Gravitational pertubation of homogeneous collisionless dark matter

Abstract

The effect of a perturbing mass on a homogeneous collisionless cloud of dark matter is considered in the linear approximation. It is shown that gravitational potential can have turning points, in sharp contrast with gravitating systems of finite extent. The model offers a reasonable explanation for the observed secondary maxima in the density distribution of rich clusters. The relevance of the model to the flatness of the rotation curves of galaxies is also discussed.