The dark matter halo mass function in the $Λ\mathrm{CDM}$ cosmology at all times and over all scales -- from planetary to galaxy cluster masses

Abstract

The dark matter halo mass function is one of the most fundamental predictions of structure formation theory and cosmological simulations. We present the full halo mass function in the $Λ$ cold dark matter ($Λ\mathrm{CDM}$) model, ranging from a planetary mass ($10^{-6}\,\mathrm{M}_\odot$; the thermal cutoff in the initial power spectrum for a fiducial CDM particle mass of $100\,\mathrm{GeV}$) to the mass of a rich galaxy cluster ($10^{15.5}\,\mathrm{M}_\odot$), and from redshift, $z=30$ to the present. To span this very large dynamic range, we combine our earlier Voids-within-Voids-within-Voids (VVV) set of simulations (Wang et al) with large volume, lower resolution cosmological simulations. We develop a subsampling method to extract subvolumes from the original simulations, allowing us to reconstruct the global halo mass function from the biased underdense VVV regions. We show that the results agree reasonably well among the sets of simulations on different scales and environments. We provide a fitting formula for the dark matter halo mass function based on the work of Reed et al. calibrated with our simulations, such that it can be applied at all scales, all environments and all times, with deviations of $\sim2-3\%$ at $z < 2$ and $\sim 7\%$ at higher redshift $z \gtrsim 5$. This formula is also accurate at least for a restricted set of models we tested with modest deviations from $Λ\mathrm{CDM}$ in the values of some of the cosmological parameters. A python code is publicly available at https://github.com/haonan-zheng/hmfc.