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Authors: Uri Keshet, Clovis Hopman, Tal Alexander

Date: 28 Jan 2009

Abstract: We analyze the distribution of stars of arbitrary mass function g(m) around a massive black hole (MBH). Unless g is strongly dominated by light stars, the steady-state distribution function approaches a power-law in specific energy x=-E/(m*sigmaˆ2)<x_max with index p=m/4M_0, where E is the energy, sigma the typical velocity dispersion of unbound stars, and M_0 the mass averaged over m*g*x_{max}ˆp. For light-dominated g, p becomes non-linear in m and can grow as large as 3/2 - much steeper than previously thought. A simple prescription for the stellar density profile around MBHs is provided.

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