Constraining the stochastic gravitational wave background with photometric surveys

The detection of the stochastic gravitational wave background (SGWB) is essential for understanding black hole populations, especially for supermassive black hole binaries. The recent promising results from various pulsar timing array (PTA) collaborations allude to an imminent detection. In this paper, we investigate the relative astrometric gravitational wave detection method, which can contribute to SGWB studies in the microhertz range. We consider the Roman Space Telescope and Gaia as candidates and quantitatively discuss the survey sensitivity in both the frequency and spatial domains. We emphasize the importance of survey specific constraints on performance estimates by considering mean field of view (FoV) signal subtraction and angular power spectrum binning. We conclude that if the SGWB is at a similar level as in PTA estimates, both Roman and Gaia have the potential to detect this frequency-domain power excess. However, both Roman and Gaia are subject to FoV limitations, and are unlikely to be sensitive to the spatial pattern of the SGWB.