Astrometric effects of a stochastic gravitational wave background

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 Ωgw(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 ∆θ ∼ 10µas would yield a sensitivity level of Ωgw ∼ (∆θ) 2 /(N T 2 H 2 0 ) ∼ 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.

Gaia-like astrometry and gravitational waves

“…From this point of view, astrometric detection of gravitational waves is independent of the distant source limit discussed e.g. in Section II.G of [2]. The source-related effects will be completely ignored in this paper.…”

“…The deflection of a light ray due to a plane gravitational wave is discussed in details be many authors [2,39,41, and reference therein]. It is well known that the deflection of light due to a gravitational wave depends on the strain of the gravitational wave both at the observer and at the source of light.…”

“…Both Pyne et al [39] and Book & Flanagan [2] considered the case of an observer at rest, e.g. at the barycentre of solar system, so that the barycentric coordinates of the observer x obs vanish.…”

“…In this case a significant part of the effects of gravitational waves changes the proper motions of the sources and only a small part of the effects (if at all) goes to the residuals of an astrometric solution. The theory of these changes due to gravitational waves has been developed by a number of authors [2,3,39]. The theory was used to give upper estimates for the energy flux of the primordial gravitational waves using geodetic VLBI observations [15,36,45,46].…”

“…The use of high-accuracy astrometry to detect various kinds of gravitational waves was discussed by many authors [2,3,15,31,36,39, and references therein]. The first subject of these studies was the effect of stochastic background of ultra-low-frequency primordial gravitational waves on the propagation of light as seen in astrometry, pulsar timing and other observational techniques.…”