Self-gravitating systems and the inhomogeneous Balescu-Lenard equation

Jean-Baptiste Fouvry (IAS)

Self-gravitating systems are ubiquitous in the Universe, ranging from the dynamics of galactic discs such as the Milky Way, up to galactic nuclei, i.e. stars in the very vicinity of a supermassive black hole.

As they are driven by gravity, a long-range interaction, these systems all share some common features.

They are (i) inhomogeneous, i.e. have intricate individual orbits, (ii) relaxed, i.e. are `dynamically frozen' on a quasistationary state, (iii) self-gravitating, i.e. live in the potential they generate themselves, (iv) resonant, i.e. orbital frequencies are attached to each motion, (v) discrete/perturbed, i.e. undergo internal/external fluctuations.
Recent progresses in the study of the kinetic theory of long-self-gravitating systems, have now made possible to track in detail the long-term effects of these specificities, through the Balescu-Lenard equation.

I will give a general review of this kinetic equation, highlight its origin, its physical content, and give a few illustrations of applications of this formalism in the astrophysical context.