Stellar Distributions around a Supermassive Black Hole: Strong-segregation Regime Revisited

We present a new analytical solution to the steady-state distribution of stars close to a central supermassive black hole of mass M _• in the center of a galaxy. Assuming a continuous mass function of the form dN / dm ∝ m γ , stars with a specific orbital energy x = GM _•/r − v ²/2 are scattered primarily by stars of mass m _d(x) ∝ x ^{−5/(4γ+10)} that dominate the scattering of both lighter and heavier species at that energy. Stars of mass m _d(x) are exponentially rare at energies lower than x, and follow a density profile n ( x ′ ) ∝ x ′ 3 / 2 at energies x ′ > x . Our solution predicts a negligible flow of stars through energy space for all mass species, similarly to the conclusions of Bahcall & Wolf, but in contrast to the assumptions of Alexander & Hopman. This is the first analytic solution that smoothly transitions between regimes where different stellar masses dominate the scattering.