Analytic Study of Mass Segregation Around a Massive Black Hole

We analyze the distribution of stars of arbitrary mass function ξ(m) around a massive black hole (MBH). Unless ξ is strongly dominated by light stars, the steady-state distribution function approaches a power law in specific energy x ≡ -E/mσ² < x _max with index p = m/4M ₀, where E is the energy, σ is the typical velocity dispersion of unbound stars, and M ₀ is the mass averaged over mξx^p _max. For light-dominated ξ, 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.