Semi-Analytical Fokker Planck Models for Nuclear Star Clusters

We study the dynamics of nuclear star clusters, the dense stellar environments surrounding massive black holes in the centers of galaxies. We consider angular momentum diffusion due to two-body scatterings among stellar objects and energy advection due to gravitational wave emission upon interaction with the central massive black hole. Such dynamics is described by a two-dimensional Fokker-Planck equation in energy-angular momentum space. Focusing on the transition between the diffusion-dominated region and the advection-dominated one, we utilize self-similarity to obtain a full solution for the Fokker-Planck equation. This solution provides the density and flux of the stellar objects in nuclear star clusters. This improves the rate estimates for extreme mass-ratio inspirals, and has interesting implications for a new class of galactic center transients called quasi-periodic eruptions.