The long-term evolution of razor-thin galactic discs: Balescu–Lenard prediction and perspectives

¹ Institut d’Astrophysique de Paris, CNRS and Sorbonne Université, UMR 7095, 98 bis Boulevard Arago, F-75014 Paris, France
² Institut de Physique Théorique, DRF-INP, UMR 3680, CEA, L’Orme des Merisiers, Bât 774, 91191 Gif-sur-Yvette, France
³ Kyung Hee University, Dept. of Astronomy & Space Science, Yongin-shi, Gyeonggi-do 17104, Republic of Korea
⁴ Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France

^⋆ Corresponding author: pichon@iap.fr

Received: 11 February 2025
Accepted: 18 April 2025

Abstract

In the last five decades, numerical simulations have provided invaluable insights into the evolution of galactic discs over cosmic times. As a complementary approach, developments in kinetic theory now also offer a theoretical framework to understand statistically their long-term evolution up to the onset of gravitational instability. The current state-of-the-art kinetic theory of isolated stellar systems is the inhomogeneous Balescu–Lenard equation. It can describe the long-term evolution of a self-gravitating razor-thin disc under the effect of resonant interactions between collectively amplified noise-driven fluctuations. In this work, comparing theoretical predictions to numerical simulations, we quantitatively show that kinetic theory indeed captures the average long-term evolution of cold stellar discs. Leveraging the versatility of kinetic methods, we then offer some new perspectives on this problem, namely (i) the crucial impact of collective effects in accelerating the relaxation; (ii) the role of (weakly) damped modes in shaping the disc’s orbital heating; (iii) the bias introduced by gravitational softening on long timescales when compared with non-softened theoretical predictions; (iv) the resurgence of strong stochasticity near marginal stability. These elements call for an appropriate choice of softening kernel when simulating the long-term evolution of razor-thin discs and for an extension of kinetic theory beyond the average evolution. Nevertheless, kinetic theory captures quantitatively the ensemble-averaged long-term response of such discs.