Master Astronomy Internship 2021

Secular relaxation of 1D self-gravitating systems

Astrophysical context

Gravity is a long-range interaction. As such, stellar systems all share some fundamental similarities: (i) they are inhomogeneous, i.e. stars follow intricate orbits; (ii) they are self-gravitating, i.e. stars evolve in the gravitational potential that they self-consistently define, allowing the system to amplify perturbations; (iii) they are resonant, i.e. orbits introduce orbital frequencies, which naturally separate the dynamical timescale with the long timescale of orbital relaxation. One-dimensional self-gravitating systems (also called self-gravitating sheets) offer then an ideal and tunable testbed to understand the long-term signatures of these essential dynamical specificities.


This internship will be focused on describing the long-term resonant relaxation of 1D self-gravitating systems. We will first develop an efficient numerical code to integrate the dynamics of that system. We will subsequently construct suitable quasi-stationary equilibrium solutions, in particular through Eddington inversion and angle-action coordinates. Once these elements set up, we will be in a position to perform the linear response theory of that system, i.e. characterise the efficiency with which this system can amplify perturbations. Finally, we will derive the appropriate Balescu-Lenard kinetic equation to describe the long-term orbital reshufflings undergone by the systems, while comparing these predictions with our own measurements from numerical simulations. All in all, these investigations will offer new clues on the intricate dynamics of long-range interacting systems, highlighting in particular the efficiency with which these systems can or cannot reach their thermodynamical equilibria.


Strong interest in theoretical astronomy, dynamics, analytical and numerical work


The internship will be co-supervised by Jean-Baptiste Fouvry (IAP, Paris), Christophe Pichon (IAP, Paris), and Pierre-Henri Chavanis (LPT, Toulouse), as part of the SEGAL ANR (


Joyce, M., Worrakitpoonpon, T., 2010, 1004.2266
Chavanis, P.-H., 2012, 1107.1475
Benetti, F., Marcos, B., 2017, 1610.06966
Fouvry, J.-B., Bar-Or, B., 2018, 1712.05862