On Socially Distant Neighbors: Using Binaries to Constrain the Density of Objects in the Galactic Center

Stars often reside in binary configurations. The nuclear star cluster surrounding the supermassive black hole (SMBH) in the Galactic Center (GC) is expected to include a binary population. In this dense environment, 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 a soft binary over the evaporation timescale, which depends on the binary properties as well as the density of surrounding objects and velocity dispersion. Similarly, collisions can also unbind a binary, and the collision rate depends on the density. Thus, the detection of a binary with known properties can constrain the density profile in the GC with implications for the number of compact objects, which are otherwise challenging to detect. We estimate the density necessary to unbind a binary within its lifetime for an orbit of arbitrary eccentricity about the SMBH. We find that the eccentricity has a minimal impact on the density constraint. In this proof of concept, we demonstrate that this procedure can probe the density in the GC using hypothetical young and old binaries as examples. Similarly, a known density profile provides constraints on the binary orbital separation. Our results highlight the need to consider multiple dynamical processes in tandem. In certain cases, often closer to the SMBH, the collision timescale rather than the evaporation timescale gives the more stringent density constraint, while other binaries farther from the SMBH provide unreliable density constraints because they migrate inwards due to mass segregation.