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DB2FBA1E-4DBE-488D-A1D6-4D4AC85ED368

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

Itai Linial, Re'em Sari
arXiv:2206.14817

Submitted on 29 June 2022

## 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 ${m}_{\mathrm{d}}\left(x\right)\propto {x}^{-5/\left(4\gamma +10\right)}$ that dominate the scattering of both lighter and heavier species at that energy. Stars of mass ${m}_{\mathrm{d}}\left(x\right)$ are exponentially rare at energies lower than $x$, and follow a density profile $n\left({x}^{\prime }\right)\propto {x}^{\prime 3/2}$ 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.

## Preprint

Comment: 8 pages, 1 figure. Submitted to ApJ

Subject: Astrophysics - Astrophysics of Galaxies