Searching for Gravitational Waves with Gaia and its Cross-Correlation with PTA: Absolute vs Relative Astrometry

TL;DR

This study evaluates Gaia's potential for detecting gravitational waves through astrometric deflections, comparing absolute and relative measurements, and explores combined sensitivity with pulsar timing arrays.

Contribution

It introduces corrected overlap reduction functions for relative astrometry and compares its sensitivity to absolute astrometry using Fisher analysis.

Findings

Relative astrometry is limited for closely spaced star pairs within a Gaia field.

Large angular separation pairs could be more sensitive but are hard to access.

Combining Gaia data with pulsar timing arrays slightly improves detection sensitivity at high frequencies.

Abstract

Astrometric missions like Gaia provide exceptionally precise measurements of stellar positions and proper motions. Gravitational waves traveling between the observer and distant stars can induce small, correlated shifts in these apparent positions, a phenomenon known as astrometric deflection. The precision and scale of astrometric datasets make them well-suited for searching for a stochastic gravitational wave background, whose signature appears in the two-point correlation function of the deflection field across the sky. Although Gaia achieves high accuracy in measuring angular separations in its focal plane, systematic uncertainties in the satellite's absolute orientation limit the precision of absolute position measurements. These orientation errors can be mitigated by focusing on relative angles between star pairs, which effectively cancel out common-mode orientation noise. In this work, we compute the astrometric response and the overlap reduction functions for this relative astrometry approach, correcting previous expressions presented in the literature. We use a Fisher matrix analysis to compare the sensitivity of relative astrometry to that of conventional absolute astrometry. Our analysis shows that while the relative method is theoretically sound, its sensitivity is limited for closely spaced star pairs within a single Gaia field of view. Pairs with large angular separations could provide competitive sensitivity, but are practically inaccessible due to Gaia's scanning law. Finally, we demonstrate that combining astrometric data with observations from pulsar timing arrays leads to slight improvements in sensitivity at frequencies greater than approximately 10^-7 Hz.