Stellar Distributions around a Supermassive Black Hole: Strong-segregation Regime Revisited
Itai Linial, Re’em Sari
Abstract
Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic">dN</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi mathvariant="italic">dm</mml:mi> <mml:mo>∝</mml:mo> <mml:msup> <mml:mrow> <mml:mi>m</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> </mml:msup> </mml:math> , stars with a specific orbital energy x = GM • / r − v 2 /2 are scattered primarily by stars of mass m d ( x ) ∝ x −5/(4 γ +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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>n</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo accent="false">′</mml:mo> <mml:mo stretchy="false">)</mml:mo> <mml:mo>∝</mml:mo> <mml:mi>x</mml:mi> <mml:msup> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:math> at energies <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>x</mml:mi> <mml:mo accent="false">′</mml:mo> <mml:mo>></mml:mo> <mml:mi>x</mml:mi> </mml:math> . 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.