Analytic study of mass segregation around a massive black hole

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.

Revised version published in Astrophys. J. Lett

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