Gravitational Wave Detection with Relative Astrometry using Roman's Galactic Bulge Time Domain Survey

Gravitational waves (GWs) are a new avenue of observing our Universe. So far, we have seen them in the ~10-100 Hz range, and there are hints that we might soon detect them in the nanohertz regime. Multiple efforts are underway to access GWs across the frequency spectrum; however, parts of the frequency space are currently not covered by any planned or future observatories. Photometric surveys can bridge the microhertz gap in the spectrum between LISA and Pulsar Timing Arrays (PTAs) through relative astrometric measurements. Similar to PTA measurements, these astrometric measurements rely on the correlated spacetime distortions produced by gravitational waves at Earth, which induce coherent, apparent stellar position changes on the sky. To detect microhertz GWs with an imaging survey, a combination of high relative astrometric precision, a large number of observed stars, and a high cadence of exposures are needed. Roman's proposed core community survey, the Galactic Bulge Time Domain Survey (RGBTDS), would have all of these components. RGBTDS would be sensitive to GWs with frequencies ranging from $7.7\times 10^{-8}$ Hz to $5.6\times 10^{-4}$ Hz, which opens up a unique GW observing window for supermassive black hole binaries and their waveform evolution. We note that small changes to the survey could enhance Roman's sensitivity to GWs, making it possible to observe the GW background signal that PTAs have recently hinted at with an SNR $\sim$ 70.