Laboratoire de Physique Théorique
Toulouse - UMR 5152

Fluctuations in a stellar disc’s gravitational field cause a long-term evolution of the orbits of stars. Fluctuations can either originate from an external perturber (collisionless framework) or from the intrinsic discreteness of the system (collisional framework).

In the collisionless framework, the resulting evolution of the system can be computed via the orbit-averaged dressed Fokker-Planck equation in angle-actions coordinates. I will 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, assuming that only tightly-wound transient spirals are present in the disc, we are able to reduce the computation of the diffusion tensor to a one-dimensional integral. In this WKB limit, the shot-noise-driven formation of narrow ridges of resonant orbits is recovered for a tepid stable tapered disc, allowing us to explain analytically the principal features of numerical simulations of such discs.

In the collisional framework, the evolution of an isolated stable self-gravitating discrete disc is described by the inhomogeneous Balescu-Lenard equation. I will also present this formalism, and relying on the same WKB assumptions, will show how one can obtain a simple and tractable quadrature for the associated drift and diffusion coefficients. Such an approach provides insight into the physical processes at work during the secular diffusion of such systems, and predicts the formation of a ridge-like structure in action-space, in agreeement with simulations.