Fluctuations in a stellar disc’s gravitational potential 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 an orbit-averaged dressed Fokker-Planck equation in angle-action coordinates. I will present the formalism that enables one to compute the diffusion tensor from a given source of perturbations while including the system’s dynamical response. Assuming that only tightly wound transient spirals are present in the disc (WKB limit), the shot-noise driven formation of narrow ridges of resonant orbits in tepid stable disc is recovered, as observed in numerical simulations.
In the collisional framework, one may rely on the inhomogeneous Balescu-Lenard equation to capture the effect of discreteness on secular timescales. I will also present this formalism and show how its WKB limit leads to simple quadratures. When applied to a tepid stellar disc, it predicts the formation of ridge-like structures in action-space, in agreement with simulations.