The secular evolution of discrete quasi-Keplerian systems. I. Kinetic theory of stellar clusters near black holes

Understand

We derive the kinetic equation that describes the secular evolution of a large set of particles orbiting a dominant massive object, such as stars bound to a supermassive black hole or a proto-planetary debris disc encircling a star.

• Because the particles move in a quasi-Keplerian potential, their orbits can be approximated by ellipses whose orientations remain fixed over many dynamical times.
• The kinetic equation is obtained by simply averaging the BBGKY equations over the fast angle that describes motion along these ellipses.
• This so-called Balescu-Lenard equation describes self-consistently the long-term evolution of the distribution of quasi-Keplerian orbits around the central object: it models the diffusion and drift of their actions, induced through their mutual resonant interaction.