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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 time-scale 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 Wentzel-Kramers-Brillouin (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.
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Jean-Baptiste Fouvry, Christophe Pichon, Simon Prunet. Secular resonant dressed orbital diffusion - I. Method and WKB limit for tepid discs. Monthly Notices of the Royal Astronomical Society, Oxford University Press (OUP): Policy P - Oxford Open Option A, 2015, 449, pp.1967-1981. ⟨10.1093/mnras/stv359⟩. ⟨insu-03644951⟩

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