Adiabatic black hole growth in S\'ersic models of elliptical galaxies

TL;DR

This study models how slow growth of a central black hole affects elliptical galaxies with Sersic profiles, revealing the formation of a central stellar cusp and specific kinematic changes.

Contribution

It provides a theoretical analysis of black hole growth effects on galaxy structure using action conservation, predicting observable central cusps and velocity profiles.

Findings

Central cusp with surface brightness ∝ R^{-1.3}

Velocity dispersion ∝ R^{-1/2}

Excess stellar mass scales with black-hole mass

Abstract

We have examined the effect of slow growth of a central black hole on spherical galaxies that obey S\'ersic or $R^{1/m}$ surface-brightness profiles. During such growth the actions of each stellar orbit are conserved, which allows us to compute the final distribution function if we assume that the initial distribution function is isotropic. We find that black-hole growth leads to a central cusp or ``excess light', in which the surface brightness varies with radius as $R^{-1.3}$ (with a weak dependence on S\'ersic index $m$), the line-of-sight velocity dispersion varies as $R^{-1/2}$, and the velocity anisotropy is $\beta\simeq -0.24$ to $-0.28$ depending on $m$. The excess stellar mass in the cusp scales approximately linearly with the black-hole mass, and is typically 0.5--0.85 times the black-hole mass. This process may strongly influence the structure of nuclear star clusters if they contain black holes.