Black Hole Motion as Catalyst of Orbital Resonances

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 f (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.