## A Self-Consistent Treatment of Dynamical Friction: New Insights into Core Stalling and Dynamical Buoyancy

**Abstract**

Dynamical friction is typically regarded as a secular process, in which the subject (`perturber’) inspirals 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 purely resonant orbits. However, dynamical friction is only of astrophysical interest if its timescale is shorter than the age of the Universe. In this talk, I will therefore discuss the consequences of relaxing the adiabatic and secular approximations in the computation of the dynamical friction torque in a linear perturbative framework. First, I will 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 with an exclusive contribution from the resonances. 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, I will present a self-consistent treatment that properly accounts for the time-dependence of the perturber potential and circular frequency (memory effect). I will then apply this self-consistent formalism to explain the origin of various dynamical phenomena that occur in the N-body simulations of orbital decay in a cored galaxy but have thus far eluded proper explanation. In particular, I will show how the memory effect results in a phase of accelerated, super-Chandrasekhar friction before the perturber stalls at a critical radius in the core (core-stalling). Inside this critical radius the torque flips sign, giving rise to dynamical buoyancy, which counteracts friction and causes the perturber to stall. Finally, I will present a novel, non-perturbative, orbit-based formalism to investigate the origin of core-stalling and dynamical buoyancy, and discuss some potential astrophysical implications of these phenomena, such as constraining the particle nature of dark matter using the dynamics of cored galaxies.