Discovering μ Hz Gravitational Waves and Ultralight Dark Matter with Binary Resonances

In the presence of a weak gravitational wave (GW) background, astrophysical binary systems act as high-quality resonators, with efficient transfer of energy and momentum between the orbit and a harmonic GW leading to potentially detectable orbital perturbations. In this Letter, we develop and apply a novel modeling and analysis framework that describes the imprints of GWs on binary systems in a fully time-resolved manner to study the sensitivity of lunar laser ranging, satellite laser ranging, and pulsar timing to both resonant and nonresonant GW backgrounds. We demonstrate that optimal data collection, modeling, and analysis lead to projected sensitivities that are orders of magnitude stronger than previously appreciated, opening up a new possibility for probing the physics-rich but notoriously challenging-to-access μHz frequency band. This improvement arises from retaining accumulated orbital dephasing in the measured residual and scales quadratically with the ratio of the observing time to the unperturbed binary period, up to eccentricity-dependent factors. We also discuss improved prospects for the detection of the stochastic fluctuations of ultralight dark matter, which may analogously perturb the binary orbits.