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

Large-scale sky surveys require companion large volume simulated mock catalogues. 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 are embedded in dark matter haloes, an important first step is to include such correlations - sometimes called assembly bias - for dark matter haloes. However, galaxy properties correlate with smaller scale physics in haloes which large simulations struggle to resolve. We describe an algorithm that addresses and largely mitigates this problem. Our algorithm exploits the fact that halo assembly bias is unchanged as long as correlations between halo property c and the intermediate-scale tidal environment α are preserved. Therefore, knowledge of α is sufficient to assign small-scale, otherwise unresolved properties to a halo in a way that preserves its large-scale assembly bias accurately. We demonstrate this explicitly for halo internal properties like formation history (concentration c_200b), shape c/a, dynamics c_v/a_v, velocity anisotropy β, and angular momentum (spin λ). Our algorithm increases a simulation's reach in halo mass and number density by an order of magnitude, with improvements in the bias signal as large as 45 per cent for 30-particle haloes, thus significantly reducing the cost of mocks for future weak lensing and redshift space distortion studies.