## [1009.4192] Astrometric Effects of a Stochastic Gravitational Wave Background

Authors: Laura G. Book (1), &#xc9;anna &#xc9;. Flanagan (2), ((1) California Institute of Technology, (2) Cornell University)

Date: 21 Sep 2010

Abstract: 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 yrˆ-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 ~ 10ˆ6 sources 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)ˆ2/(N Tˆ2 H_0ˆ2) ~ 10ˆ-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.

#### Sep 22, 2010

1009.4192 (/preprints)
2010-09-22, 19:31