Black hole motion as catalyst of orbital resonances

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 consider the case of a harmonic potential 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. 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 φ(E). We then consider orbits in the logarithmic potential and identify the response of stars near resonant energies. The kinematic signature of black hole motion imprints the stellar line-of-sight mean velocity to a magnitude ⋍13% the local root mean-square velocity dispersion σ. The high velocity dispersion at the 5:2 resonance hints to an observable effect at a distance ⋍ 3 times the hole's influence radius.