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