The Hernquist model revisited: completely analytical anisotropic dynamical models

Abstract

Simple analytical models, such as the Hernquist model, are very useful tools to investigate the dynamical structure of galaxies. Unfortunately, most of the analytical distribution functions are either isotropic or of the Osipkov-Merritt type, and hence basically one-dimensional. We present three different families of anisotropic distribution functions that self-consistently generate the Hernquist potential-density pair. These families have constant, increasing and decreasing anisotropy profiles respectively, and can hence represent a wide variety of orbital structures. For all of the models presented, the distribution function and the velocity dispersions can be written in terms of elementary functions. These models are ideal tools for a wide range of applications, in particular to generate the initial conditions for N-body or Monte Carlo simulations.