Stochastic binary perturbations from fast compact objects

Massive compact objects soften binaries. This process has been used for decades to constrain the population of such objects, particularly as a component of dark matter (DM). The effects of light compact objects, such as those in the unconstrained asteroid-mass range, have generally been neglected. In principle, low-energy perturbers can harden binaries instead of softening them, but the standard lore is that this effect vanishes when the perturber velocities are large compared to the binary's orbital velocity, as is typical for DM constituents. Here, we revisit the computation of the hardening rate induced by light perturbers. We show that although the perturbations average to zero over many encounters, many scenarios of interest for DM constraints are in the regime where the variance cannot be neglected. We show that a few fast-moving perturbers can leave stochastic perturbations in systems that are measured with great precision, and we use this framework to revisit the constraint potential of systems such as binary pulsars and the Solar System. This opens a new class of dynamical probes with potential applications to asteroid-mass DM candidates.