Secular resonant dressed orbital diffusion I : method and WKB limit for tepid discs

Abstract

The equation describing the secular diffusion of a self-gravitating collisionless system induced by an exterior perturbation is derived while assuming that the timescale corresponding to secular evolution is much larger than that corresponding to the natural frequencies of the system. Its two dimensional formulation for a tepid galactic disc is also derived using the epicyclic approximation. Its WKB limit is found while assuming that only tightly wound transient spirals are sustained by the disc. It yields a simple quadrature for the diffusion coefficients which provides a straightforward understanding of the loci of maximal diffusion within the disc.