Galactic bar resonances with diffusion: an analytic model with implications for bar-dark matter halo dynamical friction

TL;DR

This paper develops an analytic kinetic model to understand how diffusion affects resonant interactions between galactic bars and dark matter halos, revealing that stochasticity can sustain dynamical friction contrary to classical expectations.

Contribution

It introduces a simple kinetic equation incorporating diffusion for particles near a resonance, extending traditional models to include stochastic effects and applying it to bar-halo dynamical friction.

Findings

Diffusion suppresses phase-mixing, resulting in a finite torque.

Stochasticity increases bar-halo friction, even with long relaxation times.

Artificial diffusion in simulations can cause significant bar slowdown.

Abstract

The secular evolution of disk galaxies is largely driven by resonances between the orbits of 'particles' (stars or dark matter) and the rotation of non-axisymmetric features (spiral arms or a bar). Such resonances may also explain kinematic and photometric features observed in the Milky Way and external galaxies. In simplified cases, these resonant interactions are well understood: for instance, the dynamics of a test particle trapped near a resonance of a steadily rotating bar is easily analyzed using the angle-action tools pioneered by Binney, Monari and others. However, such treatments do not address the stochasticity and messiness inherent to real galaxies - effects which have, with few exceptions, been previously explored only with complex N-body simulations. In this paper, we propose a simple kinetic equation describing the distribution function of particles near an orbital resonance with a rigidly rotating bar, allowing for diffusion of the particles' slow actions. We solve this equation for various values of the dimensionless diffusion strength $\Delta$, and then apply our theory to the calculation of bar-halo dynamical friction. For $\Delta = 0$ we recover the classic result of Tremaine & Weinberg that friction ultimately vanishes, owing to the phase-mixing of resonant orbits. However, for $\Delta > 0$ we find that diffusion suppresses phase-mixing, leading to a finite torque. Our results suggest that stochasticity - be it physical or numerical - tends to increase bar-halo friction, and that bars in cosmological simulations might experience significant artificial slowdown, even if the numerical two-body relaxation time is much longer than a Hubble time.