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4 Search for Gravitational Waves: General relativity theory can be tested on Earth and in the solar system only through its weak-field, slow-motion effects. When gravita- tional fields become strong, and when matter velocities approach the speed of light, new phenomena occur. A black hole, formed by grav- itational collapse of a stellar core, is one example. Another is a wave in the space-time metric, traveling at the speed of light the gravita- tional wave. Gravitational waves interact only weakly with matter and thus are hard to detect. The detection of gravitational waves is the most important unsolved problem in experimental gravitation today. Their detection would provide an important test, in a new regime, of Ein- stein's general theory of relativity and might also open a new astro- nomical window and give new kinds of information about the sources of gravitational waves. Intriguing possible sources are collapsing stellar cores, colliding neutron stars or black holes, decaying binary systems, rotating or vibrating neutron stars, and new sources of unknown nature. Development of several kinds of gravitational-wave detector has continued for two decades, with great advances in technology, but with no discovery as yet. Current trends in technology of the detectors, together with the best theoretical guesses of strength and event rate of astronomical sources, lead one to anticipate that gravitational waves may be detected within the next decade or two. Meanwhile, the discovery and long-term observation of a radio 36
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SEARCH FOR GRA VI TA TIONAL WA VES: INTROD UCTI ON 37 pulsar in a binary stellar system has provided impressive evidence that gravitational waves do exist. The orbit of this system is decaying at just the rate expected owing to gravitational-wave damping. THEORY In any theory of long-range forces that is consistent with special relativity, the force must act at the speed of light rather than instanta- neously. Consequently there is a strong expectation that, along with the static long-range gravitational force, there must exist in nature some kind of gravitational-field excitation that travels at the speed of light and that can remove energy from an isolated system gravita- tional radiation or gravitational waves. Einstein himself showed the existence of gravitational waves in the general theory of relativity, soon after the theory was complete. However, he used the linear approximation to general relativity in deriving this result, and the fact that general relativity is intrinsically a nonlinear field theory led many to doubt the existence of waves. For about 40 years confusion reigned on the issue of whether gravitational waves were or were not a prediction of general relativity, and the theoretical issue was settled only in the early 1960s. The theoretical properties of gravitational waves, presuming the correctness of general relativity theory, are now thought to be well understood. Alternative theories of gravity usually also predict gravitational waves, although with significant differences from the predictions of general relativity. In some such theories (either those with prior geometry or with more than one metric tensor) the speed of gravita- tional waves may differ from the speed of light and from the speed of all other massless particles. The difference typically depends on the ratio of the gravitational potential to c2 and amounts to about 1 part in 106 for gravitational waves traveling in the gravitational field of our galaxy. But this already amounts to a difference of arrival time of several days between the gravitational-wave pulse and the neutrino or photon pulse from, say, a supernova in our galaxy, and a greater difference for extragalactic sources. Alternative theories also generally predict different polarization properties for gravitational waves. This is because general relativity contains only a spin 2 (tensor) field, while other theories typically also incorporate scalar fields of spin 0 or vector fields of spin 1. Therefore general relativity theory predicts only quadrupole deformations of a gravitational-wave antenna, while other theories predict monopole or dipole deformations as well.
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38 GRA VITA TION SOURCES Because of the weakness of the gravitational interaction, it seems impossible to create on Earth a source of gravitational waves strong enough to be sensed by any conceivable detector; this means that it is impossible to carry out the gravitational analog of Hertz's experiment, and we must depend on cosmic sources to excite detectors. Astrophysical phenomena involving the coherent motions of large, compact masses at relativistic speeds are the sources most likely to emit measureable gravitational radiation. It is, however, just these extreme phenomena that, if they can be observed, will allow us to test relativistic gravitation in the strong-field, high-velocity regime. A view held by many is that this is the most important reason to engage in the search for gravitational radiation. The signatures of gravitational waves may well be the most definitive means to establish the existence of black holes and to study the interactions of compact objects of all kinds with their surroundings. Thus, the detection of gravitational radiation has become an important problem in relativistic astrophysics. Estimates of the gravitational-wave spectrum incident on the Earth suffer from our limited knowledge about massive compact objects in the universe. If the precedent set by the development of radio, in- frared, and x-ray astronomy serves as a guide, chances are excellent that the first sources of gravitational waves to be detected will not have been included in the present inventory of hypothesized sources. Several classes of known astrophysical objects have been proposed as emitters of gravitational radiation. A few of these are described below, and estimates of their strength at the Earth are shown in Figures 6.2-6.4 in Chapter 6. The collapse of stellar cores in Type II supernovae may produce millisecond bursts of gravitational radiation provided there is sufficient departure from spherical symmetry in the collapse. A supernova at the center of our galaxy, if it released I part in a thousand of its total mass into gravitational waves, would produce strains* of the order of 10-~8 at the Earth. Such a strain measurement is just barely within the capabilities of currently operating detectors. The supernova rate in our * A passing gravitational wave causes two freely falling masses to undergo relative acceleration and a displacement proportional to their separation. Similarly, a strain is induced in a solid body. Thus, the strength of a gravitational wave is customarily measured by the displacement per unit separation, or strain h. This quality is also equal to the perturbation in the space-time metric accompanying the wave.
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SEARCH FOR GRA VITA TIONAL WA VES: INTRODUCTION 39 galaxy is however only about 1 per 10 years. To gain event rates of a few per year one must reach out to the Virgo cluster of galaxies with strain sensitivities of 10-2~. Detectors having such a sensitivity would be able to detect supernovae in our own galaxy in which only 10-9 of the mass is converted to gravitational radiation. Neutron stars in binary systems gradually spiral together owing to the emission of gravitational radiation. The binary pulsar PSR 1913 + 16 is an example of such a system. In the final hours of its existence the binary system will emit a strong chirp of gravitational radiation sweeping from 10 Hz to 1 kHz, terminated by the tidal disruption of one or both of the stars themselves. The event in PSR 1913 + 16 would produce strain amplitudes of 10-~8 at the Earth, but we will have to wait about 108 years for this to occur. By inferring a death rate for such binary systems from pulsar observations, one can anticipate that detectors having a strain sensitivity of 10-22, by reaching deeper into the universe, would detect several events of this type per year. The above examples illustrate impulsive or burst sources; some periodic sources have also been posited. For these the anticipated gravitational-wave strains are much smaller; and correspondingly any practical search for them will most likely be restricted to our galaxy. A compensation, however, is that the observations can be extended over long integration times to improve strain sensitivity. Pulsars (rotating neutron stars) would emit gravitational radiation as a result of any deviations from axial symmetry; the radiation frequency can be at the pulsar rotation frequency and at twice that frequency. The gravitational wave's strain amplitude is proportional to the ellipticity of the source. If the Crab or Vela pulsars had ellipticities as large as 10-s, they would produce periodic strains at the Earth of 10-26 at 60 and 22 Hz, respec- tively. These strain amplitudes could be within reach of some proposed detectors after a month of integration (see Figure 6.3 in Chapter 61. A final category of cosmic gravitational radiation is the stochastic background- a gravitational-wave background noise detectable as a correlated noise component in the output of a pair (or more) of detectors. The sources of such a background would most likely reside in the early universe, probably at epochs not accessible by electromag- netic radiation. Since a gravitational-wave background has energy density, experimental limits are usually quoted in terms of the universe's closure density Pc.* * Closure (or critical) density p<. is that density that results in sufficient gravitational force eventually to stop the universal expansion. Currently, p<. ~ 10-29 g cm-3.
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40 GRAVITATION This partial listing of hypothesized sources has focused primarily on phenomena that might produce radiation at high frequencies, say 1 Hz to 10 kHz the spectral band accessible to detectors on the ground. At lower frequencies from 1 Hz to 1 Hz, space techniques and astro- physical observations must be used to search for gravitational waves. Probable sources include classical binary star systems and white-dwarf binary systems in the 10-i to 10-s Hz region with strain amplitudes of roughly 10-22 to 10-2° and bursts associated with the formation and dynamics of massive black holes. This band contains the only astro- physical sources of gravitational radiation whose properties are well known the nearby binary stellar systems. One particularly favorable source is ~ Boo, a nearby binary system that produces a strain amplitude of around 10-2° at a period of 193 minutes. PSR 1913 + 16 is a disappointing source for direct detection because of its large distance from the Sun. The expected strain amplitude at multiples of the orbital frequency (lo-4 Hz) is of the order of 10-23. DETECTORS The first gravitational-wave detectors intended to sense waves of cosmic origin were demonstrated in the late 1960s. These detectors were aluminum cylinders instrumented to detect excitations of the bar's fundamental quadrupole mode by passing gravitational waves. The bars, typically of 1-ton mass, were suspended in vacuum chambers on shock mounts to reduce acoustic and seismic noise. They were operated at room temperature and achieved sensitivities limited only by thermal excitation of the quadrupole mode, a remarkably small noise amplitude. Coincidence detection with two separated bars was used to reduce accidental events. Experiments with such Weber bars have continued in several research groups throughout the world. Instrumentation improvements and cooling of the bars have helped to achieve a recent major improvement in sensitivity. The second main class of detectors, the laser interferometers, began development later and is less mature. In these detectors the change in propagation time of light traversing a gravitational wave is measured. The polarization of quadrupole (Einstein tensor) waves causes changes in the propagation time of light with opposite sign in orthogonal directions transverse to the direction of gravitational-wave propaga- tion. Laser-interferometer detectors exploit this polarization property by measuring the time difference of light propagating along the orthog- onal legs of an L-shaped interferometer whose mirrors are attached to three freely suspended masses. The time differences are measured
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SEARCH FOR GRA VITA TIONAL WA VES: INTRODUCTION 41 interferometrically with high precision. The effect grows with the time of interaction between the light and the gravitational wave, so multipass cavities are used. The laser detectors are currently less sensitive than bars, but a large increase in sensitivity is expected if long baselines can be achieved. A ground-based system with 5-km baselines is currently being proposed, and a Sun-orbiting interferometer with 1 06-km baselines has been . . envlslonec .. Bar and interferometric detectors have been built and operated only on Earth, not in space. Earth-based operation carries with it the heavy penalty of seismic noise and noise due to the gravitational effects of nearby moving masses. isolation from seismic noise at kilohertz frequencies is practical, but isolation becomes increasingly difficult at lower frequencies, with the eventual barrier lying probably in the range of 1-10 Hz. Therefore it is necessary to consider space-based detectors in order to search at lower frequencies. One kind of space-based gravitational-wave detector has been achieved by tracking of interplanetary spacecraft. Here the gravitation- al-wave experiment is only one of several scientific experiments sharing the mission. Passing gravitational waves cause deviations in both the spacecraft trajectory and the trajectory of the Earth; the characteristic time signature of a gravitational wave in the two-way tracking system helps to discriminate it from other effects in the tracking data. Light travel time to interplanetary spacecraft is minutes or hours, so the experiment is most sensitive to gravitational waves with frequencies in the millihertz band. Still another kind of detector is achieved by substituting a radio pulsar for the spacecraft. Here one has only one-way rather than two-way signals and is at the mercy of the stability of the pulsar pulse period and pulse shape. Nevertheless pulsar timing is currently pro- viding the best way of searching for possible gravitational waves in the microhertz frequency range.
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