Gravitational loss-cone instability: Monotonic and nonmonotonic angular momentum distributions of stars

Small perturbations of spherical star clusters around massive black holes are studied. The presence of a black hole gives rise to peculiar distributions that have no stars with low angular momenta (falling into the so-called “loss cone”). The stability of such a distribution has been found to depend significantly on whether it monotonically increases with angular momentum L (from the loss cone up to L = L _circ in circular orbits) or has a maximum at some intermediate L = L _*. In the case of spherical systems under consideration, the loss-cone instability is shown to be possible only for nonmonotonic distributions.