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

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.