Self-gravity, resonances and orbital diffusion in stellar discs

TL;DR

This paper develops a formalism to compute the diffusion tensor in stellar discs caused by gravitational fluctuations, enabling analysis of orbital evolution and density features through resonances and diffusion processes.

Contribution

It introduces a new method to calculate the diffusion tensor including the system's dynamical response, simplifying the analysis of stellar disc evolution.

Findings

Analytical explanation of density ridges in action space.

Transition from disc heating to radial migration as Q decreases.

Validation of the formalism with numerical simulations.

Abstract

Fluctuations in a stellar system's gravitational field cause the orbits of stars to evolve. The resulting evolution of the system can be computed with the orbit-averaged Fokker-Planck equation once the diffusion tensor is known. We present the formalism that enables one to compute the diffusion tensor from a given source of noise in the gravitational field when the system's dynamical response to that noise is included. In the case of a cool stellar disc we are able to reduce the computation of the diffusion tensor to a one-dimensional integral. We implement this formula for a tapered Mestel disc that is exposed to shot noise and find that we are able to explain analytically the principal features of a numerical simulation of such a disc. In particular the formation of narrow ridges of enhanced density in action space is recovered. As the disc's value of Toomre's $Q$ is reduced and the disc becomes more responsive, there is a transition from a regime of heating in the inner regions of the disc through the inner Lindblad resonance to one of radial migration of near-circular orbits via the corotation resonance in the intermediate regions of the disc. The formalism developed here provides the ideal framework in which to study the long-term evolution of all kinds of stellar discs.