Black Hole Motion as Catalyst of Orbital Resonances

TL;DR

Black hole motion influences surrounding stars by redistributing their energies and velocities, acting as a catalyst for orbital resonances and leaving detectable kinematic signatures in the stellar population.

Contribution

This paper provides an analytical and numerical study of how black hole motion induces stellar orbital resonances and energy redistribution in galactic centers.

Findings

Stars on circular orbits are split into lower and higher energy groups due to black hole motion.

Black hole acts as a catalyst without changing its own orbit significantly.

Kinematic signatures of black hole motion are detectable up to 4 times the influence radius.

Abstract

The motion of a black hole about the centre of gravity of its host galaxy induces a strong response from the surrounding stellar population. We treat the case of a harmonic potential analytically and show that half of the stars on circular orbits in that potential shift to an orbit of lower energy, while the other half receive a positive boost and recede to a larger radius. The black hole itself remains on an orbit of fixed amplitude and merely acts as a catalyst for the evolution of the stellar energy distribution function f(E). We show that this effect is operative out to a radius of approx 3 to 4 times the hole's influence radius, R_bh. We use numerical integration to explore more fully the response of a stellar distribution to black hole motion. We consider orbits in a logarithmic potential and compare the response of stars on circular orbits, to the situation of a `warm' and `hot' (isotropic) stellar velocity field. While features seen in density maps are now wiped out, the kinematic signature of black hole motion still imprints the stellar line-of-sight mean velocity to a magnitude ~18% the local root mean-square velocity dispersion sigma.