Strong mass segregation around a massive black hole

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 well known weak-segregation solution and a strong segregation solution, which is analyzed here for the first time. The nature of the solution depends on the heavy-to-light stellar mass ratio MH /ML and on the unbound population number ratio NH /NL , through the relaxational coupling parameter Δ = 4NHM 2H/[NLM 2L(3 + MH /M L )]. When the heavy stars are relatively common (Δ ≫ 1), they scatter frequently on each other. This efficient self-coupling leads to weak mass segregation, where the stars form mass-dependent cusps near the MBH, with indices αH = 7/4 for the heavy stars and 3/2 < αL < 7/4 for the light stars (i.e. max(αH - αL) ≃ 1/4). However, when the heavy stars are relatively rare (Δ ≪ 1), they scatter mostly on light stars, sink to the center by dynamical friction and settle into a much steeper cusp with 2 ≲ αH ≲ 11/4, while the light stars form a 3/2 < αL < 7/4 cusp, resulting in strong segregation (i.e., max(αH - αL) ≃ 1). We show that the present-day mass function of evolved stellar populations with a universal initial mass function (coeval or continuously star forming) separates into two distinct mass scales, 1 M ⊙ of main sequence and compact dwarfs, and 10 M ⊙ of stellar black holes (SBHs), and have Δ < 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 possible implications of a very high central concentration of SBHs around an MBH. © 2009. The American Astronomical Society. All rights reserved..