Chebyshev spectral solutions of the orbit-averaged Fokker Planck equations for modeling the relaxation evolution of dense star clusters

The Orbit-Averaged Fokker-Planck (OAFP) kinetic equations provide a fundamental and accurate mathematical model for the evolution of dense star clusters. However, their applicability has been limited by the fact that numerical integrations are typically expensive, due to the time-consuming numerical treatment of the ‘collision’ integral terms and the large gap between the dynamical and relaxation time scales. In the present work, we discuss how to overcome these difficulties by applying to the OAFP modern spectral numerical methods.  Spectral methods are known for their accuracy and efficiency but so far have found limited applications in stellar dynamics. They are often termed ‘global’ methods compared to ‘local’ methods (e.g. finite difference and Runge-Kutta method) because they do not rely on space-discretization. The advantages and usefulness of spectral methods will be demonstrated by showing spectral (Chebyshev) solution both for the self-similar OAFP equation (to model isolated star clusters) and the Bachall-Wolf model (for star clusters around a massive black hole).