Gravitational Wave Detection with Photometric Surveys

Gravitational wave (GW) detections have considerably enriched our understanding of the universe. To date, however, all events were observed via direct detection. In this paper, we study a GW detection technique based on astrometric observation and demonstrate that it offers a highly flexible frequency range that can uniquely complement existing detection methods. Using repeated astrometric measurements, periodic GW-induced deflections can be extracted and wave parameters inferred. We illustrate how Roman Space Telescope's high-cadence observations of the galactic bulge during its Exoplanet MicroLensing (EML) survey have the potential to turn it into a potent GW probe with complementary frequency range to \textit{Gaia}, pulsar timing arrays (PTAs), and the Laser Interferometer Space Antenna (LISA). We calculate that the Roman EML survey is sensitive to GWs with frequencies ranging from $7.7\times10^{-8}~{\rm{Hz}}$ to $5.6\times10^{-4}~\rm{Hz}$, which opens up a unique GW observing window for supermassive black hole binaries and their waveform evolution. While the detection threshold assuming the currently expected performance proves too high for detecting individual GWs from realistic supermassive black hole binaries, we show that binaries with chirp mass $\mchirp>10^{7.6}~M_\odot$ out to 10 Mpc can be detected if the telescope is able to achieve an astrometric accuracy of 0.11 mas. To confidently detect binaries with $\mchirp>10^{7}~M_\odot$ out to 50 Mpc, a factor of 100 sensitivity improvement is required. We propose several improvement strategies, including recovering the mean astrometric deflection and increasing astrometric accuracy, number of observed stars, field-of-view size, and observational cadence. We also discuss how other existing and planned surveys could contribute to detecting GWs via astrometry.