Properties beyond mass for unresolved haloes across redshift and cosmology using correlations with local halo environment

Abstract: The structural and dynamic properties of the dark matter halos, though an important ingredient in understanding large-scale structure formation, require more conservative particle resolution than those required by halo mass alone in a simulation. This reduces the parameter space of the simulations, more severely for high-redshift and large-volume mocks which are required by the next-generation large sky surveys. Here, we incorporate redshift and cosmology dependence into an algorithm that assigns accurate halo properties such as concentration, spin, velocity, and spatial distribution to the sub-resolution haloes in a simulation. By focusing on getting the right correlations with halo mass and local tidal anisotropy $\alpha$ measured at $4 \times$ halo radius, our method will also recover the correlations of these small scale structural properties with the large-scale environment, i.e., the halo assembly bias at all scales greater than $5 \times$ halo radius. We find that the distribution of halo properties is universal with redshift and cosmology. By applying the algorithm to a large volume simulation $(600 h^{-1}{\rm Mpc})$, we can access the $30-500$ particle haloes, thus gaining an order of magnitude in halo mass and two to three orders of magnitude in number density at $z=2-4$. This technique reduces the cost of mocks required for the estimation of covariance matrices, weak lensing studies, or any large-scale clustering analysis with less massive haloes.