Analytic study of mass segregation around a massive black hole

TL;DR

This paper investigates the distribution of stars of various masses around a massive black hole, revealing that the steady-state distribution often follows a specific power-law, with steeper profiles possible for light-dominated star populations.

Contribution

It provides a new analytic framework for understanding stellar mass segregation around black holes, including a simple density profile and application to the Milky Way.

Findings

Steady-state distribution follows a power-law with index p=m/4M_0.

For light-dominated star populations, p can reach as high as 3/2.

Application to the Milky Way's black hole environment demonstrates the model's relevance.

Abstract

We analyze the distribution of stars of arbitrary mass function xi(m) around a massive black hole (MBH). Unless xi is strongly dominated by light stars, the steady-state distribution function approaches a power-law in specific energy x=-E/(m*sigma^2)<x_max with index p=m/4M_0, where E is the energy, sigma is the typical velocity dispersion of unbound stars, and M_0 is the mass averaged over m*xi*x_{max}^p. For light-dominated xi, p can grow as large as 3/2 - much steeper than previously thought. A simple prescription for the stellar density profile around MBHs is provided. We illustrate our results by applying them to stars around the MBH in the Milky Way.