A numerical study of vector resonant relaxation

Understand

Stars bound to a supermassive black hole interact gravitationally.

• Persistent torques acting between stellar orbits lead to the rapid resonant relaxation of the orbital orientation vectors ("vector" resonant relaxation) and slower relaxation of the eccentricities ("scalar" resonant relaxation), both at rates much faster than two-body or non-resonant relaxation.
• We describe a new parallel symplectic integrator, N-ring, which follows the dynamical evolution of a cluster of N stars through vector resonant relaxation, by averaging the pairwise interactions over the orbital period and periapsis-precession timescale.
• We use N-ring to follow the evolution of clusters containing over 10^4 stars for tens of relaxation times.