Galactic Bar Resonances with Diffusion: An Analytic Model with Implications for Bar–Dark Matter Halo Dynamical Friction

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 that 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 Δ, and then apply our theory to the calculation of bar–halo dynamical friction. For Δ = 0, we recover the classic result of Tremaine and Weinberg that friction ultimately vanishes, owing to the phase mixing of resonant orbits. However, for Δ > 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.

Orbital Support and Evolution of Flat Profiles of Bars (Shoulders)

“…The pattern speeds are shown in Figure 2 (bottom panel) as functions of time. As often observed in simulations (e.g., Hernquist & Weinberg 1992;Debattista & Sellwood 1998;O'Neill & Dubinski 2003;Athanassoula 2003), the bars slow down significantly over the time span of the simulation-see also Fragkoudi et al (2021) for a recent study of cosmological simulations and Hamilton et al (2023) for a recent theoretical treatment.…”

Stream Fanning and Bifurcations: Observable Signatures of Resonances in Stellar Stream Morphology

“…Various perturbers can kick individual stars, groups of stars, or even an entire stellar stream to a different orbit. In the Galactic disk, this may lead to a suppression of resonant effects similar to the ones discussed here, as shown for bar resonances in Hamilton et al (2023). The quantity of interest for estimating the importance of diffusion for streams on the halo orbits discussed in this work is the ratio of the libration time and the time it takes to diffuse across the width of the resonance:…”

“…Studying the behavior of streams on near-resonant orbits in the presence of effects that may disrupt the delicate balance that leads to secular dynamical effects would therefore serve as an important supplement to these results. Such effects include global evolution of the Galactic potential (see, e.g., Vasiliev et al 2021;Garavito-Camargo et al 2021), which may either displace a stream or cause resonances to shift around in phase space, and the influence of diffusive processes, which add a degree of stochasticity to the otherwise regular orbits in the potentials studied here and can thus cause orbits to move into and out of resonantly trapped regions (Hamilton et al 2023).…”

“…We note, however, that even when Δ ∼ 0.1, diffusion can lead to considerable deviations from the collisionless limit, as shown inHamilton et al (2023). To truly address this question, it would be worthwhile to carefully model the evolution of streams near a separatrix in the presence of "realistic" diffusion, something that is beyond the scope of this work.…”

Trojan Globular Clusters: Radial Migration via Trapping in Bar Resonances

“…A rotating bar is expected to decelerate with time due to dynamical friction (DF) with the dark matter halo (Debattista & Sellwood 1998;Athanassoula 2002;Weinberg & Katz 2002;Ceverino & Klypin 2007;Collier et al 2019;Chiba & Schönrich 2022;Hamilton et al 2023) A bar with a decelerating pattern speed can drag particles trapped in its resonances, transporting them to higher energies and angular momenta . The Galactic bar is therefore endowed with the ability to reshape the distribution of particles in integral-of-motion space.…”