Dynamical Friction, Buoyancy, and Core-stalling. I. A Nonperturbative Orbit-based Analysis

Abstract

We examine the origin of dynamical friction using a nonperturbative, orbit-based approach. Unlike the standard perturbative approach, in which dynamical friction arises from the LBK torque due to pure resonances, this alternative, complementary view nicely illustrates how a massive perturber significantly changes the energies and angular momenta of field particles on near-resonant orbits, with friction arising from an imbalance between particles that gain energy and those that lose energy. We treat dynamical friction in a spherical host system as a restricted three-body problem. This treatment is applicable in the “slow” regime, in which the perturber sinks slowly and the standard perturbative framework fails due to the onset of nonlinearities. Hence, it is especially suited to investigate the origin of core-stalling: the cessation of dynamical friction in central constant-density cores. We identify three different families of near-corotation-resonant orbits that dominate the contribution to dynamical friction. Their relative contribution is governed by the Lagrange points (fixed points in the corotating frame). In particular, one of the three families, which we call Pac-Man orbits because of their appearance in the corotating frame, is unique to cored density distributions. When the perturber reaches a central core, a bifurcation of the Lagrange points drastically changes the orbital makeup, with Pac-Man orbits becoming dominant. In addition, due to relatively small gradients in the distribution function inside a core, the net torque from these Pac-Man orbits becomes positive (enhancing), thereby effectuating a dynamical buoyancy. We argue that core-stalling occurs where this buoyancy is balanced by friction.