In this paper we have provided a general and flexible procedure to construct self-consistent spherical equilibrium models of stellar systems populated by stars in quasi-circular orbits. The method is relatively simple and intuitive, because it makes use of and brings out clearly all the well known properties of systems where the epicyclic approximation is applicable. Starting from a given density profile, two different options have been pursued, one where priority is given to retain a simple functional form for the distribution function in phase space, and another where the models that are constructed have a density distribution that is very close to the initial chosen profile. The method has been demonstrated in quantitative detail by constructing sequences of equilibrium models with varying degrees of tangential bias in the pressure tensor distribution, all based on the isochrone potential. This study is meant to be the starting point for future stability analyses and may be also of some interest in the discussion of some spectroscopic data now available for many elliptical galaxies.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998