Spurious heating of stellar motions in simulated galactic disks by dark matter halo particles

Abstract

We use idealized N-body simulations of equilibrium stellar disks embedded within course-grained dark matter haloes to study the effects of spurious collisional heating on disk structure and kinematics. Collisional heating artificially increases the vertical and radial velocity dispersions of disk stars, as well as the thickness and size of disks; the effects are felt at all galacto-centric radii. The integrated effects of collisional heating are determined by the mass of dark matter halo particles (or equivalently, by the number of particles at fixed halo mass), their local density and characteristic velocity dispersion, but are largely insensitive to the stellar particle mass. The effects can therefore be reduced by increasing the mass resolution of dark matter in cosmological simulations, with limited benefits from increasing the baryonic (or stellar) mass resolution. We provide a simple empirical model that accurately captures the effects of spurious collisional heating on the structure and kinematics of simulated disks, and use it to assess the importance of disk heating for simulations of galaxy formation. We find that the majority of state-of-the-art zoom simulations, and a few of the highest-resolution, smallest-volume cosmological runs, are in principle able to resolve thin stellar disks in Milky Way-mass haloes, but most large-volume cosmological simulations cannot. For example, dark matter haloes resolved with fewer than $\approx 10^6$ particles will collisionally heat stars near the stellar half-mass radius such that their vertical velocity dispersion increases by $\gtrsim 10$ per cent of the halo's virial velocity in approximately one Hubble time.