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Search for Gravitational Waves: Highlights BINARY PULSAR General relativity predicts that a binary stellar system will lose energy in the form of gravitational waves, so that the orbital period will decrease as the two stars spiral together. Although many binary systems are known, only for the binary pulsar system PSR 1913 + 16 can the motion of the system be measured accurately enough to test this prediction. Moreover, most stellar systems do not provide clean tests of gravitational physics for point masses, because tidal interac- tions, changes of stellar mass distribution, and mass exchange or mass loss cause unpredictable and often large changes in the orbit. Fortu- nately the binary pulsar does seem to be clean according to available observational evidence (see section on Systems of Compact Stars in Chapter 3~. Observations of the orbit of the binary pulsar over the 10 years since its discovery have shown that the orbital period is decreasing at a fractional rate of (2.71 + 0.10) x 10-9 per year (see Figure 5.11. General relativity predicts an orbital decay rate due to gravitational- wave emission of (2.715 + 0.002) x 10-9 per year. This agreement is a most impressive and beautiful confirmation of the theory and provides strong evidence for the existence of gravitational waves. Still, one cannot completely rule out the unlikely possibility that tidal and/or mass exchange effects conspire to just compensate for an error in the 42
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SEARCH FOR GRA VI TA TIONAL WA VES: HIGHLIGHTS 43 DECAY OF Bl NARY PULSAR ORBIT - 0.2 J 0.' 0.0 ~ —~ ~ —2 A) 3 ~ _4 m 1 ~ t _ PSR 1943~16 _` - - 1976 1978 4980 4982 19" DATE FIGURE 5.1 Evidence that gravitational radiation is correctly predicted by general relativity. The predicted change in orbit phase due to gravitational radiation by the binary system is shown by the solid line; dots are the observations' including errors. Residuals are shown with the expanded scale on the upper graph. The orbital motion (period ~8 hours) modulates the phase and frequency of the pulsar. By following the pulsar phase for many years, the orbit is measured with exquisite accuracy. rate predicted by general relativity. Independent evidence that the pulsar's companion star is also a collapsed star would settle this issue. In any case, these results already place stringent restrictions on alternative theories of gravity; in many theories, the decay rate of binary systems containing neutron stars or black holes is much greater than in general relativity theory owing to dipole gravitational radiation. In general relativity, monopole and dipole radiation are absolutely forbidden, and the lowest allowed mode is quadrupole radiation. The orbital decay observed in the binary pulsar is completely consistent with the quadrupole formula of general relativity. BAR DETECTORS Bar detectors have undergone 20 years of development, resulting in improvement of strain sensitivity by more than 4 orders of magnitude (8 orders of magnitude in energy-flux sensitivity). Major improvements achieved in the past decade include the following: cryogenic cooling; increase of the Q of bar materials to values approaching 108 in aluminum and exceeding 109 in sapphire and silicon monocrystals; improvements in several transducer types including inductive, capac-
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44 GRAVITATION itive, and resonant cavities; and improvements in coupling schemes and amplifiers. Vigorous work is continuing on all these critical and generally useful technologies. Recently a bar antenna (see Figure 5.2) has been operated for several months at pulse-strain sensitivities of about 10-~8 in a narrow-band mode near 1 kHz. No gravitational-wave signals were identified, but the thermal noise limit for the 4-K bar was achieved. Operation in coincidence of two or more bar detectors, distant from one another, permits much better detection capability by eliminating noise and inter- ference events generated locally. Such coincidence observations have only been carried out over short time periods with recent detectors, although they were made over long intervals with early bar detectors. No fundamental barriers are apparent to further improvements in the sensitivity of bar detectors by several orders of magnitude. Moreover, several current instrumentation developments could significantly ex- tend the bandwidth of bar detectors. When bar detectors reach a strain sensitivity of about 10-2°, they will approach the so-called naive quantum limit. This means that gravitational-wave excitations of the fundamental mode of an initially unexcited bar will amount to about one quantum of acoustic oscillation, and issues of quantum measure- ment of the bar's state will become crucial. Techniques are now known which in principle allow one to measure an arbitrarily small fraction of a quantum of excitation. These are known as quantum-nondemolition or backaction-evasion techniques, and work is now under way to develop them in practice. When other sources of noise are reduced so much that bars are at the naive quantum limit, these techniques will be needed. INTERFEROMETRIC DETECTORS Laboratory-scale interferometric antennas with arm lengths extend- ing from 1.5 to 40 m are now in operation at several laboratories around the world. Two of these instruments have achieved displacement noise spectral densities of 10- cm HZ-/2 in the 1- to 10-kHz frequency range. The corresponding root-mean-square strain sensitivity over the 30- and 40-m baselines is 10-~7 for a 1-kHz bandwidth.* One of these * Strain spectral density in(f) [Hz-"2] is used to characterize broadband radiation and detectors with wideband frequency response. For signals of finite bandwidth B. the strain is h = h(f)Bi/2. For example, a bar detector with h = 10-~8 has sensitivity in(f) = 3 x 10-20 HZ-/2 to a 1o-3-s impulsive signal.
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SEARCH FOR GRA VI TA TIONA ~ WA VES: HIGHLIGHTS 45 FIGURE 5.2 A bar-type gravity-wave detector. The S000-kg aluminum bar is shown end-on with its transducer mount and lead vibration filters attached. Also shown are the suspending wires, the cryostats and the towers containing seismic isolation filters. This bar has been successfully operated at 4 K.
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46 GRA VITA TION detectors uses about 200 mW of laser power and 100 beam passes in each arm, corresponding to a light storage time of 10 As. The other detector uses several milliwatts of laser power and high-Q Fabry-Perot cavities to achieve a storage time of about 1 ms. At high signal frequencies the sensitivity of interferometric detectors is limited by the available laser power. The principal technical efforts to improve detector performance are in two areas. The first is to enhance the displacement sensitivity by increasing the laser power in the interferometer while controlling the effects of scattered light. The power can be increased by using more powerful lasers and/or by recycling the light from the output port of the interferometer back to the input. The second major effort is to reduce the influence of random forces on the interferometer masses. The development of improved suspensions to reduce thermal noise and coupling to external acoustic and seismic noise is actively being pursued and is required in order to achieve adequate detector perform- ance at low frequencies. An important feature of interferometer antennas is that they are inherently broadband and can detect and measure the wave forms of all classes of sources: impulsive, periodic (even if the period is not known in advance), and the stochastic background. However, an interesting new concept would enable the antenna to be tuned to a possible source of known period and phase, for example a fast pulsar. The light beams in the two arms would be exchanged in synchronism with the source, thus accumulating signal while averaging out noise. PULSAR TIMING AND MILLISECOND PULSARS The observed slowing-down rates of a number of radio pulsars are stable enough to afford useful upper limits on the amplitudes of low-freque~cy gravitational waves. Gravitational waves would shake the Earth or the pulsar and cause deviations in the observed uniformity of the period drift rate. Until 1982 the fastest known pulsar was the Crab nebula pulsar with a period of 33 ms. Then a radio pulsar, known as PSR 1937 + 214, with a period of only 1.6 ms (a rotational frequency of 642 Hz) was discovered during investigation of a known peculiar radio source. The slowing-down rate for this object has unprecedented stability for a pulsar; indeed, over time intervals longer than a few months it seems to have as stable a drift rate as any known clock, natural or man-made. The best-known limits on gravitational waves in the microhertz fre-
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SEARCH FOR GRA VI TA TIONA ~ WA VES: HIGHLIGHTS 47 quency range come from observations of this pulsar; already it has been shown that waves in this band cannot contribute more than 5 x 10-4 of the critical mass density of the universe (see Figure 6.4 in Chapter 61. SOURCES OF GRAVITATIONAL WAVE~RECENT DEVELOPMENTS Earlier we used nonspherical collapse of a stellar core as one example of an impulsive source of gravitational waves. However, current theoretical models of Type II supernovae manage to agree roughly with the observations by assuming that the core is spherically symmetric during collapse. Thus there is no good reason to believe that Type II supernovae are strong sources of gravitational waves. Type I supernovae are less well understood, and a consensus model does not exist, although many believe that short-period binary systems are involved. Some models of Type I events predict strong gravity-wave emission; others do not. For instance, one model posits a close pair of white-dwarf stars as the presupernova object; mass accretion causes one star to spin up and eventually collapse, perhaps to a neutron star. Such a binary system would be a strong source of gravitational radiation at frequencies below 1 Hz; and the stellar collapse would be highly nonspherical, producing a strong burst of gravitational waves with frequencies around 1 kHz. The properties of collapsing, rotating stellar cores are now the subject of active investigation, often involving large-scale numerical work. Discovery of the binary pulsar, which probably consists of two neutron stars, emphasized the possibility that decaying compact/ compact binary systems are strong sources. Discovery of millisecond pulsars showed that rapidly rotating neutron stars do exist. If born rapidly rotating, these cores could have been moderately strong sources of gravitational-wave bursts. If, on the other hand, they owe their fast rotation to subsequent spinup by mass exchange with a close companion, they could have been sources of periodic gravitational radiation. (This model assumes that they have been spun up above the threshold for secular instability for gravitational-wave emission.) It should be noted that only a few years ago, before these discoveries, most theorists saw little hope that neutron stars could be sources of detectable gravitational waves. Again nature has outrun our imagina- tions, emphasizing the need for sensitive measurements. More conjectural sources might exist at millihertz and microhertz
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48 GRAVITATION frequencies. These include collisions of massive or supermassive black holes, which may exist in galactic nuclei, and even primordial gravi- tational waves from an early inflationary era of the universe's expan- sion, or waves emitted by decaying cosmic strings, which, according to certain grand unified theories, would have been created by phase transitions in the early universe. Perhaps detection of their gravita- tional waves will be our best handle on these intriguing processes.
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