A new class of galaxy models with a central BH -- I. The spherical case

TL;DR

This paper introduces a new class of spherical galaxy models with a Jaffe stellar profile, a dark matter halo, and a central black hole, providing analytical solutions for their dynamical properties and stability conditions.

Contribution

It derives conditions for physically consistent dark matter halos, solves Jeans equations analytically, and determines stability limits, enhancing galaxy modeling accuracy.

Findings

Analytical expressions for velocity dispersion profiles.

Conditions for phase-space consistency and stability.

Models compatible with NFW profiles at key radii.

Abstract

The dynamical properties of spherically symmetric galaxy models, where a Jaffe (1983) stellar density profile is embedded in a total mass density decreasing as $r^{-3}$ at large radii, are presented. The orbital structure of the stellar component is described by the Osipkov--Merritt anisotropy; the dark matter halo is isotropic, and a black hole is added at the center of the galaxy. First, the conditions for a nowhere negative and monotonically decreasing dark matter halo density profile are derived; this profile can be made asymptotically coincident with a NFW profile at the center and at large radii. Then the minimum value of the anisotropy radius for phase-space consistency is derived as a function of the galaxy parameters. The Jeans equations for the stellar component are solved analytically; the projected velocity dispersion at the center and at large radii is also obtained, for generic values of the anisotropy radius. Finally, analytical expressions for the terms entering the Virial Theorem are derived, and the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability is determined as a function of the galaxy parameters. The presented models, built following an approach already adopted in our previous works, can be a useful starting point for a more advanced modeling of the dynamics of elliptical galaxies, and can be easily implemented in numerical simulations requiring a realistic dynamical model of a galaxy.