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

TL;DR

This paper introduces a new analytical model for the distribution of stars around a supermassive black hole, accounting for different stellar masses and their scattering behaviors, revising previous assumptions about stellar flows.

Contribution

It provides the first analytical solution that smoothly transitions between regimes dominated by different stellar masses in the scattering process.

Findings

Predicts a negligible stellar flow through energy space for all masses.

Identifies the dominant stellar mass for scattering at each energy level.

Revises previous models by showing a smooth transition between mass regimes.

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 $x = GM_{\bullet}/r - v^2/2$ are scattered primarily by stars of mass $m_{\rm d}(x) \propto x^{-5/(4\gamma+10)}$ that dominate the scattering of both lighter and heavier species at that energy. Stars of mass $m_{\rm d}(x)$ are exponentially rare at energies lower than $x$, and follow a density profile $n(x') \propto x'^{3/2}$ at energies $x' \gg x$. 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.