The dynamical structure of isotropic spherical galaxies with a central black hole

¹ Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281-S9, 9000 Gent, Belgium
² European Southern Observatory, Casilla 19001, Santiago, Chile e-mail: mbaes@eso.org

Received: 26 August 2004
Accepted: 2 November 2004

Abstract

We discuss the kinematical structure of a two-parameter family of isotropic models with a central black hole. The family contains the slope of the central density cusp and the relative black hole mass as parameters. Most of the basic kinematical quantities of these models can be expressed analytically. This family contains three distinct models where also the distribution function, differential energy distribution and spatial LOSVDs can be expressed completely analytically. Each of these models shows a drastically different behaviour of the distribution function. Although the effect of a black hole on the distribution function is very strong, in particular for models with a shallow density cusp, the differential energy distribution is only marginally affected. We discuss in detail the effects of a central black hole on the LOSVDs. The projected velocity dispersion increases with black hole mass at small projected radii, but the effect of a black hole on the shape of the LOSVDs (characterized by the h₄ parameter) is less straightforward to interpret. Too much reliance on the wings of the LOSVDs and the value of the h₄ parameter to determine black hole masses might hence be dangerous.