Secular resonant dressed orbital diffusion II : application to an isolated self similar tepid galactic disc

Abstract

The main orbital signatures of the secular evolution of an isolated self-gravitating stellar Mestel disc are recovered using a dressed Fokker-Planck formalism in angle-action variables. The shot-noise-driven formation of narrow ridges of resonant orbits is recovered in the WKB limit of tightly wound transient spirals, for a tepid Toomre-stable tapered disc. The relative effect of the bulge, the halo, the disc temperature and the spectral properties of the shot noise are investigated in turn. For such galactic discs all elements seem to impact the locus and direction of the ridge. For instance, when the halo mass is decreased, we observe a transition between a regime of heating in the inner regions of the disc through the inner Lindblad resonance to a regime of radial migration of quasi-circular orbits via the corotation resonance in the outer part of the disc. The dressed secular formalism captures both the nature of collisionless systems (via their natural frequencies and susceptibility), and their nurture via the structure of the external perturbing power spectrum. Hence it provides the ideal framework in which to study their long term evolution.