Analytic Study of Mass Segregation around a Massive Black Hole

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/mσ2 < xmax with index p = m/4M0, where E is the energy, σ the typical velocity dispersion of unbound stars, and M0 the mass averaged over mgx p max. 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. Subject headings: Galaxy: kinematics and dynamics — stellar dynamics — black hole physics