Simulating the complexity of the dark matter sheet II: halo and subhalo mass functions for non-cold dark matter models

We present "sheet+release" simulations that reliably follow the evolution of dark matter structure at and below the dark matter free-streaming scale, where instabilities in traditional N-body simulations create a large population of spurious artificial haloes. Our simulations sample a large range of power-spectrum cutoff functions, parameterized through the half-mode scale $k_{\rm{hm}}$ and a slope parameter $\beta$. This parameter space can represent many non-cold dark matter models, including thermal relic warm dark matter, sterile-neutrinos, fuzzy dark matter, and a significant fraction of ETHOS models. Combining these simulations with additional N-body simulations, we find the following results. (1) Even after eliminating spurious haloes, the halo mass function in the strongly suppressed regime ($n_{\rm{X}}/n_{\rm{CDM}} < 5\%$) remains uncertain because it depends strongly on the definition of a halo. At these mass scales traditional halo finders primarily identify overdensities that are unbound, highly elongated, dominated by tidal fields, or far from virialized. (2) The regime where the suppression is smaller than a factor of 20 is quite robust to these uncertainties, however, and can be inferred reliably from suitable N-body simulations. (3) Parameterizing the suppression in the halo- and subhalo mass functions through the scales where the suppression reaches $20\%$, $50\%$ and $80\%$, we provide simple formulae which enable predictions for many non-cold dark matter models. (4) The halo mass-concentration relations in our sheet+release simulations agree well with previous results based on N-body simulations. (5) In general, we confirm the validity of previous N-body studies of warm dark matter models, largely eliminating concerns about the effects of artificial haloes.