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.

15 pages, 1 figure

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• Resonant thickening of self-gravitating discs: imposed or self-induced orbital diffusion in the tightly wound limit
• Self-gravity, resonances and orbital diffusion in stellar discs
• Collisional relaxation in the inhomogeneous Hamiltonian-Mean-Field model: diffusion coefficients
• Dressed diffusion and friction coefficients in inhomogeneous multicomponent self-gravitating systems
• The secular evolution of discrete quasi-Keplerian systems. I. Kinetic theory of stellar clusters near black holes
• Secular diffusion in discrete self-gravitating tepid discs I : analytic solution in the tightly wound limit
• Dynamical friction and feedback on galactic bars in the general fast-slow regime