Mock halo catalogues: assigning unresolved halo properties using correlations with local halo environment

Large-scale sky surveys require companion large volume simulated mock catalogs. To ensure precision cosmology studies are unbiased, the correlations in these mocks between galaxy properties and their large-scale environments must be realistic. Since galaxies embedded dark matter halos, an important first step is to include such -- sometimes called assembly bias for halos. However, correlate with smaller scale physics halos which simulations struggle resolve. We describe algorithm addresses largely mitigates this problem. Our exploits fact that halo unchanged as long property $c$ intermediate-scale tidal environment $\alpha$ preserved. Therefore, knowledge of sufficient assign small-scale, otherwise unresolved a way preserves its accurately. demonstrate explicitly internal like formation history (concentration $c_{\rm 200b}$), shape $c/a$, dynamics $c_{v}/a_{v}$, velocity anisotropy $\beta$ angular momentum (spin $\lambda$). increases simulation's reach mass number density by order magnitude, improvements signal 45% 30-particle thus significantly reducing cost future weak lensing redshift space distortion studies.