Detection of anisotropies in the gravitational-wave stochastic background

By correlating the signals from a pair of gravitational-wave detectors, one can undertake sensitive searches for a stochastic background of gravitational radiation. If the stochastic background is anisotropic, then this correlated signal varies harmonically with Earth's rotation. We calculate how the harmonics of this varying signal are related to the multipole moments which characterize the anisotropy, and give a formula for the signal-to-noise ratio of a given harmonic. The specific case of the two LIGO (Laser Interferometric Gravitational Observatory) detectors, which will begin operation around the year 2000, is analyzed in detail. We consider two possible examples of anisotropy. If the gravitational-wave stochastic background contains a dipole intensity anisotropy whose origin (like that of the cosmic background radiation) is the motion of our local system, then that anisotropy will be observable by the advanced LIGO detector (with 90% confidence in one year of observation) if Omega(GW)>5.3X10(-8)h(100)(-2). We also study the signal produced by stochastic sources distributed in the same way as the luminous matter in the galactic disk, and in the same way as the galactic halo. The anisotropy due to sources distributed as the galactic disk or as the galactic halo will be observable by the advanced LIGO detector (with 90% confidence in one year of observation) if Omega(GW)>>1.8X10(-10)h(100)(-2) Omega(GW)>6.7X10(-8)h(100)(-2), respectively.