Collisional Shaping of Nuclear Star Cluster Density Profiles

Abstract

A supermassive black hole surrounded by a dense, nuclear star cluster resides at the center of many galaxies. In this dense environment, high-velocity collisions frequently occur between stars. About 10% of the stars within the Milky Way’s nuclear star cluster collide with other stars before evolving off the main sequence. Collisions preferentially affect tightly bound stars, which orbit most quickly and pass through regions of the highest stellar density. Over time, collisions therefore shape the bulk properties of the nuclear star cluster. We examine the effect of collisions on the cluster’s stellar density profile. We show that collisions produce a turning point in the density profile, which can be determined analytically. Varying the initial density profile and collision model, we characterize the evolution of the stellar density profile over 10 Gyr. We find that old, initially cuspy populations exhibit a break around 0.1 pc in their density profile, while shallow density profiles retain their initial shape outside of 0.01 pc. The initial density profile is always preserved outside of a few tenths of a parsec irrespective of initial conditions. We generalize this model to an arbitrary galactic nucleus and show that the location of the collisional break can be simply estimated from the nuclear properties. Lastly, we comment on the implications of collisions for the luminosity and color of stars in the collisionally shaped inner cluster.