  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.

Astrophysics of Galaxies