Fast Bayesian method for coherent gravitational wave searches with relative astrometry

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-signal-to-noise ratio 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 𝒪⁡(100), while remaining accurate to within 1% over 2 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 ℎ₀ ≃10^(−11.4), and Kepler is sensitive to strains above ℎ₀ ≃10^(−12.4). At this strain, we can detect a source with a frequency of 10⁻⁷ Hz and a chirp mass of 10⁹⁢𝑀⊙ at a luminosity distance of 3.6 Mpc for Kepler and 0.3 Mpc for Roman. We finally discuss possible strategies for improving on these strain thresholds.