The nature of voids: II. Tracing underdensities with biased galaxies

We study how the properties of cosmic voids depend on those of the tracer galaxy populations in which they are identified. We use a suite of halo occupation distribution (HOD) mocks in a simulation, identify voids in these populations using the ZOBOV void finder and measure their abundances, sizes, tracer densities, and dark matter content. To separate the effects of bias from those of sampling density, we do the same for voids traced by randomly down-sampled subsets of the simulation dark matter particles. At the same sampling density, galaxy bias reduces the total number of voids by ~50% and can dramatically change their size distribution. The matter content of voids in biased and unbiased tracers also differs. Deducing void properties from simulation therefore requires the use of realistic galaxy mocks. We discuss how the void observables can be related to their matter content. In particular we consider the compensation of the total mass deficit in voids and find that the distinction between over- and under-compensated voids is not a function of void size alone, as has previously been suggested. However, we find a simple linear relationship between the average density of tracers in the void and the total mass compensation on much larger scales. The existence of this linear relationship holds independent of the bias and sampling density of the tracers. This provides a universal tool to classify void environments and will be important for the use of voids in observational cosmology.