Astrometric Effects of a Stochastic Gravitational Wave Background

TL;DR

This paper analyzes how a stochastic gravitational wave background causes detectable fluctuations in the apparent positions of distant sources, providing detailed statistical predictions for future high-precision astrometric measurements.

Contribution

It computes the detailed statistical properties of angular deflections caused by a stochastic gravitational wave background, including correlation functions and spectral characteristics.

Findings

Fluctuations are concentrated at low frequencies and large angular scales.

Magnetic and electric components of fluctuations have equal power.

Sensitivity of astrometry can be comparable to pulsar timing for gravitational wave detection.

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 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.