Breaking boundaries: extending the orbit-averaged Fokker-Planck equation inside the loss cone

TL;DR

This paper introduces a new reaction-diffusion formulation of loss cone theory that improves modeling of tidal disruptions and related phenomena by accounting for complex physical processes within a unified, orbit-averaged framework.

Contribution

It presents a novel, physically motivated formulation of loss cone theory as a reaction-diffusion system that overcomes classical constraints and can incorporate additional physics.

Findings

Analytic form of relaxed distribution of disruptive orbits

Agreement with non-averaged models for tidal disruption predictions

Framework suitable for including complex physics like gravitational waves and stellar collisions

Abstract

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, that has a simple analytic form and agrees with the pericentre of tidal disruption events at disruption predicted by non-averaged 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.