Mock halo catalogs: 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 are embedded in dark matter halos, an
important first step is to include such correlations -- sometimes called
assembly bias -- for dark matter halos. However, galaxy properties correlate
with smaller scale physics in halos which large simulations struggle to
resolve. We describe an algorithm which 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 $\alpha$ are preserved. Therefore, knowledge of $\alpha$ is
sufficient to assign small-scale, otherwise unresolved properties to a halo in
a way which preserves its large-scale assembly bias accurately. We demonstrate
this explicitly for halo internal properties like formation history
(concentration $c_{\rm 200b}$), shape $c/a$, dynamics $c_{v}/a_{v}$, velocity
anisotropy $\beta$ and angular momentum (spin $\lambda$). 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% for 30-particle
halos, thus significantly reducing the cost of mocks for future weak lensing
and redshift space distortion studies.
