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Density Wakes due to Dynamical Friction in Cored Potentials

Dynamical friction is often modeled with reasonable accuracy by the widely used Chandrasekhar formula. However, in some circumstances, Chandrasekhar's local and uniform approximations can break down severely. An astrophysically important example is the "core stalling" phenomenon seen in N-body simulations of massive perturber inspiralling into the near-harmonic potential of a stellar system's constant-density core (and possibly also in direct observations of dwarf galaxies with globular clusters). In this paper we use the linearized collisionless Boltzmann equation to calculate the global response of a cored galaxy to the presence of a massive perturber. We evaluate the density deformation, or wake, due to the perturber and study its geometrical structure to better understand the phenomenon of core stalling. We also evaluate the dynamical friction torque acting on perturber from the Lynden-Bell--Kalnajs (LBK) formula. In agreement with past work, we find that the dynamical friction force arising from corotating resonances is greatly weakened, relative to the Chandrasekhar formula, inside a constant density core. In contrast to past work, however, we find that a population of previously neglected high-order and non-corotating resonances sustain a minimum level of frictional torque at ~10 % of the torque from Chandrasekhar formula. This suggests that complete core stalling likely requires phenomena beyond the LBK approach; we discuss several possible explanations. Additionally, to study core stalling for multiple perturbers, we investigate approximate secular dynamical interactions (akin to Lidov-Kozai dynamics) between two perturbers orbiting a cored stellar system and derive a criterion for instability arising due to their close encounters.