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Stars often reside in binary configurations. The nuclear star clustersurrounding the supermassive black hole (SMBH) in the Galactic Center (GC) isexpected to include a binary population. In this dense environment, a binaryfrequently encounters and interacts with neighboring stars. These interactionsvary from small perturbations to violent collisions. In the former case, weakgravitational interactions unbind a soft binary over the evaporation timescale,which depends on the binary properties as well as the density of surroundingobjects and velocity dispersion. Similarly, collisions can also unbind abinary, and the collision rate depends on the density. Thus, the detection of abinary with known properties can constrain the density profile in the GC withimplications for the number of compact objects, which are otherwise challengingto detect. We estimate the density necessary to unbind a binary within itslifetime for an orbit of arbitrary eccentricity about the SMBH. We find thatthe eccentricity has a minimal impact on the density constraint. In this proofof concept, we demonstrate that this procedure can probe the density in the GCusing hypothetical young and old binaries as examples. Similarly, a knowndensity profile provides constraints on the binary orbital separation. Ourresults highlight the need to consider multiple dynamical processes in tandem.In certain cases, often closer to the SMBH, the collision timescale rather thanthe evaporation timescale gives the more stringent density constraint, whileother binaries farther from the SMBH provide unreliable density constraintsbecause they migrate inwards due to mass segregation.

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