Description of the evolution of inhomogeneities on a dark matter halo with the Vlasov equation

We use a direct numerical integration of the Vlasov equation in spherical symmetry with a background gravitational potential to determine the evolution of a collection of particles in different models of a galactic halo in order to test its stability against perturbations. Such collection is assumed to represent a dark matter inhomogeneity which is represented by a distribution function defined in phase-space. Non-trivial stationary states are obtained and determined by the virialization of the system. We describe some features of these stationary states bymeans of the properties of the final distribution function and final density profile. We compare our results using the different halo models and find that the NFW halo model is the most stable of them, in the sense that an inhomogeneity in this halomodel requires a shorter time to virialize.