Astrometric Effects of a Stochastic Gravitational Wave Background
  A stochastic gravitational wave background causes the apparent positions of
distant sources to fluctuate, with angular deflections of order the
characteristic strain amplitude of the gravitational waves. These fluctuations
may be detectable with high precision astrometry, as first suggested by
Braginsky et al. in 1990. Several researchers have made order of magnitude
estimates of the upper limits obtainable on the gravitational wave spectrum
\Omega_gw(f), at frequencies of order f ~ 1 yr^-1, both for the future
space-based optical interferometry missions GAIA and SIM, and for VLBI
interferometry in radio wavelengths with the SKA. For GAIA, tracking N ~ 10^6
quasars over a time of T ~ 1 yr with an angular accuracy of \Delta \theta ~ 10
\mu as would yield a sensitivity level of \Omega_gw ~ (\Delta \theta)^2/(N T^2
H_0^2) ~ 10^-6, which would be comparable with pulsar timing. In this paper we
take a first step toward firming up these estimates by computing in detail the
statistical properties of the angular deflections caused by a stochastic
background. We compute analytically the two point correlation function of the
deflections on the sphere, and the spectrum as a function of frequency and
angular scale. The fluctuations are concentrated at low frequencies (for a
scale invariant stochastic background), and at large angular scales, starting
with the quadrupole. The magnetic-type and electric-type pieces of the
fluctuations have equal amounts of power.
