How to Zoom: Bias, Contamination, and Lagrange Volumes in Multimass
  Cosmological Simulations
  We perform a suite of multimass cosmological zoom simulations of individual
dark matter halos and explore how to best select Lagrangian regions for
resimulation without contaminating the halo of interest with low-resolution
particles. Such contamination can lead to significant errors in the gas
distribution of hydrodynamical simulations, as we show. For a fixed Lagrange
volume, we find that the chance of contamination increases systematically with
the level of zoom. In order to avoid contamination, the Lagrangian volume
selected for resimulation must increase monotonically with the resolution
difference between parent box and the zoom region. We provide a simple formula
for selecting Lagrangian regions (in units of the halo virial volume) as a
function of the level of zoom required. We also explore the degree to which a
halo's Lagrangian volume correlates with other halo properties (concentration,
spin, formation time, shape, etc.) and find no significant correlation. There
is a mild correlation between Lagrange volume and environment, such that halos
living in the most clustered regions have larger Lagrangian volumes.
Nevertheless, selecting halos to be isolated is not the best way to ensure
inexpensive zoom simulations. We explain how one can safely choose halos with
the smallest Lagrangian volumes, which are the least expensive to resimulate,
without biasing one's sample.
