2018MNRAS.473.1719L

A Langevin equation is set up to model the dynamics of a supermassive black hole (massive particle) in a rotating environment (of light particles), typically the inner region of the galaxy, under the influence of dynamical friction, gravity and stochastic forces. The formal solution is derived, and the displacement and velocity two-point correlation functions are computed. The correlators perpendicular to the axis of rotation are equal to one another and different from those parallel to the axis. By computing this difference, it is suggested that one can, perhaps, observationally determine the magnitude of the rotation. In the case with sufficiently fast rotation, it is suggested that this model can lead to an ejection. If either one of dynamical friction and Eddington accretion is included, it is shown that a near-identical Langevin equation follows, allowing us to treat the two cases in a unified manner. The limitations of the model are also presented and compared against previous results.