Dust dynamics in RAMSES -- II. Equilibrium drift velocity distributions of charged dust grains

TL;DR

This study models the equilibrium drift velocities of charged dust grains in MHD turbulence, revealing how grain size and charge-to-mass ratio influence their velocity distributions, with implications for astrophysical processes.

Contribution

It provides new quantitative insights into dust grain drift velocities in turbulence, combining simulations with analytic models to understand their dependence on physical parameters.

Findings

Root-mean-square drift velocity scales with grain size as a power law.

Distribution shape depends strongly on charge-to-mass ratio.

At 1 parsec in cold neutral medium, 0.1 μm grains drift at about 40% of turbulent velocity.

Abstract

We investigate the gas-grain relative drift velocity distributions of charged astrophysical dust grains in MHD turbulence. We do this using a range of MHD-PIC simulations spanning different plasma-$\beta$, sonic/Alfv\'en Mach number, and with grains of varying size and charge-to-mass ratio. We find that the root-mean-square drift velocity is a strong function of the grain size, following a power law with a 1/2 slope. The r.m.s. value has only a very weak dependence on the charge-to-mass ratio. On the other hand, the shape of the distribution is a strong function of the grain charge-to-mass ratio, and in compressible turbulence, also the grain size. We then compare these results to simple analytic models based upon time-domain quasi-linear theory and solutions to the Fokker-Planck equation. These models explain qualitatively the r.m.s. drift velocity's lack of charge-to-mass ratio dependence, as well as why the shape of the distribution changes as the charge-to-mass ratio increases. Finally we scale our results to astrophysical conditions. As an example, at a length scale of one parsec in the cold neutral medium, 0.1 $\mu$m grains should be drifting at roughly 40% of the turbulent velocity dispersion. These findings may serve as a basis for a model for grain velocities in the context of grain-grain collisions, non-thermal sputtering, and accretion of metals. These findings also have implications for the transport of grains through the galaxy, suggesting that grains may have non-negligible random motions at length-scales that many modern galaxy simulations approach.