Strong mass segregation around a massive black hole

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Abstract
We show that the mass-segregation solution for the steady state distribution of stars around a massive black hole (MBH) has two branches: the known weak segregation solution (Bahcall & Wolf 1977), and a newly discovered strong segregation solution, presented here. The nature of the solution depends on the heavy-to-light stellar mass ratio M_H/M_L and on the unbound population number ratio N_H/N_L, through the relaxational coupling parameter \Delta=4 N_H M_H^2 /[N_L M_L^2(3+M_H/M_L)]. When the heavy stars are relatively common (\Delta>>1), they scatter frequently on each other. This efficient self-coupling leads to weak mass segregation, where the stars form n \propto r^{-\alpha_M} mass-dependent cusps near the MBH, with indices \alpha_H=7/4 for the heavy stars and 3/2<\alpha_L<7/4 for the light stars (i.e. \max(\alpha_H-\alpha_L)~=1/4). However, when the heavy stars are relatively rare (\Delta<<1), they scatter mostly on light stars, sink to the center by dynamical friction and settle into a much steeper cusp with 2~<\alpha_H<11/4, while the light stars form a 3/2<\alpha_L<7/4 cusp, resulting in strong segregation (i.e. \max(\alpha_H-\alpha_L)~=1). We show that the present-day mass function of evolved stellar populations (coeval or continuously star forming) with a universal initial mass function, separate into two distinct mass scales, ~1 Mo of main sequence and compact dwarfs, and ~10 Mo of stellar black holes (SBHs), and have \Delta<0.1. We conclude that it is likely that many relaxed galactic nuclei are strongly segregated. We review indications of strong segregation in observations of the Galactic Center and in results of numeric simulations, and briefly list some possible implications of a very high central concentration of SBHs around a MBH.

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