Stellar Distributions Around a Supermassive Black Hole: Strong Segregation Regime Revisited

Abstract

We present a new analytical solution to the steady-state distribution of stars close to a central supermassive black hole of mass $M_{\bullet }$ in the center of a galaxy. Assuming a continuous mass function of the form $dN/dm\propto m^{\gamma }$, stars with a specific orbital energy $x=G{M}_{\bullet }/r-v^2/2$ are scattered primarily by stars of mass $m_{\mathrm{d}}(x)\propto x^{-5/(4\gamma +10)}$ that dominate the scattering of both lighter and heavier species at that energy. Stars of mass $m_{\mathrm{d}}(x)$ are exponentially rare at energies lower than $x$, and follow a density profile $n(x^{\prime })\propto x^{\prime 3/2}$ at energies $x^{\prime }\gg x$. Our solution predicts a negligible flow of stars through energy space for all mass species, similarly to the conclusions of Bahcall & Wolf (1977), but in contrast to the assumptions of Alexander & Hopman (2009). This is the first analytic solution which smoothly transitions between regimes where different stellar masses dominate the scattering.

8 pages, 1 figure. Submitted to ApJ

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