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

TL;DR

This paper develops an analytical approach using the inhomogeneous Balescu-Lenard equation and WKB approximation to model the secular evolution of thin, self-gravitating galactic discs, predicting features like radial migration and resonances.

Contribution

It introduces a tractable analytical formalism for secular diffusion in discrete galactic discs, emphasizing the role of tightly wound spirals and resonances, with applications to various astrophysical systems.

Findings

Predicts the importance of corotation resonance in inner disc regions.

Foresees formation of a 'ridge-like' feature in action space.

Overestimates the timescale for feature development, suggesting swing amplification may help.

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.