L
9.I THE DENSITYOFTHE UNIVERSE readingthisbookmayhavenoticedan interesting trendamongastronorr, Psychologists in thc ( lr, thegrandest concepts that,whilsttheypretendto understand andcosmologists ideasandunitsto makeit comprehensilrl verse,theyareforeverinventingnewparticles, they inventedthe lil in milesbecamefar too largeto conceptualise, Whendistances tl year.Whenthe plethoraof sub-atomicparticlesbecametoo dizzying,theydevelopc
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Instcatlol'cliscussing Inass.wo arc goingto uscil rclatedquantity,density,becausethis takesinto accountthc cxpansiottof thc Universc.Chapter4 introducedthe Friedmann cquation(4.29) which rclatccltlrc glorvth ofthe scalc factor to the interplaybetrveenthe Universe'spotentialgravitationalcnergyand its kinetic energy.Thesequantitieswere relatedto tlredensityin the cascofthe potentialenergyand the rateofthe expansion,as quantificd by the tlubblc constantI'or the kinetic energy.Three possibleoutcomeswere briefly introduced:the open,'flat'or closedscenarios. which one of theseUniverseswe Iive in dependsupon tlte quantitiesofthe Hubble constantand the densiry.The sign ofthe energyconstant,k, in the Friedmannequationis the diagnosticfeaturewhich allows us to distinguishbetweenthesealternatives.Positivevalucsofk correspondto open Universes. In the case of an open Universethe amount of matter it containsis too small to create enoughgravity to halt its expansion.Arr open Universe will expand forever rvhilst the relativerateofthe expansionis givcn by the magnitudeofk.
9.2 OPEN UNIVERSES As the openUniverseexpands,the clustersof galaxicswill becomeevermoredistantfrorn one another.The continuedexpansionof the Universewill make the superclustersmore extendedand tenuous,but the individual clustersshould remain relatively undisturbed becausetheir force of self-gravityis strongenoughto overcomethe l-lubbleexpansion.As statedin chapter7, the halos of matter which have been observedaround some galaxies may still be feedingthesevast star-formingsystemsrvith raw materials.such galaxies_ predominantlyspiralsand certaintypesofirregular- will continueto form starsfrom their gasreservesfor many billions of yearsto come.Thosestarsmay then continueto shinefor many more billions of years after that, dependingupon their size. The amount of raw materialin the Universe,whilst vast in quantity,is not infinite. Stellaractivity must cease at somepoint when the universe becomesdepletedof usefulgases.This is the stagewhich is expectedto be reachedafter it passesan age ofabout l0r2 - lOrayears.That is approximately70 to 7,000 tirnesthe currentage of the Universe. Although the universe will no longer containbright, hydrogen-bumingstars,galaxies in the broadestsenseshould still be identifiableas large congiomerationsofmass. They will containstellarremnants,suchas white dwarfs,neutronstarsand black holes,orbiting aroundthc nucleusin much the sameway as the luminousstarsonce did. As the Universe agcsstill furlher, the number of close encountersbetweenthesestellar remnantswill becotnesignificant.It is irnportantto t'ememberthat in this futuretime the frequencyof these cncountcrsis not likely to increasefrom their presentday scarcity,but thby receive our attcntionbecausethere is nothing else more interestinggoing on! As a consequenceof lhcir rclativescarcity,the time scaleson which they influencesignificantchangebecomes very large indeed.In thc encounters,kinetic energycan be transferredfrom one remnant to anothcr.Thus, whilst one is givcn more energy so that it may escapefrom the galaxy altogether,the other'losesenergy and falls towards the central regions.The stellar remnantswhich escapeseemdestinedto wanderthe depthsofintergalactic spacefor the rest of eternityor until they are capturcdby sorneother hcavily gravitatingbody. Thosc which fall towardsthe centreof the galaxy rvill incrcascthc densitythere anrJallow massive
Sec.9.2l
OpenUniverses 175
blackholesto form. If a blackholealreadyexists,it will contributemoremassto it and, as morestellarremnantsfall into thesecentralregions,a brief resumptionof activity, mayoccur. similarto thatfoundin activegalaxies, by a verydiffuseseaof interBy theageof l0't years,the Universewill be populated wereejected.The galaxies they which galaxies from parent galaiticualubondsundth. themselveswill containa paltry populationof stellarremnantsdominatedby a central' black hole.Eventuaily,afteraroundl02oyears,the galaxieswill be nothing supermassive black holes.After this, the variousclustersof thesegalacticremains bui supermassive andformevenlargerblack (whichwereonceclustersofgalaxies)will graduallycoalesce This processwill protogether. coalesced holesin the sameway that the stetlarremnants black gigantic cluster-mass a single, but nothing of consist which remnants ducecluster an ageof approxto be in thisstateby thetime it reaches hole.The Universeis expected imatelyl03oyears. are allowedfor within the scopeof Rt itris point in futurehistory,two possibilities modernphysics.which onewill actuallyhappenwill dependuponwhetheror not protons by certaingrandunifiedtheories' Thisdecayis predicted will decayintolighterelements. force.It doesthis by predictelectroweak to the force whichseekto link thestrongnuclear (suchas electrons)'Thc into leptons be turned protons) can (such as hadrons that ing to takeplaceis as folprocessis supposed by wtrichttrishypothetical prlcisemechanism quarks. lf the quarksare of three proton is made 2, the chapter iows. As discussedin thoughtto be the sizeof gotf balls,the protontheycreateactsas if it werethe sizeof thc solaisystem.The three quarksare moving aroundinsidethat volume and attracteach othervia the elastic-likeinterquarkforce.The volumeofthe protonis definedbecause,if a quarkbeginsto straytoo tar, it is yankedbackby the othertwo. Shouldtwo ofthe three quarksconiainedwithin the protonmovecloseenoughto oneanother,theywill exchangc a virtual particle,and the protonwill decayinto a neutralpi mesonand a positron.The pi-mesonwill thenannihilateitself becauseit is be composedof an up quarkand its antimattercounterPart. Assumingfor now thatthis canoccur,the lifetimeof a protonis calculatedto be someyears.Whentheydecaytheyeventuallytum into lighter - 1035 wherein the regionof 1030 particlesknownasleptons.Leptonsareparticlessuchaselectrons,Photonsandneutrinos' Thus,if protonsdo decay,atomswitl no longerbe ableto existand so any remaining The Universewill becomea dilute seaof leptons, will be dissociated. stellarremnants possiblackhole.Not eventhis unpleasant supermassive pock-marked by theoccasional arc holes black about ideas Hawking's lf Stephen end,however. bitity markstheeventual to place close take vacuum in the quantum fluctuations when evaporate can right, they ttt-eireventhorizoni.Whenthis happensa pair of virtual particlesis created,oneof which falls into the blackhole,depletingit, whilst its counterpartescapesandgivesthe impresThis incrediblyslow processgraduallyconverts sion that the black hole hasevaporated. all theblackholesinto leptonsafterl0r@years. If, however,protonsdo not decaythenspacewill still be filledwith a few densestellar Eventually suchasneutronstars,evenafterall theblackholeshaveevaporated. remnants, thattheUniversewill reacha positionwhereit is in thermalequilibrium' it is conceivabte In this situation,all chemical will be at thesamelow temperature. i.e.all its constituents death'' the'heat to died have is said andtheUniverse cease, reactions
I
I' I | 76
' f he fa te o f tlr e lJn ive r sc
lch.9
'Flnt 'llnlvcr r crI
Sec.9.4l
f
9.3 CLOSED UNIVEIISI'S
9.4 'FLAT'UNIVERSES
Anotherpossibilityis thatthe signof the encrqyconstarrt is negative.This leadsto a Universewhich is closed.In casessuchas thesc,the lJniversecontainsso much matterthat its gravity can halt the expansionand therrrevcrseit. This rvill lead to a collapseof the Univcrseand a big crunchl In this scenario,the clustersof galaxiesrvill eventuallyslow each other down, by the force of their rnutualgravity. and will then begin to attracteachother. Whilst it may appear, at first sight. as if the Llniverseis runrringin reverse,it is importantto rememberthat time will still flow forwards:for instance,hy'dlogenwill still fuse into helium in the centre of stars.So, starswill still be born out of collapsinggas clouds,they rvill live out their naturallives and die by beconringeither planetarynebulaeor supernovae.The only difrerencewill be that the galaxiesget closertogetherratherthan farther apart,becauseinstead of an expansionthere will be a contractionof the spacetimecontinuum. 'I'hemost noticeable changethat this will induce is that, insteadof a redshift, the distant galaxies will display a blueshift,becausetheir spectraarc being squashedby the collapsing Universe ratherthan stretchedby an expandingone. 'l he other obvious differencewill be that the tcmperatureof the cosmic microwave backgroundradiation will appearto increase,becauseits photonswill be blueshiftedto highcr energies.For the majority of the time, however, life in a collapsingUniversewill be very similar to that in an expandingone. Only during the final billion yearsof its existencewill the eventsbecomeinteresting! The first thing to happen,as the volume of the Universe shrinks, is that superclusters and then clustersof galaxieswill merge.This rvill increasethe number of galaxy interactions which take place.The incrediblyfrail spiral galaxieswill be the immediatecasualties ofthis consequence. They rvill be convertedthroughmergersand interactionsinto inegular and elliptical galaxies.Giant elliptical systems,similar to the cD galaxiesfound at the centresof clusters,will form in abundance.lnteractionsand mergerswill become such conrmonplaceoccurences that, probably 100 million years before the end, the universe itself will simply be a huge collectionof slars.Therewill be no individualgalaxiesof wlrich to speak,sincethey will all have lost rheir identitiesin this titanic merger. As time continuesto pass,the individual starsand planetswill continue to be pulled togetherby the force of their nrutual gravity. some of theseobjects will collide and, as they accumulatemore tnassand becomenrorc dense,will becomeblack holes.Thesewill then grow at a prodigious rate becausethe density of the Universe will make collisions highly likely. If the remainingstarsand planetsescapethe black holes, they will simply evaporateinto space.This bizarre fate is causedby the increasingblueshift ofthe cosmic nticrowavebackgroundradiation. Its teurperalurewill rise so much that it will be as if spaceitselfhas reacheda temperatureofsevcral tensofthousandsofK. Tlre varioustypes of star will all dissolveas spacebeconreshottcr than their surfaces.Eventually,the Universe will reach a stagervhereatoms will bc dissociated,and then baryons broken into quarks.fq the final few secondsbefore the calaclysmicend, the conditions may be very sirnilarto thosewhich existedin the first ferv instantsfollowing the Big Bang. This notion has led some to suggestthat tlre Universe rnay 'rebound' and that out o[ the big crunch anotherBig Bang will occur. Others believe that the Universe will sinrply retum from whenceit came(see later).
The dividing line between the open and closed Universe possibilities is a spccittl ' '' il 1ht known as a 'flat' Universe.This correspondsto the energyconstant,k=Q, llg66n3c tt ll ol fntc thc time, of length infinite an tainsjust enoughmatterto stop expandingafter lltin At Universc. an open of I"" that from indistinguishable be actually Universewould rvlrr' it is also worth mentioningthat it is possiblethat our universe is a closed [lnivcrsc just happensto be very long lived as well. In this caseit will evolve along the littcs ol tpen Uni.rrersebut eventualty collapse into a big crunch after the stars have ccnserl shine. is ttotl With the theoreticalcosmologistshaving defined the various possibilities'it tylt'' in which determine to evidence Tor the to search astronomers to the observational will tto tln" Universewe live. This, as thosewho have read the book from the beginning tlttr' have alreadyguessed,is no easymatter.As we statedearlier in this chapter,tltc iwo ctttt"'t the llubblc are live in, we of Universe type the define to tities needed,in order pinning {owtt lr and the density.Chapter5 discussedthe difficulties astronomershavc in this btxrk wc lr" throughout argument' value of the Hubble constant. For the sake of vnlttt'ill t tho to estimate us leaves This km/s/Ir4pc. 75 value of often used the average xilrl sotttc density.The first thing we can do is restrictthe rangeof possibledensiticsby deductivereasoning. The value of the Hubble constantis of crucial importanceto theseestimat€$bcctttt"' tr helps to set a tower timit to the amount of mass containedwithin the Universo, lltrrl tltc cot't' and higher much have been would mais been too low, the Hubble constant tlr 11r' would have expandedso much that its constituentswould not have been ablc ltnvtr l" togetherthrough gravity. In a Universe such as this, galactic structureswould 20 ltill unable to form. Conversely,the fact that the Universe is about l0 billion to contaitrs it matter of amount the that means redshift) a (and stilt displaying yearsold ' not be toogreat either. If the density were very large the Universe would be cxpitttrl' cascs,lr' only very slowly, or would have already begun its collapse or, in extreme wc ' general observations, very some than more little using .otiapseOalready.Thus, by in A ttrttr point somewhere one lie at must the Universe of the density that conciude rangeofvalues. ll'a r';' in order to quantifi that range we need to introducea slightly new concept. |r i Friedtnann the from easily very shown it can be is assumed, for the Hubble constant it trt lhc as tion (4.29) that the density required to create a 'flat' Universe is known density, p",i' dfld is given bY: n
rcrtr
=-
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is tct I The actualdensity ofthe Universe,p, is usually expressedas a ratio to this and C):
Q =-!Pcrir
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Opcn Onivcrscsoccltrwllotl!)-:1, iln(lcloscdllnivcrsesrvhenf)>1. Fronrthe sirnplcfact thatrvc cxisl in an cxPandittgUnivcrscrvhiclrcorrtains gravitationally-built constructions, we cattcslinratctltatottr [.]ltivcrsoliessorrrervhr:rc in the region0. l
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testsof inflationtheory 179 Observational
Sec.9.51
of a positively curved Universe,however,the edgeswould have to be squashedin order to flatten it. This would causethe dots to dppeardenserthe further away they were viewed. The situationcan also be visualisedby thinking of circles drawn on the various geometries.If a circle were drawn on a sphereits circumferencewould be smallerthan 2nr. Thus, if it were to be mapped on a flat surface, the circumference would have to be stretched. Conversely, a circle drawn on a hyperboloid would have a circumference greater than 2fir, which would necessitatecompressing the circumference in order to map it on a flat surface. If we replace the rubber sheet with the spacetime continuum and the painted dots for galaxies,then it can easilybe seenhow this analogyrelatesto our Universe. ln principlc, it should be possible for the astronomer to calculate the curvature of the Universe frorn sourcecount observations.A numberof complicatingfactorsmake this more diflicult than it sounds,however.As alreadystated,the expansionofthe Universecausesus to observc an increasein density.We must try to separatethe two phenomenato seewhetherthere is any residualdifferencein density.The secondproblem is to ensurethat all the galaxiesitr the sample are detected. Looking further and further into space, the fainter members bccome much more difficult to observe.Therefore,it is very easyto observean overdensity of galaxies in the nearby Universe becauseyou simply cannot see the galaxies which arc far away. These various challengeshave so far conspired to make the source count obsen ations inconclusive. The secondway in which we could attemptto determinewhether or not spacetimeis flat is to use our concept of the astronomicalcensusand thus calculatehow much mass there is in the Universe.We have assertedin the previouschapterthat a componentof thc Universe is in the form of non-baryonicmatter. It is now time to start placing a morc 'l'o concrete figure upon just how much of the Universe is composed of exotic particles. lumijust amount of the Estimating is how much baryonic. determine we must start with, nous baryonic matter is relatively straightforward, and although it is subject to a fair margin of error the result is very important. The density of luminous baryonic matter, p$. is found to be severely lacking tvhat rvould be necessaryto close the Universe:
Q,o=b=o.ol-o'03
(9lr
pcrit
of luminousmatterdensityandthecriticaldensitr between theestimates Thediscrepancy hasbecomeknownasthe'missingmass'problem.Our firststeptowardssolvingtheprob just how muchbaryonicmatterthereis in total. lem comesin our attemptsto estimate forms:ftrr almostcertainlythereare vastamountswhich are in non-luminous because in interstellar cloudsand matterin the halosof galaxies.Massdetermination' instance, madefromtherotationcurvesofgalaxiesshowthat M r o tr f Mlurinoo,
-2
- l0
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within the halo in ordert,' mattermustbe contained The majorityof this non-luminous tlr, hasrevealed givetheshapeofthe rotationcurves.Veryhighcontrastimageprocessing Theseimageshaveshownthathalosareoftenflattenedsystcrrl halosofseveralgalaxies. bolsterstheideathattheyarepreclottrr whichareoblatein shape.Thissingleobservation
I 80
T h e fa te o f th c tJn ivcr sc
l ch.9
nantly baryonicbecauseas orbiting baryonicmatterlosesenergyit will tend to flatten into a disc. . . 1'heqiQ.ects contposingthe baryonicconrponentof galactichalosare known generically as MACHOs - 'massive and compact halo objects'. lt is thought that they are mostly stellar renlnantssuch as neutron stars and black holes, or failed stars known as brown dwarfs. The best way to directly detect these MACHOs is to watch for their effect on distantbackgroundstars.If the MACHO's orbit carriesit in front of a star, that star will be gravitationally lensed.The gravity of the MACHO is only weak, however, and the imagesit causeswill not be distinguishable.lnsteadthey will combine to make it appear as if the backgroundstar has brightened.TheseMACHO events,as they are called, have beenobservedseveraltimes; most notably in 1993,when a star in the Large Magellanic Cloud was observedto brightenin responseto the passageofan unseenobject within the halo of our Galaxy. Thus, we can give a rough figure for the total density of baryonic matter,pb,in both luminousand non-luminousfonns:
Oo=I!-=g.1
(e.5)
Pcrit
Corroborating this picture is the present-dayabundanceof the hydrogen isotope deuterium, formed during the early Universe as an intermediatepart of the proton-proton chain rvhichresultsin heliunr.'fhisreactionis shownin (l.l) with the deuteriumbeing producedin the first stage.'l'hus,the abundanceofdeuterium can be seenas a measureof how cfficiently the heliunr fusion processtook place in the era of nucleosynthesis.If it were 100 per cent efficient then thereshouldbe no deuteriumin today's Universe.This is becausethis isotopeis not synthesisedin any greatquantitiesby the presentday Universe. In fact, ifit is part ofa star,deuteriumis destroyed.Young stars,suchas T Tauri stars,can be spectroscopicallyobservedto containdeuterium,but older starsshow no trace ofthis elernent. Thus the estimateofdeuterium to hydrogen,in interstellarenvironments,can provide a meansof estimatingthe amountof baryonic matterin the Universe.This is becausethe densityof baryonsduring the era of nucleosynthesis is one of the defining conditionsfor its efficiency.Had the densitybeentoo great,there would be no deuteriumleft becauseit would all have been convertedinto helium. Too few baryonsand the abundanceof deuteriurn would be much higher. Using this idea we can estimatethe density of baryons basedupon our knowledgeof nuclearreactionsand the observedquantitiesof deuterium in today's Universe.It turns out that from this considerationthere can be no more than l0 per cent of the critical density in the fornr of baryonic matter, otherwisethe deuterium abundancewould be inconrpatiblewith currentobservations. This would seemto imply that the Universeis open.However, if rve move up the size scaleto clustersof galaxiesand estirnatethe arnountof luminousmatter as a ratio to the total massgiven by dynamicalobservationsrve find that
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bcctttt:" This ratio provides,as its upperlimit, enoughmatterto closethe Universc, the-unrrristrrk then Universe Soif we live in an inflationary ' [(9.3)we statedC),0-0.01. darkmattermayprovideup to 99 percentof thclllilllt r [is thatnon-baryonic cstitturl'' "on"lurion our universe!our estimateof baryonicdark matterled us to (9.5) and an of ttr;rt ob-0.1, but thatstill meansthat90 per centof the universeis in exoticforms arrr' lirr thought quite a sobering is That . disiovered whichwe maynot yet haveeven t lllrt' cross 'i's and L the dot is to cosmology for is left that all that notion temptedby the - thema.iorily.l ' andmodellingconstraints Ii- asseemtlikely fromobservational to snyxhorrl';r very interesting darkmatteris cold darkmatter,thenwe havesomething llrrrlrl we sttltc.d. 3 In chapter applicable. principle is cosmological scaleon whichthe lr L milliorl 600 only on scalesgreaterthan300 million to Universeis homogeneout h'' lutninotts the only took which wasbasedupona redshiftsurvey years.Thatestimaie only onepcr cctll ('l 'f If this typeof matterrepresents Lnic matterinto consideration. tlttttil thencanwe reallymakesucha boldassrrrnption totaldensityof theUniverse, :''' L good wc lltttlltt'l ns as Luminousbaryonicmattermaynotbe therealmaisdistribution? t If thedensityof darkmttttcrfollorvt'rl at tracingoutthemattercontentof theUniverse. in theratioof lrrrlrirrorr densityof luminousmatter,thenwe shoutdnot seean increase I' to clustersto supcrclttstct thescalefrom individualgalaxies " L totalmassaswe increase gal ax i es
t i
average de ns i tY
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Thuswe haveclearevidencethat the Universocontainsmorematterthanits baryonic content. Continuing up thesizescale,thelargcstscalestreaming motionsindicatethat
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S e c.9 .6 l
Itorvcvcr,thc dalk rraltol is spr-catl lair'lyrrrrilblrnlvthroughoutspace,then as the volume unclcrinvestigation increases so tlremassratio rvill also increase.Ilot dark matterwould naturallybehavclikc thisbecausc, travellingat high speeds, it would resistclumping.Cold dark rnattercan bchave in the sarneway, and lhis introducesus to the conceptofbias in our rnodels. Iliasingin a cold dark nrattcr[Jniversenreansthatnot all concentrations ofdensityrvill beconregalaxies.Ifwe imaginethat largescaleundulationsare presentin.the cold dark matter,representing superclusters and voids,then,superimposed on top ofthese are fluctuationsin the baryonicmatter.Only when the lotal densityof both typesof matterexceeds a certainlevel doesa galaxy form. This allorvsfor a much more homogeneousdistribution of matterthroughoutthe Universethan is indicatedfrom the simple distribution of luminousgalaxies(seeFig. 9. I ).
9.6 COSMOLOGICAL MODBLS The Friedmannequation(4.29) can be usedto constructgraphsofthe scalefactor versus time which allows a visual interpretationof variousuniversalgeometries.In the first and sinrplestcasewe shall look at an open Universewhich is filled with nothing but radiation. This would havebeenthe casewith ours if the C. P and T invarianceshad all held individually and precisely.The variousmodelsare namedafter the peoplelvho first derivedthem. This model is known as the Milne model. We will begin with the Friedmannequation (4.29) but substitutefor the Ilubble constantusingequation(4.3l). After a trivial piece of sinrplificationwe obtain the Friedmannequationin the following form: i r .8 n Gp R' K- =
3
- kc2
(e.8)
Strictlyspeaking,our constantk is not the sameas the k in (4.29)becausewe have changed its sign convention to retain tlre energy constantdefinitions of the open and closed Universes.We have also dividetl it by c2 in ordcr to give it the appearanceof a general relativistic interpretation.ln an open, radiation-filled Universe, p=0 and k=-1. Substitution ofthesevaluesleaclsto R=*c
(e.e)
This eqliJitiontells us that the rate ofchange ofthe scalefactor is a constant,i.e. the rate is neitheraccclcratingnor decelerating.1'hc constantin this casehappensto be the speed of light,andcan bc intcgratetl lo give us the cxplicittime-dependent evolutionofthe scale lactor: ll = +'ct
-[
I(:h,9
(e.ro)
So, in a radiation-orrly opcrt[.lniverscthc rate of cosmicexpansionis a constantwith a magnitudcof lhe spccclol'liglrt.Notc that tlrc 'l- invarianceis presentin this model by the inclusionol'tllc t sign (cirrrsctl by squalcrooting,ct;. This meansthat a radiation-filled tlniverse could cvulvr: irt cxaclly thc samcrval,regardlessof whethertime ran forwardsor backwards(scc l;ip,,().2).
havc Fig. 9.2. The Milne cosmological modcl provides an idea of how our [Jnivcrsc would exf,anded had it contained only rartiation. ln this model, the Hubble timc is thc precisc agc ol tlrc Universe.
The age of a radiation-filled Universecan be derived very easily. In chapter-5tltc ' ion of the Hubble time was mentioned.The Hubble time, t, is the reciprocalof the I lrrl constant: I
r ,t
Ho The Hubble time can be thoughtof as the time it would take for a celestialobject to d"' its distanceifthat object is not subjectto any accelerationor decelerationin its vclr" This would imply that it is also the time taken for the object to reach its current disl;r' Thus, the Hubble time is an estimate of the age of the Universe if the expansiorr remainsconstant.In a radiation-dominatedUniverse, equation(9.9) tells us thtrt tlr' pansionrate does indeedremain constant. Combiningequations(4.31) and (9.11) allows us to calculatethe Hubble timc irr following way:
R
(tl
R (9.9)and(9.10)into(9.12)gives: Substituting +
-
|
('
givesus theagc,' Thus,in thecaseof theMilnemodel,theHubbletimeaccurately Universe. The nextcasewe wishto consideris a Universewhichcontainsthecriticaldcnsi' it is tht' matter.In thiscasep=p">0 andk=0. We havechosento featureit because thesearethc p:' because but it is alsohighlyinstructive simplestcasemathematically;
l l l l l l l l l l l l l l
''x
l{t4
I ' h e fa te o fth c lln ive r se
fch e
Cosmological models
S e c . 9.6 l
I tl5
etersof an inflationaryI Inivclsc.It is kno',vnas the Einstein-deSitterrnodeland, once again,sonresimplificationof tlrc slarrdard lrriedrnann equationis required.-l'histime, becausewe are dealingwith a non-zerOdensityof nratteran actualvalue must be substituted. We statcdseveraltintcs in chapter4 that the densityof matteralterswith the inversecube of the scale factor. l'his allows us to constructan equationfor the density p, of the Universeat any time, frorn its value at the presentepoch,po,and the ratio ofthe presentscale factor Rnto the scalefactor at any time. R:
(n"\' 0 = oo[-*J
(e.| 4)
When this and the energyconstantis substitutedinto the Friedmannequationwe obtain
oz 8nGpoRus 3R
(e.l 5) +-zlgT
From this we can seewhere equation(4.32) camefiom becausewe can define a constant: ^
SnG poRs l
present day
(e.16)
J
and then statethe proportionality:
!)'* 1 R,=rg \ dt l R
T (e.r7)
which is equivalentto (4.32). (9. I 7) can then be arrangedinto the integral:
()f period of time for our Universe to have been in existence, based upon the age estimates
Rt
lR'dRc
(e.| 8)
ldt
JJ
00
which evaluatesto (4.30) and providesus with the time dependencyof the scalefactor:
(e.re)
R = at'l'
l'his time the scale factor of the Universeis agnin dependenton a consfant,a, but this is not the speedof light, and the scale factor altersrvith time becauseof the term involving t. Differentiationgives the rateof clrangeof the scalefactor with time:
"'l' n = 3u1
(9.20)
J
The agc ofan Einsteintlc Sittcrtlnivcrseis lhclefioregivenby 3 itt
t/'
3
1,n1,i, z,
modelshowshow a 'flat' Universeexpandsbecausc Fig.9.3,'l'heEinstein-desittercosmological it containsboth matterand radiation.ln this casegravity graduallyslowsthe expansion.and so of the ageofthe Universe. the Hubbletime is an overestimate
iome stars. The members of some globular clusters, for instance, are approximately l0 bitlion years old. We shall return to this dilemma when we consider the cosmological constant. Open and closedUniverseswhich containmatterare more complicatedto handleusinl' the Friedmann equation, but they too can be reduced to diagrams showing the way irr which the scale factor changeswith time (see Fig. 9.4). The fact that the rate of changeof the scalefactor, given in (9.20), is a function of tirrrl meansthat it, too, changeswith time. In other words, the universal expansioncan eitltcr accelerateor decelerate. We know, from our consideration of the fundamental forccs ol nature in chapter l, that gravity is the shaping force of the Universe on the largest scalc'; and so we would expect a decelerationrather than an acceleration.If we diffcrcntiirt' equation(9. I 5), the decelerationequationis
*l(
(e . r) 2
which statcsthat thc llubblc tirrrcis an over-estirnate of the ageby a factorof two thirds (see Fig.9.3). T'ltisrncirnsllral, in nn llinstein--
= --
4nGpR
( 9 .2 ?t
J
Usually the decelerationis wrapped rrp in a dimensionlessquantityknown as the decclcr;r tion parameter,q, which is defined in the following way:
RR
O' R=z --:-=
( 9 .2 1)
186 'l'hc fatevithc llnivcrsc
lch.e
Sec.9.7l
General rel ati v i ty
r r
lllT
q- 0..5. In the caseof the Milne model, q=0. A 'flat' Einstein-deSitter Universepossesses Open Universesare those in which q< 0.5, and in closedUniverses,q>0.5.
fll-
Mi l ne model f)-n
K =-l
9.7 GENERAL RELATIVITY
Open Q<0 K <0
So far, everythingin this book hasbeenpresentedin Newtonianphysics.Generalrclativitv has been mentionedseveraltimes and yet the mathematicalnoteshave managedto avoirl using it! Generalrelativity is inextricably linked to cosmology,however, and is unavoitl' able in its continued study. The reason for this is that the Universe is governed,on ilr; largestscales,by the gravity ofthe objects it contains.Its entire evolution is detcrnrincrl by the amountof masswithin it, and the only applicablegravitationaltheory that wc possess is generalrelativity. The theory grew out of Einstein's special relativity, in which he investigatedwhat it would be like to travel at speedsclose to that of light. The special theory was restrictcrl becauseit dealt only with unaccelerated(inertial) casesof motion, and Einsteinwantcd t() extendhis work to encompassacceleratedframesof motion. lt has been known since tlrr' time of Calileo, from his legendary(although probably apocryphal)experimentof drop ping objectswith different massesfrom the leaningtower of Pisa,that the Earth's gravitir tional field actson all objectsequally,regardlessof their individual masses.'l'he actiorrol the Earth's gravity is to induce objects to accelerate,which is why generalrelativity cln be usedto investigategravity. The force of gravity is given by equation(1.3). In that equation,if m, refersto the nrns,i ofthe Earth, then it can be seen that the strength ofthe gravitational force is dircctly proportional to the mass of the object upon which it acts. This proportionality is also applicableto some other forces,notably cenhifugal force and Coriolis force. It allows us to define a set of forcesknown as 'kinematic forces'. Theseare all indistinguishablelrorrr accelerationsand directly proportionalto the massofthe objectsupon which they act. The mass,mr, in equation(1.3) is called the gravitationalmass,ms, becauseit causcs the force of gravity. Newton's second law of motion statesthat the inertial mass of arr object is the quotientofthe force, F, acting upon it to the acceleration,a, which that forcc is producing:
Flat (Einstein-de Sitter () = 1 modet) K =0
C l osed ct> 1 K >0 p r e se n l oaY
t
Fig.9.4.open andcloscdmodclsofthe universe
mi = -
F a
Gm r a- ---;
( 9 .2 5 1
t-
Fig 9.5. A Universccontaininga cosnrological constantcan be a Lemailrehesitationuniverse ln thiscase,the tlubbletirneis an undercstimate ol'thr:agcofthe Universe.
l_
t t
Q.2at il:
Theprincipleof equivalence is theconcisestatement of theexperimental factthatincrtirrl massand the gravitationalmassare exactlythe sameto a very largedegreeof accuracy Usingtheprincipleofequivalence we caneasilyshowthatall objects,regardless of thcir mass,areaccelerated in the sameway by a gravitational field.To do this,simplyequatc ( I .3)and(9.24),whichthensimplifiesto present day
t_ t_
Einsteinencapsulated his principleof equivalence in a seriesof four 'thoughtexperiments'whichsoughtto describewhatan observerinsidea sealed'box' (lesssadistically termeda laboratory)couldor couldnot sayabouthis locationandstateof motion.
I
il t il
t
t
):
I
rrl
I
tl
lr l1 l'']
l l l l l l l l
I ttfl
'l
he fllc of ltr e I lr r ir er .r r
Itna ginca lili c or r t ir ir r irar gl) c r s onanc la l r l l l l 'h e l i l t i s s e a l e di n s u c ha i v a y t h a t n o obscrvations of tltc otrlsitlcrvorlclcanbe ntade.ln the first experimentthe lift is takenilto spacc,rvcllaway liorrtarryplanctor starrvhichrvouldexerta gravitational pull upon it. A rockct nlotor is attachcdto lhc baseoflhc lifl and the rvholeasscntblyacceleraled to 9.8 rn/s2by ignitionol'tltc t'ockct.1'hepersoninsidethe lift then lets go of the ball and watchcsas it falls to thc floor. 'l'hc accelerationof the ball towards the floor rvoulclbe equal.but in the oppositeclircction, to the acccleration ofthe lift. ln the secondexpcritncnt,the rocketnrotorsare turnedoff. The lilt lvoulclcontinueto drift at its final velocity.'t'histinre if the ball u,crepickedup and released,it rvouldhang motionless in mid-airbecause no lbrcesrvouldbe actinguponthe lift. The occupantrvould alsofeel weightless. In the third experiment, the lilt is broughtto Darthand suspended, unmoving,in a lift shaft. The ball is released,and we knorv frorn common sensethat it would accelerate towardsthe floor. The rnagnitucle of that acceler.ation, causedby the Earth'sgravity,is 9.8 m/s'. In the fourthand final experinrent. the lift is crrtfrom its suspension and allowedto fall freely down the shaft.Tlre lift and its contents(the occupantand the ball) are all accelerated undergravity so this time, when the ball is released,since it is alreadyfalling -that downwardsat 9.8 m/s2,it actually appearsto rernainstationaryinside the lift. Again the occupantfeelsweightless. To the personinsidethe lilt, the first and thir(l experimentsare indistinguishable,as are the sccondand fourth. In the first experinrentthe accelerationon the ball is causedby the force of the rocket.In olher rvorclsit is a straiglrtforrvard exampleof Newton's secondlaw ofmotion, and so the ntassinvolved is the inertial mass.In the third experintentthe force is gravitationalin origin and concerrrsitself with the gravitationalmass.Both, however, causethe ball to accelerate downrvards and. lrccauseofthe principleofequivalence,are indistinguishablefronr one another.Imaginefrrrtherrvhatwould happento a rocket acceleratingaway from the Earth at 9.3 nr/s2.sincc tlre downward pull of gravity would try to accelerateit in the oppositedircction at exacrly the same rate, the rocket would get nowlrere. To place the conchrsions ol thcsethoughtcxperimenlsin a sontervhatnrorecolrcise way: Einsteinstatedthat accelcrations and gravitationalfieldsare indistinguishable from one another;so indistinguishable, in fact,that a corrcctlychosenand appliedacceleration can counteractthe elfi:ctsof a gravitationalficld and vice versa.In essence, this is the principleof equivalcnccand shorvswhy gener.al relativity,which soughtto describean accelerating frameol'rcfclcncc'sviov of thc Universe,alsodescribes gravity. The next conccptrvhiclris ccntralto gencralrclativityis that ofthe spacetirne conttnuum. -I'hc idea ol'a lirttr-tlintcnsiottal represcnlation of the Universervlrichdescribed evcntslry referencirrg thcir tlrrcc-tlirrrcnsional spirtialcoordinates (x,y,z)and the time,t, at which thcy lrok placc.rv's li.sr tlc5clibs4by Ilc.rnannMinkowski in 190g. Itl thrccclitncltsiotts tltc tlisllrtccbclwccntr.vo1'roints in a Cartesiangriclis givcn by
;r
As " = Ax ' r Av
ll 'll
I ( - h .9
r At . '
(9.26\
In sp lrc r ic alpolir rc oor t lir r alcllr s is is ,\sl
Ar r , r ' ( A, pr r . ; ir r ' , 1r , \ { ) r )
(9.27)
Generalrcletivitl- 1'
Sec.9.7l
To extendthis idea to a spacetimeframework,imaginetwo events,eachone characteri" by three spatialcoordinatesand a time. To transformthe times into units of distancetlr, must both be multiplied by the speedof light, The interval betweenthe two can therr I calculated:
As2=At2.i(*t
+Av2+Az2)
(().' '
In sphericalpolar coordinatesthis becomes
As2= at2*{(nrt \ c'
+r'A,trt+r2 sin24ae2)
(e ."
' The concept of space-likeand time-like separation,introducedin chapter 3, can norv I treatedmathematically.The interval betweentwo eventsis space-likeif an observercr',' not be presentat both events,and tirne-like ifthe observercould be presentat botlr cvcrr, ! In the case of a space-likeseparationAs2<0.Time-like separationis charactcrisccl '.'' the conical possibilities by is represented AsL0. The dividing line betweenthesetwo face of the light cone in Fig.3.3 on page46. Theseare the pathsfollowed by lighl r:, away from the first event. Ifthe secondevent lies on the edgeofthe first's light conc, r rays of light leaving the first event are the only things which can be presentat the sccOr event, then the interval between them is said to be null becauseAs':0. Ilvery tittrc ' observean event in a celestialobject - say the explosion of a supernova- the inlcrr betweenthe event and the act ofobserving it is null. In the sameway that As2of equation(9.21)describesa tiny portion of spacebclrv'' two points, so the As'of equation(9.29) describesa tiny portion of spacetimebetwcent' events.Recall now the cosmologicalprinciple, which statesthat the Universe is both l, mogeneousand isotropic.Therefore,As2must be the sameat each point on the spacclil continuum.This severelyrestrictsthe possibilitiesand leads to the positive and ncgalr curvatureswhich we haveconsidered.The 'flat' caseof no curvatureis also allowed rrrrrl the cosmologicalprinciple. Equation(9.29)is known asthe 'Minkowski metric'.A 'metric' is the term for an ct1" tion which can mathematicallydescribea four-dimensionalstructuresuch as the spacctrr continuurn.In order to take into accountthe cosmologicalprinciple, Robcrtsotr:r, Walker modified it to become \ 1 r R2( ao2 ) .a ). r ctL 6 ' +o 'si n 2 4 Ae 2 | Asr =a tr - ". | "" " c'\l - ko ' )
(()
where o=r/R. In this equationo is a co-moving radial ordinateand k is the energy first rr in the Friedmannequation. In this generalrelativistic context it is usually known as t 'curvatureconstant'. To illustratethat this metric describesthe spacetimecontinuumlct us considcrorrr' its fundamentalqualities:expansion.Equation(7.1) is the spectralratio,which we slirl' rvithoutproof, gave the expansionfactor of the Universe.If the redshiftingof radiirtiorr indeedproducedby the expansionof the spacetimecontinuumthen, using thc Ilolr,' son-Walkermetric,we shouldbe able to derivethis behaviour,becausethe expansiorr embodiedin (9.i0) in the scalefactor.R.
lr
'1.
190
The fatc ofthe
Univcrse
Scc.9.8l
lch.9
c " l- k o'
lrl 9.8 THE COSMOLOGICAL CONSTANT Beforethe discoveryof the expanding Universe,all cosmologists had assunrcO rfrIrrrr ll[cosmoswasstatic.The only two peoplewho suspected it might not be wcrc Alckrrrr, ll Friedmann andGeorgeLemaitre,as explainedin chapter3. Theywerebothcnrlyex1,, nentsof Einstein'sgeneralrelativity.ChapterI explained how Einsteinhadinitinllyl', , 1;perplexed at his theory'sfailureto predicta staticUniverse.In theend,hisconstcrrrrrtr, /l ledhim to introducea newtermwhichhe calledA, the cosmological constant. lt is rrlt, "' stated,especiallyamongthosewishingto derideEinstein'swork, that this wasn 'lirl,l factor'designed to fudgethe equations. That is probablya little harsh,becauscthcr( lf somejustificationllom thetheoryfor it to be present. l]L WhenEinstein setthistermto a positivenumberit provided rvlrr, a cosmicrepulsiorr couldbe fine-turned to resistthegravitational attraction andholdthetJnivcrscstntic,| | modifiedformof theFriedmann equationis
(e.3I )
This carrbe rearrangedand transfornredinto an integrationto give the changein the scale factor betweenthe time of emissionand observationof the first crest:
'i-0,-= 'f -l-
,r"
*1 ,j*(,)""1u6-
(e.32)
A sirnilar integralcan be formulatedfor the enrissionand observationof the secondwave crest.This new equationwould havea right-handside identicalto (9.32) becausethe lim_ its will still be 0 and o, (remenrberingthat o is a co-movingradial ordinate).Thus, (9.32) transformsinto the following equality:
'i.+=,i+
8 n Gp R 2 * r =+l ( cK-
to
33
*N
(e.33)
(e.34)
The time between the emissionof thetwo wavecrestsis very small.Similarly,the time betweenthe observation of two wavecrestsis very small.over very smallintervalsthe scalefactorR(t)canbe regarded asconstant. l'his allowsusto write:
= RFJ RFJ dt o
dt "
AR 2
(t l
'
--a-
4nG pR AR 33
(t,
i
(e '
wheree <<1.This causes a'hesitation'Universe in whichthe expansion is severellr' estedfor a cosmological epochbeforecontinuing.This causesestimates of the llulrl timeto be too smallwhencompared with theactualageof theUniverse(seeFig.9.5t theperiodofarrestedexpansion occursat a scalefactor,R",thenan observational corl quenceofthis typeofUniverseis thattherewill bea concentration ofobjectsat a redsll z. definedas
(e.35)
lo = Ro Re
=
I = A. ( l +e)
If we usetheslightmodification of equation (2.1),l,=cdt,we canrearrange (9.35)to give l' "
+-
rt t It
! I l t I t I
In orderto find thevalueof A whichholdstheUniversestatic,Einsteinplacedboth19 t and (9.38)equalto 0, k=+l and solvedthemsimultaneously. This criticalvalueol knownas A", was shownto be superfluous by Hubblewhenhe provedthe expanrli' Universe,andEinsteinimmediatelycalledthe constanthis greatestmistakeandbarrislr it from his furtherconsideration. l This,however,hasnot sincestoppedits occasionnl by cosmologists, andit canin fact be shownto give an escaperoutefrom the agedilcrrrr pointedout earlier.GeorgeLemaitrepostulated a Universein whichthevalueof thc l mologicalconstantwasvery slightlyhigherthanthecritical value:
t.
' '
,)
andthedeceleration equation becomes
By investigationof the limits, (9.33) can be substitutedfor
'"*i'"o, '"*l'"u, .J *(il= J -O
'', I I
wavelengths is equalto the ratio ofthe scalefactorsat the epochsofobscrvutiorr;rr, emission. lf
As we definedearlier in this chapter,the observationof a distantgalaxy is said to be a null interval,in which As2=0."l'hedistantgalaxy is at o:o" and the time of enrissionof the first wavc crest is tc.The secondwave crestis then releasedat te+At". The time of observation, t., is when the obscrver,at o=0, seesthe first wave crestarriving. The secondwave crest is then observedat to+ Ato.Galaxieswill not exhibit any appreciablechangein their positionson the sky planebecauseoftheir great distances,and so de:d0=0. Using this to simplify the Robertson-Walkermetric we obtain
o=at2-g-4gl
.i
The cosmologicnl conitlnl
(e.36)
which is equivalentto the spectralratio, | +2, in cquation(7. I ). Thus, our earlier assertion that the spectralratio was a measureof the expansionlactor of the Universeis shown here to be true. This is becausewe have proved tlrat the ratio of the observedand emitted
l+z=
Ro Rc
rl
(e
t I t I
L
"l
t
192
1 1 ']
1 1 -]
IC h e
rvorthnotitlgis thc trtrcxplairlcd of quasars. Menrionecl l)cirkirrtlrcspacerlt:rrsity briefly at the ettclol'chapter(r, r;uasars appcarto clusteraroundredshift2. Coulclthis be an indication thal the [Jniverscslowed ils expansionconsitleratrly when it wasjust a third of its presentsizc?Convcntionalwisdornis not consiclering this possibilitytoo stronglyat the lrroment.I)ultditsprcfcrto itlvesligatc the line of rcasoningthatthe quasarpeakis an evolutionarycflect,with Inanyol-lheseaclivegalaxieslcachinga vigorousstateof activityby that stagcin the Universe.Biggcrand bcttertelescopes could resolvethe problernby detenniningifnornral galaxicsalso clustcrat that ledshift.Ifthey do not, the,hesitation' tJniversetheorydies. In morc recentyears, the cosmological constantliasagainbeenconsidered by cosrnologists.This is because its interprolation hasbeenastheencrgyofspace;a.rracuunrenergy', as it is krrorvn.So, spaceis not er))l)tybut seethcsu,ith virtual particlesand errergy.This energyprovidesa buoyancywhich resiststhe collapseofthe Urriversethat gravityseeks to causc.'l'hus,as well as prolongingthe lilb of tlrc [,lniverse, tlris naturalbuoyancyor springiness would also providea supportmecharrisrn, which would leadto the lbrmation of very lal'gescale.structures.l-he firral reasonfor the new-found excitententover A is that, by endowing the vacuutn rvith cnergy, an arlditionalgravitationaleffect is created becauscenergyis equivalentto nrass(equation( | .2-)).'l'hismeansthat a tjniversewith a cosnrological constantrnaynot rrccdany dark rnattor,bccauseit is the energyrvhichprovidcs tlrc additionalgravityto lrold supcrclustcf-s (jtc.together.All in all, this rnakesthe cosnrological constanta l)rcttyseductivcidea.ll'tlre inflationarytheoryis right and we do livc in a llat [Jniverse, a cosrrologicalconstantwrrrlclrnodifuthe conditionfor .flatness' in tlrc lirllowingway: ()t A= l
l Il
I I I
l l r e lh tc o f lh r I Ir r ivr rsc
:)
(e.4 r)
Attotltcrotrservatiottal testofthe cosnrological cclnstant is that gravitationallensesshould bc lltotc llulDerotlsin a [.Jrtivelsc with a non-zct'oA. 'Ihe higher tlre magnitudeof the costttolttgtcal constal)t, thc greatcrtlrenumbero{:lr:r)ssystetns. Estimates of C)suggestthat A riliglrtlrc as high as 0.8 or 0.9. I:ronrthcory,this shouldresult in an increasein the Ittltttbcrof'gravitatiortal lcnseslry a lactorol"bctrvccrrl0 and 100.Unfortunatcly,this is .iuslnot obsclvcd.A reccntsurveyrnadeby the I'lutrbleSpaceTelescopeand analysedby .lohn llahcall ol'tlre Institutelbr Advancedstudl,in princeton,looked at alrnost500 (luilslrslxrt foundorrlya handfulof lensedsystetns. (iravitationallensesare in any caseso scarcethat solle astronomers are not convinced llllt this sitrgleobservationis crroughto altogethelrulc out A, and the cosnrological consliultrcntlinsan inrpoltant,ifsorrrcrvlrat ecccnlr.ic. cosntological parameter today.
''] r!
j
il
!"
9.9 't'il8 WAY FOIIWARI) In solllo rvays,costnological theoricslravcdevclopcdlal fastertfiarrobservations. Only rvlrenf'undamental new observittiotts ale rnadccarrcetsrnologists really test lhcir curr.ent theories.Iror exantple,rvlrcnCOIItr discovcrcdthc arrisotropies in the nricrorvavcbackgroundlacliation,the rrpperlirnits it set, in terrnsol'tlre strengtlrof the fluctuationsand their angularextent,discoutttedsorneof the nroreoutlandishcosmologicalpossibilities.
S e c . 9.9 l
The way forward l9l
Only the models which have been describedin this book survived. What is continuall\' neededare new observationswhich allow theoretical predictions to be compared willr actualdata. With this in mind, this final sectionof the book will preview someof the ncw technologiesand observationaltechniqueswhich will enhanceour understandingof the Universeand allow cosmologyto develop. without a doubt, one of the most important cosmological images taken to date is th<: Hubble Deep Field (Fig. 7.8 in the colour section).This imagehasbeenmade freely available to anyonewho wishesto analyseit. Over the coming monthsand years,the wealth ol information this single frame contains will be explored by astronomersall around tlrt' globe. The discoveriesare liable to be very exciting and certainly worthy of attentiorr They should ceftainly illuminate and help constrainthe detailsof galaxy formation. The Hubble SpaceTelescopeis also involved in anothermajor cosmologicalinvestigrr tion. A stated aim of the science team responsiblefor the orbiting telescope is that ir 'fhis lril shouldtry to refine the Hubble constantto within l0 per cent of its actual value. availirblt' the So far, here. but warrants reiteration in chapter 5, previouslybeen mentioned Flubbledata would appearto be closing in on a figure consistentwith the averagevaltrc o l 75 km/s/Mpc which we have usedthroughouttttis book. One of the most exciting piecesof observationalcosmology is being undcrtakcnbv ,, joint Britishand Australianteamof astronomers, Again this hasbeenmentionedin cltirplIr 5. It is the 2o field (2dF) mapping project, which is being undertakenby the Angk' AustralianObservatory.Whereasconventionaltelescopeshave been limited to taking tlr, spectrumof a single galaxy at a time, the 2dF will be able to take up to 400 spectrain tlr, time it previouslytook to recordjust one. The 2dF is a self-containedpiece of instrumentation,mountedon the top of the Anglo AustralianTelescope(a 3.9-metretelescopesited on Siding Spring Mountain, New Soullr Wales).A systemof lensesconvertsthe telescopeinto a wide-angleinstrumentwith a ficl(l ofview spanning2o, hencethe name.Then, a robot placeseach ofthe 400 optical fibrcr. preciselyover the galaxy imagesin the field of view, and their light is simultaneouslyftrl to a spectrographwhich records the information. These spectracan be tumed into rc
194 l'he fateofthe llniversc
': l
ii
i,
[Ch.9
These new redshift maps will be the nearestthings cosmologistspossessto threedimensionalmaps of the Univcrse.This will allow much better comparisonbetweenthe prcdictionsoftheory and thc actual Universe. Iror instance,the ideas about biasedcold dark nratterwill be more readily tested.Large-scalestreamingmotions will becomemuch more appa{nt, and this will allow the constraintson the position and mass of dark matter depoSitsto be much better understood.Also, the precipitousrise in known redshifts will greatly help in the questto determinethe value of the Hubble constant.In particular'.it will help assessthe quality of tertiary distanceindicators,i.e. those which rely on galaxiesof the samel-lubbtetype possessing sinrilarphysicalproperties,suchas diameter and mass. Another critically irnpodantset of observationsare thosewhich will study further the cosmicmicrowavebackgroundradiation.Ever sinceCOBE confirmedthe existenceof the fluctuations,astronomershave wanted a better look at them. This involves studying this diff'useradiationusing more sensitivetelescopes,lvhich possessbetter angularresolution than COBE did. Thereare severaldesigns,now on the drawing boardsin America, Europe and Rtrssia, to do just that. NASA is in the processofstudying severaldesignsas part oftheir'faster, cheaper, better' approachto satellitedesignand execution.The EuropeanSpaceAgency investigated a spaceprobe known as COBRAS/SAMBA after a British-led team proposedthe Cosnric BackgroundRadiationAnisotropy Satcllite (COBRAS) and a French team proposedthe Satellitefor the Measurenrent of BackgroundAnisotropies(SAMBA). The Russiansarealsoconsideringa microwavebackgroundsatellite. One thing that all of thesehave in conrmon is that they would not be placed in Earth orbit in the same way as COBE. The interfercnceof temestrialand solar signals made COBE's job rathernroredifficult thanwas desirable.The other problem was that the Earth and the Sun kept getting in the way! This was a particularproblem with the Sun because the instrumentson board COBE were very sensitivein order to pick up the background radiation,and one peek at the Sun would have destroyedthem. The next generationof microwavesatelliteswill thereforebe placed as far away fiom the Earth as possible,insteadof rushing around it, to give controllersan easiertime of keeping it pointed out of harm's way. It will probably be placedat one 01'theLagrangianpoints either in front of, or behind,the Earth. In additionto the varioussatellitemissionsto studythe backgroundradiation,there are severalground-basedtelescopes.I'he CambridgeAnisotropy Telescope(CAT) is a three elementinterferometerrvhichhasbeenbuilt insidea SecondWorld War bunker to prevent its sensitivedetectorsbeing srvanrpedby terrestrialmicrowave sources.whereas coBE found fluctuationsat roughlythe ten-degreescale,CAT is designedto look for differences on a scaleof l0-60 arc minutes. Another British experiment,locatedon 'l'enerife,has alreadycorroboratedthe COBE results,and other experimentsare taking placeall over the world. For exarnple,a seriesof balloon-borneexperimentsare being continually undertakenat Princeton University in America.Two other Americanmicrowaveprojectsare sitedat the Centreof Astrophysics, locatedat the geographicSouth Pole in Antarctica.Many microwaveobservationswill be forthcomingin the next fcrv ycars,and theservill allow tighter constraintsthan ever to be placeduponcosmological thcories.
Sec.9.9l
i /i il
The way forward l'/
The other types of telescopewhich will gradually rise in cosmologicalsignificancc'I' the technologybehind them progresses,are the neutrino detectorsand the gravitatiorr radiation detectors.As mbntionedin chapter8, both will eventuallyprovide ways ol'r'l servingthe Universebeforethe decouplingofmatter and energy. As well as technologicaladvances,theoreticaladvancesare required in order lo tttttlr' stand the Planck era and, perhaps,even the moment of creation. In previous ycars' ll' questionof what happenedbeforethe Big Bang was usuallyansweredby a (sniflily) rlt'lr ered reply that time was createdin the Big Bang so the conceptof 'before' is meanirrplt' This has proven unsatisfactoryto many scientists,and ideasnow abound about thc lrirt of our Universe. Central to the understandingof these ideas is the concept o[clttntrlr. cosmology, a marriage of quantum theory and general relativity. Mentioned briclll' chapter4, this fascinatingnew branchofcosmology postulatesour Universeto lravc b' ' createdwith ten dimensions(only four of which have survived in ordcr to give us a s1r:" time continuum). Quantum cosmology predicts that the creation of our Universe took place al otl(' ',1' cific point in an endless'multiverse' in which quantumfluctuationscan appcar likc lrrrl" les in a pan of boiling water. They are similar to thosewhich, in our Universc, lltrlr('tirl the seedsof today's galactic structures.These spontaneousevents rapidly cxpittrtl ;r becomeUniverses;some of them will be similar to ours but the vast majority will bc v' differentl Cosmology is a rich field, full of impressivescience,technologicalwtlndcrs :tttrl l 'l'he qucsliotrs(tl (", I c€ptsfar strangerthan any a sciencefiction writer could dreamup! ence have tantalisedmankind for so long now that it is an integral part ofour cvcllrr lives. At long last, we have made some measureof progresstowards explaining lrorv got here. Perhapswe can look forward to understandingeven more when tltc fitrnl pi,'' of the Big Bang fall into place. Perhapswe should contemplatethe even morc cx( rl' possibility that someobservationswill prove impossibleto fit into the Big Bang arrtltlr' rists will be left graspingfor a totally new idea. Whateverhappens,it is going to hc ltrn revise this book in five years' time and to seewhich theoriescan stay and which ltitv' be discarded!
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Appendix1: Physicaland astronomicalconstants Astronomicalunit Boltamann'tconstant Elecfon volt
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Glossary
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l0 parmagnitudeTheapparentmagnitudeof a celestialobjectat a distanceof Absolute secs. ActivegalaryAnyga|axywhichisemittinglargequantitiesofnon.thermalradiation, .mirror image'of matter,oppositein chargebut equalin massandspin t0 AntimatterThe rare' ordinarymatter.It is comparatively a celestialobjectas it appearsin the nightsky' of bri'ghtness magnitudeThe Apparent
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hadrons'Neutrrltt:r BaryonA particlemadeof threequarks.Baryonsarea subsetof the particlessuchas tltt' shorter-lived but heavier the are as baryons, proions are und lambdaandtheomega. Big BangTheinitialpointof creation. onebillion is definedasan Americanbillion, ic of cosmology, BillionForthepurposes 1,000million. greatthatnot evenligltt BlackholeA volumeof spacein whichthedensityof matteris so the known laws ol hole black a Inside aftraction. gravitational its can escapefrom physicsbreakdown. emissionlinesin its Bizir Ahighlyvariableactivegalaxywhich,in general,displaysno spectrum. radiation,broughtabout by tlrc Blishift The increasein frequencyof electromagnetic observer' and betweenthe source relativedistancedecreasing It is denotedby atr Boson Aparticlewhich doeJnotobey Pauli'sexctusionprinciple. integer(or zero)sPin. scenarioin which small galaxiesform first' Bottoi-uj scenarii A galaxy-formation in duecourse' formed then Largerandlargerstructuresare given out by electronsinteractinlr radiation Electromagnetic radiation Bremsstrahlung with the ionsin an ionizedgas. contentcalr ClosedIhniverseAny modelof the Universein whichthegravityof the matter reversethe expansionandcausea collapse'
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Appendix2: GlossarY 201
20() Appcndix2: (ilossary Cold dark nutter Any clark tttatlcr carrclidatcr.vhiclrrvas non-relativisticat the Doint of dccoupIing. 'l'hcscaltcringol'photonsby licc electronsin ('rtmptonscullering an ionizednre{ium. Comptonwavelength'l hc wavclcrrslhof a photon containingthe rest energyof a particular particle. Co-moving coordinaresA set ol'coordinatesrvhich do not change in an expanding(or otherrvise moving)nrediunr.i.e. thc coordinates ol'a distantgalaxydo not changejust becauseofthe expansionofspace. CosnticttricrowavebackgrounrlA conslantflux of electromagneticradiation rvhich has been rcdshiftedinto the microwaveregion of the spectrum.The photonsof cosmic nlicrorvave backgroundradiationoutnumberthe ntatterparticlesby 1,000million to L CosmicsubsrratumAn idealised,snroothcosmic fluid which is spreadthroughoutspace evenlyand thuspossesses a collstantdensity.It is equalin massto the Universe'sconstituents. Cosmologicalprinciple states that the Universe is both homogeneousand isotropic to observcrsat restwithin the substratum. CPT invarianceA symmetrywhicli is believedto hold true for all particlesthroughoutthe courscof universalhistory. It statesthat nlatter and antimatterwould only react in the sameway if the spinsof' the antinratter particlcsrverereversedand the reactionwas causcdto run backrvards in tirnc. Dark muttcr Any fonn of mattcrwhich existsin the Universein a non-luminousform. Decouplingof mailer and energ,,A cosmic epochduring which the matter contentof the LJniverse ceasedto be ionized.This led to a dccreasein the opticaldepthofthe Universe,and the photonsof radiation (rvhich rve norv observeas the cosmic microwave background)becameable to travel largedistanccsrvithoutinteractingwith matter. Dianreterdi.stanceAny distanccto a celestialob.jectwhich is based upon the use of a standardruler. Doppler effecl The alteration in fi'cquencyof elcctromagneticradiation due to relative motion betweenthe sourccand observer. Einstein-tleSilter cosntologic'ulnrotlcl A Friednrarrnmodel of the Universe in rvhich the spacctinre continuunris not ctrrvctl. Electronagnelrslr One of thc fcrLrrfundarnentalfirrcesof nature,governing the electric and rnagnc(icinteraction bctrvcurlrarliclcs. [:leclntn A lcfiort wilh an clcclric clralgcol'-1. An elcctronis also a ferrrion becauseit ha sa spinof onc hlt lf. '['ltc cotttbirr;rliorr Elecrrov'aak.fitrcc ol lhc clcctrorrragnetic force and tlre weak nuclear forcc wlriclrtakcspllcc ;rt ll11hcncr.giy. EventA ltappcltstattcc itt tltc s1t;rcclirrrc continurrrrrcl'crenced by threespatialcoordinates an d a c ot t r plc r r . t olr lt11111111y r r y ; r Iot r lir 1 r llc . f;uitil hlut gulu.t:.1, A tlistrrl, irreriul;rr'11' slrirpctlg,irlirxyin which a largeamountof star fo rrn:r liorisr t ak ir r g' plir , cc. l;e rnrio rtA par lic lcr v lr ic ltolr c lr ;t lr c I ' r r ulit : r c l u . ; i ol r) rr i n c i p l eI.t i s d e n o t e dh 1 ,a h a l f i n t c g rll spir r .
Friedmann equation A mathematicalexpressionwhich allows the expansionof the tJniverseto be studied. Flatnessproblern Posesthe question:why, out of an infinite number of possibilities,is out Universeso closeto the one specialcase:the 'flat' Universe? 'Flat' (JniverseA Universe in which there is no curvatureto the spacetimecontinuunr. This meansthat the kinetic energyofthe expansionis exactlybalancedby the potential gravitationalenergy of the matter. Thus, after an infinite amount of time the Universc will stop expanding. Galaxy A collection of matterwhich usually manifestsitself by the production of stars. Galilean transformation The non-relativistic method of relating observations from onc frame ofreference to another. Grand Unified Theory Any theory which seeksto unif the strong nuclear force with llrt electroweak force. Cravity One of the four fundamentalforcesof nature,and the one most different from tht' other three. Iladron Any particle made of quarks. ITeisenberguncerlainty principle Statesthat the position and momentum of a particle crrrr only be known to a certain level of precision. The more precisely one quantity i' known, the lesscertainthe precisionof the other. A similarly linked pair of quantitic'. is the time and energycontentin a volume of space. Helium problen Posesthe question:what physical processcausedthe current abundarrc( of helium in the Universe? Horizon problenr Posesthe question:why is the cosmic microwave backgroundradiatiorr isotropic acrossthe whole sky, when different regions ofthe sky could not have bccrr causallyconnectedat the time of decoupling? Hot darkmatter Any form of dark matterwhich was relativistic at its point of decoupling Hubble classification of galaxies A morphological classification sequenceof galaxies dc vised by Edwin Hubble. It splits galaxies into ellipticals, lenticulars,spirals, barrcri spiralsand irregulars. Hubble constant The constantof proportionality in the Hubble law. Its value must vat'. with time, so it is often referred to as the Hubble parameter.The Hubble constanl i generallyused to mean the value ofthe Hubble parameterat the current epoch, and i somewberebetween50 and 100 km/s/Mpc with possiblya value close to 75 km/s/Mpt Itubble flow The movementof the galaxiesaway from us causedby the expansionof tlt' Universe. Ilubble law The Iinear proportionality, noticed by Hubble, between the distance o{' ;' galaxy and its redshifl. Hubble timeThe time it would take for a galaxy to double its distancefrom the Mill' Way. This meansit can also be usedas an estimateof the age of the Universe. tnflationA theory which postulatesthat, at l0-35secondsafter the Big Bang, the spacctirrr continuum underwentan intenseperiod of exponentialexpansion,in responseto llt' separationofthe strongnuclear force from the electroweakforce. This idea solvcs llr flatnessand horizon problems.
202
Appendix2: Glossary
Invariant Any physicalpropertywhich doesnot changeunderthe transformationfrom one franreofrcference to another. IRASgalaxy Any galaxy which was discoveredby the Infra-Red Astronomical Satellite (IRAS) to possessan excessiveamountof infrarcdemission. JeansmassThe critical massa voluureof spacemust containbefore it will collapseunder the force of its own gravity. Lepton A fermion which is not madeof quarks. Light cone A cone representingthe transmission,at the speedoflight, ofan event's existenceon a spacetimediagram. Long scale The cosmologicaldistancescale which usesa tlubble constantof approximately 50 kmis/Mpc. Lorenlz transformation The trantfonnation which keeps the speed of light invariant between relativisticframesof reference. Low surface brighrness galaxy A galaxy which is very faint because it contains a very limited numberof stars. LuminositydistanceAny distanceto a celestialobject which has been calculatedusing a standardcandle. Lyman-a foresr The appearanceof many differentially redshifted Lyman-cr absorption lines in a quasar'sspectrum,causedby interveninghydrogenclouds along our line of sight to the quasar. MACHO A massivecompacthalo object. Theseare black holes,neutronstarsand brown dwarfs,noneof which are luminousand all of which are postulatedto exist in the halos of galaxies.They are a form of dark matter. Malmquist bias The systematic distortion in a standard candle's effective range due to failure in detectingthe fainterexamplesofthe standardcandleat large distances. Meson Any particlenradeof two quarks.Examplesare the pion (pi-meson)and the kaon. Milne cosmological model A Friedmann model of the Universe in which matter does not exist. Only radiation is presentin a Milne Universe. Missing mass problem Poses the question: why does the universe seem to have much more mass in it than can be seen with a telescope? Dynamical and theoretical constraints plap! the proportion of missing massto be somewherebetween 90-99 per cent ofthe total rhiss ofthe Universe. Neutron A baryon made of one up quark and two down quarks. It possessesno electromagneticchargeand can only be found in atomic nuclei. Neutrino A tiny, possiblymassless,particlewhich travelsat the speedof light and carries energy and momentum away from interactionsinvolving the weak nuclear force. A possiblecandidatefor hot dark matter. Nucleosynthesrs The act of building heavierand heavieratomic nuclei from the fusion of protons and other atonric nuclei. The Universe is postulatedto have gone through an era of nucleosynthesis, lasting lor about four minutes,during which time helium was made.This solvesthe helium problem.
radiation. ObserverAnythingin receiptof electromagretic Olbers' ParadoxAsks why the night sky is dark. If the Universewere infinite in extcrrt staticandcontainedstars(or galaxies)scatteredthroughoutit at random,the night skr shouldappearasbright asthe Sun. OpenUniverseAny modelof the Universewhich doesnot containenoughmatterto h:rll its expansion. ParticleacceleratorAn experimentaldevice,designedto accelerate chargedparticlcst, energiescomparablewith thosepresentduringthe first minuteof the Universe'sexi'; tence. ParticlehorizonThe distancea photonofradiationcouldhavetravelledsincethecrcalior' of theparticle. Pauli exclusionprinciple Statesthat particleswith half integerspinscannotoccupytlr, samequantumstates. Thismanifests itselfasthereasonwhy solidobjectscannotcxi'r in thesamephysicalspace. quantumparticleof electromagnetic radiation. PhotonThe fundamental Physicscan currentlys:r Planckera The first l0t3 secondsof the Universe's.existence, very little aboutthis time.Quantumgravityis neededbeforequantumcosmologyc;'' be fully realised. PositronThe antimattercounterpartof an electron. Principle of equivalenceStatesthat inertialmassis indistinguishable from gravitatior;, mass. ProtonA baryonmadeof two up quarksanda downquark.It possesses a positivcclcclr'', magneticchargeandcanonly be foundin atomicnuclei.A singleprotonis a hydro;',' nucleus.
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QuantumcosmologtThestudyof the Planckera. l1 fluctuationof energyin a volumeof spacc.A corr QuantumtluctuationThespontaneous F ll sequence of the Heisenberg uncertaintyprinciple. ll quantum gravity A theory of gravity in which gravitonstransmitthc forcc b, Quantum '- l/ tweenparticles,ratherthanthe curvatureof the spacetimecontinuum,as in thc gcrrcr,, Il theoryof relativity. lf '' QuantumtheoryA theorywhichseeksto explainthattheactionof forcesis a resultol tl' ll 'exchangeof sub-atomicparticles. ll buildingblock of thehadrons. QuarkA sub-atomicparticlewhich is a fi.rndamental ,_ li objectwhich superficiallyresembles a star.M()' ll QuasarAn intenselybrightextragalactic exi stat ver yhighr edshif t sandar et her ef or et hought t obet henucleiof act ivegala t,
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Radiogalary Agalaxywhichdisplaysananomalouslylargeoutpouringof radioemissior,,. Il RedshiftThe decreasein frequencyof electromagnetic radiation,broughtabout by tl', // ,t relativedistanceincreasingbetweenthe sourceandobserver. , Robertson-l{alkermetic An equationwhichdescribes thespacetime continuumin a I Jrr ll ,, principle. versewhichadheres to thecosmological ll il ScalefactorAn arbitrarymeasureof thesizeof the Universe.
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204 Appcndix2: Glossnry radiusat which a given nrasstums irlto a black hole. Schwarrrchild rutlius'l'l"rc Seyfertgalaxy A spiral galaxy with an overly bright nucleuswhich is not being produced by stars. Short scale The cosmologicaldistancescale which usesa Hubble constantof approximately 100 km/s/Mpc. ,sourceAnything which is enrittingelcctromagneticradiation. spacetimecontinuumA four-dimensionalframework in which eventstake place. SparticlesHypotheticalparticleswhich are predictedby someGrand Unified Theories. ip""tro! ratio The ratio of electrontagneticwavelengthsfrom diflerent cosmic epochs. This givesthe expansionfactor of the Universe. Spln A quantumpropertyof all particleswhich denotesthe intrinsic angularmomentumof the particle. Standardcandle Any luminouscelestialobject which is more or lessconstantin its absolute magnitude.It can be used to gauge distances,becausethe further arvay it is, the fainter it will appear. Standardruler Any extendedcelestialobject which is more or lessconstantin its diameter. It can be usedto gaugedistances,becausethe further away it is, the smaller it will appear. Starburstgalary Any galaxy in which an anornalouslylargerateof star formation is taking placc. Strongnuclearforce Oneofthe four lundamentalforcesofnature. It governsthe interaction betweenparticlesin atomic nuclei. Sunyaev-Zel'dovichprocessCompton scatteringbetweenthe photonsof the cosmic microwavebackgroundradiationand electronsin galaxyclusters. SuperforceThe force which is dominantin Grand Unified Theories.lt combinesthe electroweak force with the strong nuclear force. SymnretryA set of invariances. Top-down scendrio A scenarioofgalaxy formation in which large structuresform first and then fragmentto becomegalaxies. lVeaknuclear force One of the four fundamentalforces of nature. Controls the interaction of ncutrinos. WIMP A weakly interactingmassiveparticle. A genericterm for a class of hypothetical particlc which may form the missingmass.A form of non-baryoniccold dark matter. llorld line The trajectory of a body moving through spacetime.
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i: ":t I S | readby everyonebeforetheysubscrihc ^\ solelya rn"urur"t"na oiai'tun""' Shouldbe in hereis hardto dismiss' ' t the Big Bangpartyfint, ut t"tt "fthe evidence Principle' O.1fo19Universit 5t i Cosmological inthropic fn" i"lTipler, & J.D. Barrow, to stimulatetli' S guaranteed press.19g6.a p.ouo"otin.notion;*.il worthreadingand cussion. AdamHilger' 1989' :^ R Berry,M., Principlesof Cosmologtand Graitation' D' (eds')'ObseruationalCo'snr" f &Irrtaccagri' T' Chincarini,G', Iovino, A', Maccacaro' N volume 5I' 1993' sotitrylitit p"in' 9^"]t^f#c; Series' ogy,Astronomi.ur I{ studv scientific the of story f;iit 1993-' Chown,M., Afterglowtli-iit"''Anow' 'htthe scientistsinvolved.A g<x' tr ' ilre point of view of the microwaveb..d;;;;m oron. ur,roni..i;J**[*rri.h accounr
'light' read' exanrirr'$ r.e' 1997 of tlertfordshi 'A thoroughnon-technical Clark,S.,Redshift,University t ionof t hisph"nom enonandwhat causesit , andsom eof t hepr oblem sinm od mology' < A a nact-oradtrate research resear( tome: vt'" $ post-graduate Wiley' 1995' cJr, i"a Lucchin,F.,Cosmologtt, A good,but not for thefaint-hearted' :.'-::'-:. .-^,,., barYonictlrrr'* of account Excellent 1995' ^o Evans,A., TheDustyi;;'':;';;,Wiley-Praxis' matterwithintheMilky WaY' e82. $ 1982' Ferris,T., Galaies,stewart,TaborandChang' SPringer-Vcrlrr' Relativity, iri"n"rot course $ Foster,J. & Nightingale,J.D.,A Short
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