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We examine the stability of spherical, non-rotating galaxies using an N-body code to evolve a set of initially equilibrium models generated from three distribution functions. All the models have the same initial density profile, which is essentially a de Vaucouleurs law. The first family is characterized by a velocity ellipsoid which becomes more radial outwards; The second is most radial at the center; and the third has a constant anisotropy. All three families are unstable to the formation of a bar when the velocity distribution was sufficiently anisotropic. In the first family the transition to instability occurred suddenly as anisotropy increased, while the other families appear to be unstable even for very small total anisotropies. Our results are inconsistent with a recent proof of the stability of a wide class of anisotropic systems.
Merritt et al. (Sun,) studied this question.