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.
