Resonant Dynamical Friction: Analytical Description by Yonadav Barry Ginat et al. on Tuesday 29 November

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.

arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2211.14784v1