Stellar Systems with Negative Temperatures

An attempt is made to incorporate the results of the simulations of van Albada (1982) of collisionless stellar systems into a family of equilibrium distribution functions. Van Albada showed that one can produce an excellent fit to de Vaucouleur's (1948) R to the 1/4 law by relaxing an initially 'cold' configuration in approximate spherical symmetry. The kinematics of the final state are determined by the initial ratio of kinetic to potential energies. The spatial distribution of matter in van Albada's models is less strongly dependent on initial 'temperature'. The form of this distribution function is derived through consideration of the radial orbit model, the endpoint of an infinitely cold collapse. A 'negative temperature model' is derived, arising from the need to avoid unphysically divergent central densities in a model dominated by radial orbits. A set of surface brightness profiles derived from the negative temperature distribution function is shown. The model is structurally very similar to real elliptical galaxies, however the kinematic similarity may be different, and so this property is explored. The question of whether the model is dynamically stable is also discussed.