A Self-Consistent, Time-Dependent Treatment of Dynamical Friction: New Insights regarding Core Stalling and Dynamical Buoyancy

TL;DR

This paper develops a time-dependent model of dynamical friction that explains core-stalling and dynamical buoyancy phenomena, extending beyond traditional adiabatic and secular approximations, and aligns with N-body simulation results.

Contribution

It introduces a generalized LBK torque with transient oscillations and a self-consistent, time-dependent treatment of orbital decay, revealing new insights into core-stalling and dynamical buoyancy.

Findings

Transient oscillations due to non-resonant orbits damp out over time.

Perturbers experience accelerated friction before stalling at a critical radius.

Inside the critical radius, torque reverses, causing dynamical buoyancy.

Abstract

Dynamical friction is typically regarded a secular process, in which the subject ('perturber') evolves very slowly (secular approximation), and has been introduced to the host over a long time (adiabatic approximation). These assumptions imply that dynamical friction arises from the LBK torque with non-zero contribution only from pure resonance orbits. However, dynamical friction is only of astrophysical interest if its timescale is shorter than the age of the Universe. In this paper we therefore relax the adiabatic and secular approximations. We first derive a generalized LBK torque, which reduces to the LBK torque in the adiabatic limit, and show that it gives rise to transient oscillations due to non-resonant orbits that slowly damp out, giving way to the LBK torque. This is analogous to how a forced, damped oscillator undergoes transients before settling to a steady state, except that here the damping is due to phase mixing rather than dissipation. Next, we present a self-consistent treatment, that properly accounts for time-dependence of the perturber potential and circular frequency (memory effect), which we use to examine orbital decay in a cored galaxy. We find that the memory effect results in a phase of accelerated, super-Chandrasekhar friction before the perturber stalls at a critical radius, $R_{\mathrm{crit}}$, in the core (core-stalling). Inside of $R_{\mathrm{crit}}$ the torque flips sign, giving rise to dynamical buoyancy, which counteracts friction and causes the perturber to stall. This phenomenology is consistent with $N$-body simulations, but has thus far eluded proper explanation.