Stellar Dynamics around a Massive Black Hole II: Resonant Relaxation

Understand

We present a first-principles theory of Resonant Relaxation (RR) of a low mass stellar system orbiting a more massive black hole (MBH).

• We first extend the kinetic theory of Gilbert (1968) to include the Keplerian field of a black hole of mass $M_\bullet$.
• Specializing to a Keplerian stellar system of mass $M \ll M_\bullet$, we use the orbit-averaging method of Sridhar & Touma (2015; Paper I) to derive a kinetic equation for RR.
• This describes the collisional evolution of a system of $N \gg 1$ Gaussian Rings in a reduced 5-dim space, under the combined actions of self-gravity, 1 PN and 1.5 PN relativistic effects of the MBH and an arbitrary external potential.