LISA Galactic Binaries in the Roman Galactic Bulge Time-Domain Survey

Short-period Galactic white dwarf binaries detectable by LISA are the only guaranteed persistent sources for multi-messenger gravitational-wave astronomy. Large-scale surveys in the 2020s present an opportunity to conduct preparatory science campaigns to maximize the science yield from future multi-messenger targets. The Nancy Grace Roman Space Telescope Galactic Bulge Time Domain Survey will (in its Reference Survey design) image seven fields in the Galactic Bulge approximately 40,000 times each. Although the Reference Survey cadence is optimized for detecting exoplanets via microlensing, it is also capable of detecting short-period white dwarf binaries. In this paper, we present forecasts for the number of detached short-period binaries the Roman Galactic Bulge Time Domain Survey will discover and the implications for the design of electromagnetic surveys. Although population models are highly uncertain, we find a high probability that the baseline survey will detect of order ~5 detached white dwarf binaries. The Reference Survey would also have a $\gtrsim20\%$ chance of detecting several known benchmark white dwarf binaries at the distance of the Galactic Bulge.