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

Abstract

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. Hence, it is the master equation that describes the secular effects of resonant relaxation. We show how it captures the phenonema of mass segregation and of the relativistic Schwarzschild barrier recently discovered in $N$-body simulations.

24 pages, 3 figures

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Cited by in corpus (13)

• The impact of vector resonant relaxation on the evolution of binaries near a massive black hole: implications for gravitational wave sources
• Quiescent and active galactic nuclei as factories of merging compact objects in the era of gravitational-wave astronomy
• Scalar Resonant Relaxation of Stars Around a Massive Black Hole
• Relaxation in self-gravitating systems
• Vector Resonant Relaxation of Stars around a Massive Black Hole
• Revisiting relaxation in globular clusters
• Mildly-Hierarchical triple dynamics and applications to the outer solar system
• Resonant thickening of self-gravitating discs: imposed or self-induced orbital diffusion in the tightly wound limit
• Dressed diffusion and friction coefficients in inhomogeneous multicomponent self-gravitating systems
• Formation and relaxation of quasi-stationary states in particle systems with power law interactions
• The secular evolution of discrete quasi-Keplerian systems. II. Application to a multi-mass axisymmetric disc around a supermassive black hole
• The S stars' zone of avoidance in the Galactic center
• Resonant Dynamical Friction in Nuclear Star Clusters: Rapid Alignment of an Intermediate-mass Black Hole with a Stellar Disk