Self-similar Gravitational Collapse in Stellar Dynamics

Self-similar gravitational collapse of a globular cluster is studied using the nonlinear kinetic standard model of stellar dynamics consisting of the Fokker-Planck-Vlasov transport equation coupled self-consistently to Poisson's equation for the Newtonian gravitational potential. It is shown rigorously that any locally integrable self-similar solution to these equations must approach a mass density profile ρ( r , t ) ∝ r -α , α = 3, in the final stage of the collapse. The discrepancy between the exact value α = 3 and previous results in the range 2 < α < 2.5 obtained from the orbit-averaged approximation to the kinetic model raises some questions about the validity of this popular approximation.