Breaking Boundaries: Extending the Orbit-Averaged Fokker-Planck Equation Inside the Loss Cone

In this Letter, we present a new formulation of loss cone theory as a reaction-diffusion system, which accounts for loss cone events through a sink term and can be orbit averaged. It can recover the standard approach based on boundary conditions, and is derived from a simple physical model that overcomes many of the classical theoretical constraints. We test our formulation by computing the relaxed distribution of disruptive orbits in phase space, which has a simple analytic form and agrees with the pericenter of tidal disruption events at disruption predicted by nonaveraged models. This formulation of the problem is particularly suitable for including more physics in tidal disruptions and the analogous problem of gravitational captures—e.g., strong scatterings, gravitational waves emission, physical stellar collisions, and repeating partial disruptions—that can all act on timescale shorter than two-body relaxation and might cause the tension between the observed vs theoretically predicted population of tidal disruptions.