Black Hole Discs and Spheres in Galactic Nuclei -- Exploring the Landscape of Vector Resonant Relaxation Equilibria

Understand

Vector resonant relaxation (VRR) is known to be the fastest gravitational process that shapes the geometry of stellar orbits in nuclear star clusters.

• This leads to the realignment of the orbital planes on the corresponding VRR time scale $t_{\rm VRR}$ of a few million years, while the eccentricity $e$ and semimajor axis $a$ of the individual orbits are approximately conserved.
• The distribution of orbital inclinations reaches an internal equilibrium characterised by two conserved quantities, the total potential energy among stellar orbits, $E_{\rm tot}$, and the total angular momentum, $L_{\rm tot}$.
• On timescales longer than $t_\mathrm{VRR}$, the eccentricities and semimajor axes change slowly and the distribution of orbital inclinations are expected to evolve through a series of VRR equilibria.