Info

h + =-cos 2Mt (Strain for coalescing neutron stars; (12.14)

R in meters)

In our Galaxy, only a few cases of neutron star mergers are expected per 10 000 years. Planned experiments should be able to study several thousands of galaxies in the nearby Virgo cluster of galaxies. At a distance of R ~ 60 MLY = 6 x 1023 m to the far side of the cluster, the expected strain for an equatorial observer is h+ = 0.6 x 10-21 cos 2at (12.15)

This is somewhat higher than more careful estimates. Even so, it is an extremely small fractional displacement, but detectors are close to reaching these levels of sensitivity and beyond.

Final chirp

Many years from now, the neutron stars of the H-T pulsar will have spiraled in to be within several neutron star radii of one another, and the losses to GR will become huge. The final seconds of a neutron-star binary would thus be characterized by a rapid and accelerating decay of the orbit. The orbital frequency and amplitude would increase at rapidly increasing rates and then suddenly go silent, like the chirp of a bird or cricket (Fig. 8b). This would be the last signal from the binary. Detection of this chirp requires sensitivity (15) and is a prime objective of G-wave astronomers.

We remind the reader that gamma-ray bursts may be another ramification of such mergers. Also neutrino flashes (Section 2) should be forthcoming from them.

Detectors

The chirps of merging neutron stars are probably the most reliably predicted source of G waves. There are, however, other possible sources of G waves, namely supernovae and hypernovae, normal stellar binaries, gamma-ray bursts, and even the early universe. Searches with past and current detectors have failed to detect G waves, but this is not surprising in view of the predicted weakness of the signals. Here we describe briefly the two principal types of detectors.

Resonant bars

The first searches were carried out with large cylindrical bars (Fig. 9a) operated in isolated and sometimes cooled environments to shield them from vibrations and ambient disturbances. The natural resonant frequency of the bar is where it is most sensitive. The first such experiment was carried out in the 1960s. It made use of a 1400 kg aluminum bar which was resonant at 1660 Hz, roughly the frequency one might expect from closely orbiting neutron stars or in a supernova collapse. Cryogenically cooled bars have greater sensitivity.

Laser interferometers

Long baselines between test masses are desirable because the absolute displacements for a given strain are proportionally larger. A favored technique now is to place two masses several kilometers apart (in a long vacuum tank) and to measure their separations with a laser interferometer. The geometry is similar to the famous Michelson interferometer (Fig. 9b). Laser light from a common source is split and sent down the two arms of the interferometer. At the ends of the arms, mirrors send the light waves back to the common point where the two beams interfere. Interference fringes are the result. If one arm is lengthened momentarily by a passing G wave, say by A/10, the round trip light path is increased by A/5. The fringes would translate by 20% of a fringe cycle.

The US Laser Interferometer Gravitational-wave Observatory (LIGO) has arms of length 4 km. A strain of 10-21 over a distance of 4 km yields a displacement of h /10-21\ 3 18 At = -t = i j (4 x 103) = 2 x 10 m (12.16)

which is 1000 times less than the size of a proton, —10-15 m!

Note that the wavelength of the laser light used at LIGO (1064 nm = 1x 10-6m) is huge by comparison; exotic interferometry techniques are clearly required. This would seem to require measurements of a fractional fringe shift of AX/X « 2(2 x 10-18)/(1 x 10-6) « 4 x 10-12. Multiple bounces (-100) of the laser beam effectively lengthen the path leading to a fringe shift A\/\ ~ 4 x 10-10. Detection of such a small shift is essentially a signal-to-noise problem; one must measure the maxima of the fringe intensity with this precision. With sufficient

(a) Bar detector

Piezoelectric strain guages

(a) Bar detector

Piezoelectric strain guages

Oscillation —1.53 m-

(b) Interferometer c^

Mirror (test mass)

Light storage arms

Half silvered mirror beamsplitter

Mirror (test mass)

Light storage arms

Half silvered mirror beamsplitter

Interference fringes

Figure 12.9. (a) Sketch of a bar detector as used in the first serious search for gravitational waves by Joseph Weber. (b) Sketch of a modern interferometer for gravitational-wave detection with the 4-km arm lengths of LIGO.

Interference fringes

Figure 12.9. (a) Sketch of a bar detector as used in the first serious search for gravitational waves by Joseph Weber. (b) Sketch of a modern interferometer for gravitational-wave detection with the 4-km arm lengths of LIGO.

numbers of photons accumulated, it can in principle be done. Of course, the measurements require that noise sources exceeding these levels be suppressed.

Multiple antennas

A gravitational signal may come in the form of a single brief pulse. Unwanted events due to local phenomena can be discarded if two detectors are operated independently and at a large distance from one another. A genuine gravitational pulse would be detected almost simultaneously in both whereas a spurious local pulse would appear in only one. The neutrino flash from the supernova 1987A was highly credible because two detectors saw it at the same time, one in Japan and one in Ohio.

In fact, multiple observatories allow one to deduce the arrival direction of a pulse of gravitational radiation as the plane wave will arrive at the different stations at slightly different times. The principle is the same as that used to determine the arrival directions of EAS (Section 3). The time delay between two stations provides a line of possible source positions that is a circle (great or small) on the sky. A third detector can provide a crossing line of position (another circle) to obtain two localized celestial positions while a fourth can narrow it down to one position. Gamma-ray astronomers use this technique with satellites to find the celestial positions of gamma-ray bursts.

For this reason the LIGO project has two stations separated by 3000 km, one in the state of Louisiana and the other in Washington State in the USA. In addition, the VIRGO French-Italian observatory near Pisa with 3-km arms and the GEO-600 German-UK instrument can help verify signals and resolve celestial positions. Planned observatories of comparable sensitivities are the Australian AIGO and Japanese TAMA.

LIGO should be able to detect neutron-star mergers in the Virgo cluster when it reaches its design sensitivity. A planned major upgrade in a few years should make it 10 to 15 times even more sensitive. Other instruments will undergo similar upgrades. In the meantime, the several observatories continuously monitor the gravitational sky to ensure we do not miss the unexpected pulse of gravitational radiation from a nearby supernova or gamma-ray burst.

The LIGO and similar instruments are currently sensitive to G-wave frequencies in the range —100 to —104 Hz, the lower limit being due to seismic ground motions. With improved isolation of the detectors and test masses, they should be able to approach —1 Hz, a hard limit due to mechanical filtering and local mass motions (human, atmospheric, ground vibrations). Such instruments can study rapid motions such as spiraling neutron stars, gamma-ray bursts, and supernovae events as described.

Lower frequency studies (seconds to hours) will be carried out by the ambitious NASA/ESA Laser Interferometer Space Antenna (LISA) program to be launched in ~2010. It will consist of three satellites that will define the legs of an interferometer. The separations will be huge ~5 x 109 m, (3% of an astronomical unit) and their relative positions must be measurable to 10-12 m or to 10-5 fringes. Low frequency G waves are expected from motions of stars in longer-period binary orbits, the merging of two massive black holes (active galactic nuclei) into a supermassive black hole, massive objects circulating around and spiraling into the black holes of active galactic nuclei, and space-time ripples originating in the early universe.

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