Analytic study of mass segregation around a massive black hole
  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.
