Gravitational wave detection with photometric surveys

Gravitational wave (GW) detections have considerably enriched our understanding of the universe. To date, all GW events from individual sources have been found by interferometer-type detectors. In this paper, we study a GW detection technique based on astrometric solutions from photometric surveys and demonstrate that it offers a highly flexible frequency range that can uniquely complement existing detection methods. From repeated point-source astrometric measurements, periodic GW-induced deflections can be extracted and wave parameters inferred. We emphasize that this method can be applied widely to any photometric surveys relying on relative astrometric measurements, in addition to surveys designed to measure absolute astrometry, such as Gaia. We illustrate how high-cadence observations of the galactic bulge, such as offered by the Roman Space Telescope's Exoplanet MicroLensing (EML) survey, have the potential to be a potent GW probe with a complementary frequency range to Gaia, pulsar timing arrays, and the Laser Interferometer Space Antenna. We calculate that the Roman EML survey is sensitive to GWs with frequencies ranging from 7.7 ×10^-8 Hz to 5.6 ×10^-4 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 in light of the expected supermassive black hole binary population distribution, we show that binaries with chirp mass M_c>10^8.3 M_⊙ out to 100 Mpc can be detected if the telescope is able to achieve an astrometric accuracy of 0.11 mas. To confidently detect binaries with M_c>10⁷ M_⊙ 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 photometric surveys could contribute to detecting GWs via astrometry.