On Socially Distant Neighbors: Binaries as Density Probes in the Galactic Center

Stars often reside in binary configurations. Surrounding the supermassive black hole, the nuclear star cluster in the Galactic Center represents a dense environment, in which a binary frequently encounters and interacts with neighboring stars. These interactions vary from small perturbations to violent collisions. In the former case, weak gravitational interactions unbind the binary over the so-called evaporation timescale, which depends on the orbital properties of the binary and environmental properties such as the stellar density and velocity dispersion. Similarly, the collision rate depends on the density, and certain collisions can also unbind the binary. Thus, the detection of a binary with known properties can place constraints on the underlying density in the Galactic Center. We estimate the density necessary to unbind a binary within its lifetime for an orbit of arbitrary eccentricity about the supermassive black hole. A density above this threshold is forbidden: the binary would have already unbound. We demonstrate that this procedure can probe the density in the Galactic Center. Conversely, a known density profile provides constraints on binary orbital properties.