Fully analytical solutions for Bondi accretion in galaxies with a central Black Hole

TL;DR

This paper derives fully analytical solutions for isothermal Bondi accretion onto central black holes within galaxy models characterized by Jaffe profiles, linking hydrodynamics and stellar dynamics.

Contribution

It introduces new analytical solutions for Bondi accretion in Jaffe galaxy models with central black holes, connecting gas and stellar properties through temperature relations.

Findings

Analytical formulas for flow properties and accretion rates.

Linking gas temperature to stellar virial temperature.

Useful for modeling black hole accretion in galaxies.

Abstract

The fully analytical solution for isothermal Bondi accretion on a black hole (MBH) at the center of JJ two-component Jaffe (1983) galaxy models is presented. In JJ models the stellar and total mass density distributions are described by the Jaffe profile, with different scale-lengths and masses, and to which a central MBH is added; all the relevant stellar dynamical properties can also be derived analytically. In these new accretion solutions the hydrodynamical and stellar dynamical properties are linked by imposing that the gas temperature is proportional to the virial temperature of the stellar component. The formulae that are provided allow to evaluate all flow properties, and are then useful for estimates of the accretion radius and the mass flow rate when modeling accretion on MBHs at the center of galaxies.