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.
