Drifting through the medium: kicks and self-propulsion of binaries within accretion disks and other environments

Compact binaries are within the reach of gravitational and electromagnetic wave detectors, and are important for our understanding of astrophysical environments and the composition of compact objects. There is a vast body of work devoted to the evolution of such binaries in background media, such as in common-envelope evolution, accretion disks and dark matter mini-spikes. Here, we explore further gravitationally-bound binaries evolving within an environment. We show that dissipative effects such as gravitational drag and accretion impart a momentum to the center of mass of asymmetric binaries. We numerically evolve the binaries in a Newtonian setup and show that, depending on the medium density, the center of mass can accelerate to high speeds -- in some cases $300\, {\rm km/s}$ or more -- during inspiral, with potentially observable signatures. Our numerical results are fully consistent with an \textit{analytical} result for the CM evolution at first order in the medium density.