http://arxiv.org/abs/2211.14784
We derive an analytical model for the so-called phenomenon of `resonant dynamical friction’, where a disc of stars around a super-massive black hole interacts with a massive perturber, so as to align its inclination with the disc’s orientation. We show that it stems from singular behaviour of the orbit-averaged equations of motion, which leads to a rapid alignment of the argument of the ascending node $\Omega$ of each of the disc stars, with that of the perturber, $\Omega_{\rm p}$, with a phase-difference of $90^\circ$, for all stars whose maximum possible $\dot{\Omega}$ (maximised over all values of $\Omega$ for all the disc stars), is greater than $\dot{\Omega}_{\rm p}$; this corresponds approximately to all stars whose semi-major axes are less than twice that of the perturber. This persists until the perturber enters the disc. The predictions of this model agree with a suite of numerical $N$-body simulations which we perform to explore this phenomenon, for a wide range of initial conditions, masses, \emph{etc.}, and are an instance of a general phenomenon. Similar effects could occur in the context of planetary systems, too.
Y. Ginat, T. Panamarev, B. Kocsis, et. al.
Tue, 29 Nov 22
77/80
Comments: Submitted for publication. Comments welcome