A Fast Bayesian Method for Coherent Gravitational Wave Searches with Relative Astrometry

TL;DR

This paper introduces an efficient Bayesian method for detecting coherent gravitational waves using relative astrometry, significantly reducing computational costs and providing sensitivity forecasts for space telescopes like Kepler and Roman.

Contribution

The authors extend a pulsar timing array Bayesian search technique to astrometric datasets, enabling large dataset reduction while maintaining accuracy for gravitational wave detection.

Findings

Reduced dataset size by up to 100 times with 1% accuracy

Roman can detect gravitational waves with strain above 10^{-11.4} in the 10^{-8} to 10^{-6} Hz range

Kepler can detect strains above 10^{-12.4} in the same frequency range

Abstract

Using relative stellar astrometry for the detection of coherent gravitational wave sources is a promising method for the microhertz range, where no dedicated detectors currently exist. Compared to other gravitational wave detection techniques, astrometry operates in an extreme high-baseline-number and low-SNR-per-baseline limit, which leads to computational difficulties when using conventional Bayesian search techniques. We extend a technique for efficiently searching pulsar timing array datasets through the precomputation of inner products in the Bayesian likelihood, showing that it is applicable to astrometric datasets. Using this technique, we are able to reduce the total dataset size by up to a factor of $\mathcal{O}(100)$, while remaining accurate to within 1% over two orders of magnitude in gravitational wave frequency. Applying this technique to simulated astrometric datasets for the Kepler Space Telescope and Nancy Grace Roman Space Telescope missions, we obtain forecasts for the sensitivity of these missions to coherent gravitational waves. Due to the low angular sky coverage of astrometric baselines, we find that coherent gravitational wave sources are poorly localized on the sky. Despite this, from $10^{-8}$ Hz to $10^{-6}$ Hz, we find that Roman is sensitive to coherent gravitational waves with an instantaneous strain above $h_0 \simeq 10^{-11.4}$, and Kepler is sensitive to strains above $h_0 \simeq $ $10^{-12.4}$. At this strain, we can detect a source with a frequency of $10^{-7}$ Hz and a chirp mass of $10^9$ $M_\odot$ at a luminosity distance of 3.6 Mpc for Kepler, and 0.3 Mpc for Roman.