Astrometric Effects of Gravitational Wave Backgrounds with non-Einsteinian Polarizations

TL;DR

This paper explores how gravitational wave backgrounds with non-Einsteinian polarizations affect astrometric measurements, proposing methods to detect these effects and compare them with pulsar-timing data.

Contribution

It introduces a new correlation matrix decomposition for various gravitational wave polarizations and links astrometric signals with pulsar-timing data for joint analysis.

Findings

Derived a correlation matrix for all GW polarizations

Identified an astrometric analog of the Hellings-Downs curve

Calculated cross-correlation between redshift and astrometric signals

Abstract

The Gaia mission offers a new opportunity to search for the low frequency gravitational wave background using astrometric measurements. In this paper, the astrometric effect of gravitational waves is reviewed, with a particular focus on the effect of non-Einsteinian gravitational wave polarizations. A stochastic gravitational wave background generates a correlated vector field of astrometric deflections on the sky. A convenient decomposition for the correlation matrix is introduced, enabling it to be calculated for all possible gravitational wave polarizations and compared to the redshift correlations from the pulsar-timing literature; in the case of a GR background of transverse traceless gravitational waves, this also allows us to identify an astrometric analog of the famous Hellings-Downs curve. Finally, the cross-correlation between the redshift and astrometric signal is also calculated; this may form the basis for future joint pulsar-timing and astrometry searches for arbitrarily polarized gravitational wave backgrounds.