Secular diffusion in discrete self-gravitating tepid discs III. Resonant thickening in the tightly wound limit

TL;DR

This paper models the long-term vertical thickening of self-gravitating galactic discs using the Balescu-Lenard equation in the WKB limit, predicting resonant orbit formation and comparing with numerical simulations.

Contribution

It derives a simplified double quadrature for diffusion coefficients in the thick WKB limit and applies the formalism to predict disc thickening, highlighting the role of resonances and finite-N effects.

Findings

Resonant orbit ridges form towards larger vertical actions.

The Balescu-Lenard formalism overestimates the timescale of thickening.

Finite-N effects and molecular clouds influence disc thickening.

Abstract

The secular thickening of a discrete self-gravitating galactic disc is investigated using the inhomogeneous multi-component Balescu-Lenard equation. The thick WKB limit for the diffusion and drift coefficients is found using the epicyclic approximation, while assuming that only radially tightly wound transient spirals are sustained by the disc. This yields a simple double quadrature for the drift and diffusion coefficients, providing a clear understanding of the positions of maximum vertical orbital diffusion within the disc induced by the effects of a finite number of particles. When applied to a tepid stable tapered disc, the Balescu-Lenard formalism predicts the formation of ridges of resonant orbits towards larger vertical actions, as found in direct numerical simulations, but over-estimates the timescale involved in their appearance. Swing amplication is likely needed to resolve this discrepancy, as demonstrated in the case of razor-thin discs. The joint evolution of a population of giant molecular clouds within the disc may accelerate the secular disc's thickening induced by finite${-N}$ effects, but the observed number of clouds in the Milky Way does not seem to be sufficient to explain its thick disc.