Secular diffusion in discrete self-gravitating tepid discs I : analytic solution in the tightly wound limit

Abstract

The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is described using the inhomogeneous Balescu-Lenard equation. Assuming that only tightly wound transient spirals are present in the disc, a WKB approximation provides a simple and tractable quadrature for the corresponding drift and diffusion coefficients. It provides insight into the physical processes at work during the secular diffusion of a self-gravitating discrete disc and makes quantitative predictions on the initial variations of the distribution function in action space. When applied to the secular evolution of an isolated stationary self-gravitating Mestel disc, this formalism predicts initially the importance of the corotation resonance in the inner regions of the disc leading to a regime involving radial migration and heating. It predicts in particular the formation of a "ridge like" feature in action space, in agreement with simulations, but over-estimates the timescale involved in its appearance. Swing amplification is likely to resolve this discrepancy. In astrophysics, the inhomogeneous Balescu-Lenard equation and its WKB limit may also describe the secular diffusion of giant molecular clouds in galactic discs, the secular migration and segregation of planetesimals in proto-planetary discs, or even the long-term evolution of population of stars within the Galactic center.

22 pages, 12 figures

References in corpus (4)

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• Self-gravity, resonances and orbital diffusion in stellar discs
• Secular resonant dressed orbital diffusion I : method and WKB limit for tepid discs
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Cited by in corpus (11)

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• 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
• Formation and relaxation of quasi-stationary states in particle systems with power law interactions
• The secular evolution of discrete quasi-Keplerian systems. II. Application to a multi-mass axisymmetric disc around a supermassive black hole
• Functional integral derivation of the kinetic equation of two-dimensional point vortices
• Functional integral approach to the kinetic theory of inhomogeneous systems