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 haloes 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 haloes living in the most clustered regions have larger Lagrangian volumes. Nevertheless, selecting haloes to be isolated is not the best way to ensure inexpensive zoom simulations. We explain how one can safely choose haloes with the smallest Lagrangian volumes, which are the least expensive to resimulate, without biasing one's sample.