Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity

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I O Grovitotionol Radiation

where ama,is the effective cross-section of the antenna a t resonance, given by setting ru = ru, in (10.7.12), (10.7.13), (10.7.14), or (10.7.15). If @(m)is roughly constant over the frequency range wo - l- to o, + r, then it can be taken out of the integral, and we have

For a source that radiates for a time much longer than the antenna relaxation time l/r,a quasi-steady state will be reached in which the mean energy E in the resonant mode is such that the loss rate ET just balances the absorbed power P:

I n this case, a measurement of the mean excitation energy of the resonant mode serves to measure, or a t least to set an upper limit on, the power flux a t the resonant frequency. For instance, the earth has a fundamental spheroidal oscillation with a period 2n/w of 54 min and a decay rate l- of order 5 x mode14 sec-l, in which the mass density perturbation is of the form p , ( r ) YZm(B,q). The gravitational decay rate l-,,, of this mode will be roughly of order G M e R e Z ~ 4 / ~ s sec- SO the branching ratio q is of order [compare Eq. (10.5.18)],or about The cross-section (10.7.15) a t resonance is here 7.5 x 10271 cm2, or roughly lo7 to 10' cm2. From seismic measurements of the mean strain in the earth7s crust during quiet periods, Forward et al.'' in 1961 set an upper limit on @(oo) of roughly 20 watts/cm2-Hz.I t is hoped that a much better upper limit on @ can be set by placing a gravimeter on the moon,I6 which is very much quieter seismically than the earth. Yor a "burst" source that radiates for a time t less than the antenna relaxation time 1/r,the total energy picked up by the antenna will be

Thus the energy per unit area in tlie burst reaching the antenna within the beam width may be determined as

However, if the source radiates for a time T < l/r,its bandwidth must be greater than llt, so the total energy per unit area in the burst must be larger than b by a factor greater than (tr)- l . The only positive indication so far of the presence of gravitational radiation in the universe comes from the experiments of Weber,' which use as antennas the

7 Detection of Gravitational Radiation

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aluminum cylinders described in Section 10.5. These antennas have the frequency and "branching ratio"

[sce Eq. (10.5.20)l so by setting o = wo and averaging over helicities in Eq. (10.7.13), we find a cross-section a t resonance

If the smallest energy increment AE that can be distinguished from thermal fluctuations is k T , or 4 x 10-l4 ergs a t room temperature, Ohen according to (10.7.19), a burst of gravitational radiation will be detectable if the energy d per unit area within the beam width satisfies the condition

(It is actually possible to do a little better than this by careful data processing.) The mere observation of a number of pulses in a single cylinder would leave open the possibility that these pulses were due t o nonthermal noise, such as seismic disturbances, electric storms, or cosmic rays, so Weber looked for coincident pulses in aluminum cylinders 1000 km apart, a t College Park in Maryland and the Argonne National Laboratory in Illinois. I n 1969 Weber reported over 100 coincident pulses, occurring a t a rate that indicates a mean gravitational radiation flux (within the bandwidth 0.1 Hz) of about 0.1 erg cm-' sec-'.l7 Shortly thereafter,18 Weber found that the rate of coincident pulses was correlated with sidereal time, in a manner consistent with the expected sin4 0 antenna pattern if the gravitational radiation is coming from the center of our galaxy. (See Figure 10.1.) The galactic center is about 2.5 x 10'' cm from the earth, so an observed flux of 0.1 erg cm- sec- would indicate a n energy production of about 8 x ergslsec, or 0.013 M,cZ/year. This would not in itself be so remarkable, but since Weber's antennas are not tuned to any particular frequency, an energy production of 0.01 M,c2 in a bandwidth of 0.1 Hz a t 1660 Hz presumably represents a total energy production lo3 to lo5 times larger, or 10 to lo3 M , ~ ' / ~ e a r .At this rate, the whole mass of the galaxy would be used up in lo8 to 10'' years! If Weber is really observing gravitational radiation from the galactic center, then either he accidently picked the precise frequency a t which most of this radiation is emitted, or else he has discovered an incredibly powerful nensource of energy. Weber has also looked for scalar radiation, using a disk with a monopole mode of oscillation having the same frequency, 1660 Hz, as the cylinders. The coincidence rate is observed to be much less than for the pair of cylinders; the apparent correlation of coincidences with sidereal time agrees with a pure tensor theory. l Plans are now in train t o repeat Weber's experiments with much greater sensitivity. One important improvement that is being planned a t Stanfordzo is

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