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 < xmax with index p = m/4M0, where E is the energy, σ is the typical velocity dispersion of unbound stars, and M0 is the mass averaged over mξxpmax. 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.

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