TARGETED OBJECTS

Low-frequency gravitational waves produced by two orbiting masses are the targets of this effort. The advantage of considering these binary sources is that they will be continuous and reproducible as opposed to the impulses targeted by other gravitational wave detection efforts. The disadvantage is that the signal strength is likely to be weak unless the target is a binary system with an extremely large mass, or a system with a moderately-sized mass that is close to earth.

The period of the generated gravity waves will be half the orbital period of the binary system if the orbits are circular. If the orbits have significant eccentricity, much of the generated gravitational wave energy will be emitted at the higher frequency harmonics of the orbital periods. Thus, a system with an eccentric orbit might produce significant energy in the frequency range being analyzed here, where a system with the same mass and a circular orbit with the same period would not (Peters and Mathews, 1963, Barone, et. al., 1987).

Previous attempts to detect the effects of low-frequency gravitational waves on the earth have focused on the excitation of the earth's normal modes by frequencies close to the resonant frequencies. The events targeted by these attempts would be either impulses or a stochastic background. Only a narrow frequency range around the resonant frequencies was covered. In this paper, I am considering a larger range of frequencies corresponding to periods of one-half hour to 24 hours. While the sensitivity of the earth to gravitational waves at the frequencies away from the resonant frequencies will be low, low-frequency undertones (Aki and Richards, 1980, Perkeris and Accad, 1972) may increase the expected sensitivity of the earth at frequencies lower than that of the 54-minute resonance. While no large or close binary systems that would produce detectable motions are known to exist, they cannot be ruled out.

Other attempts to detect gravitational waves have targeted catastrophic events such as supernovae and stellar collisions and have concentrated on high-frequency, short-duration impulsive signals that may be detected by the vibrations of large cylinders isolated from the earth and cooled to reduce thermal vibrations (Douglas and Braginsky, 1979) With these detectors, it was assumed that an impulsive arrival would excite the detector at its resonant frequency. Since impulsive events tend to be rare and generally are not reproducible, confirming any detected event would be a problem unless multiple detectors were used. Using the earth's response to these short-term events would be difficult since the integration over time is not possible as it is with constant-frequency waves, and short-term events would be generally indistinguishable from seismic noise.

The orbital frequency $\omega$ of a pair of masses is

$$\omega = \sqrt{\frac{G (m_1 + m_2)}{a^3} }$$ (1)

where a is the radius of the orbit, m₁ and m₂ are the masses of the bodies, and G is the gravitational constant. From Schutz (1988), the amplitude of the waves will go as

$$A \; \propto \; \frac{m a^2 \omega^2}{r}$$ (2)

or

$$A \; \propto \; \frac{m^{5/3} \omega^{2/3} }{r}$$ (3)

or

$$A \; \propto \; \frac{m^2}{r a}$$ (4)

where r is the distance from the binary system, and m = m₁ + m₂. The wave amplitude gets larger with smaller radius and gets larger quickly with increasing mass.

For example, a pair of pulsars, PSR 1913+16, appears to be showing changes in its orbits from the emitted gravitational radiation. While the radiation from this system is too weak to be detected with the IDA network, larger objects with smaller orbital periods might be detectable. While the pulsars in PSR 1913+16 have masses of about 1.4 solar masses, larger objects, such as large black holes are better targets. Where $M_{\odot}$ is one solar mass, a billion $M_{\odot}$ binary system at the center of our galaxy would produce gravitational waves with an amplitude of $9 \times 10^{-8}$ if it had an orbital period of 8 hours. This compares to an amplitude of about 10^-20 for PSR 1913+16. There is some evidence that black holes exist in the center of certain galaxies, and other smaller and closer black holes have been strongly suspected (Jayawardhana, 1992). With objects having masses from $1 M_{\odot}$ to $10^{12} M_{\odot}$available to produce gravitational waves, a weak response of the earth to these waves may be enough for detection. It has been suggested that a 3 $\times 10^6 M_{\odot}$ object, probably a black hole, is at the center of our galaxy (Blandford, 1987). If this is a binary object with a short period, it might be detectable using the IDA network data.

While the direct detection of binary systems with periods greater than 24 hours is difficult, systems with orbits having significant eccentricities will generate waves with shorter periods. With greater eccentricity, more power will be output from the system (Peters and Mathews, 1963) and much of this power will be radiated at the higher harmonics of the orbital frequency (Barone, et. al. 1987). As an example, an object with an orbital period of 48 hours and an eccentricity of 0.75 will have the maximum energy radiated at a period of about 2 hours.