Simple galaxy models with massive haloes

Abstract

The axisymmetric logarithmic potential introduced by Binney as a simple model of a galactic halo has an elementary distribution function depending on the two classical integrals of motion, binding energy E and angular momentum parallel to the symmetry axis L z. The spherical limit is an isothermal distribution of two stellar populations whose masses and central densities are in the ratio 1:2. It is more realistic to build composite models, in which a luminous component is embedded within a massive dark halo. The gravitational potentials of the dark matter and the stars are together the axisymmetric logarithmic potential. Pleasingly simple galaxies are generated by taking the distribution function of the luminous component to be an isothermal. The luminosity density is then stratified on similar concentric spheroids and can fall off asymptotically like r~ 3 or r" 35 , as is appropriate for modelling elliptical galaxies and bulges. The kinematics are isotropic and the observables-the isophotes and line-of-sight second moment-are all simple. The surface brightness is a reasonable fit to the de Vaucouleurs profile. The non-rotating models have line profiles, or distributions of line-of-sight velocities, that are everywhere exactly Gaussian. The distortions to the line profiles caused by rotation are investigated by building distribution functions for three different rotation laws. The maximum deviation from Gaussian occurs for the maximum streaming model. At a slight cost in mathematical simplicity, it is possible to construct luminous components with anisotropic kinematics in the dark halo by modifying the isothermal distribution function. The observables and projected quantities are still elementary functions. The line profile is given for models with and without rotation.