Stochastic tidal heating by random interactions with extended substructures

Understand

Gravitating systems surrounded by a dynamic sea of substructures experience fluctuations of the local tidal field which inject kinetic energy into the internal motions.

• This paper uses stochastic calculus techniques to describe `tidal heating' as a random walk of orbital velocities that leads to diffusion in a 4-dimensional energy--angular momentum space.
• In spherical, static potentials we derive analytical solutions for the Green's propagators directly from the number density and velocity distribution of substructures with known mass & size functions without arbitrary cuts in forces or impact parameters.
• Furthermore, a Monte-Carlo method is presented, which samples velocity 'kicks' from a probability function and can be used to model orbital scattering in fully generic potentials.