Sparse sampling, galaxy bias, and voids

To study the impact of sparsity and galaxy bias on void statistics, we use a single large-volume, high-resolution N-body simulation to compare voids in multiple levels of subsampled dark matter, halo populations, and mock galaxies from a halo occupation distribution model tuned to different galaxy survey densities. We focus our comparison on three key observational statistics: number functions, ellipticity distributions, and radial density profiles. We use the hierarchical tree structure of voids to interpret the impacts of sampling density and galaxy bias, and theoretical and empirical functions to describe the statistics in all our sample populations. We are able to make simple adjustments to theoretical expectations to offer prescriptions for translating from analytics to the void properties measured in realistic observations. We find that sampling density has a much larger effect on void sizes than galaxy bias. At lower tracer density, small voids disappear and the remaining voids are larger, more spherical, and have slightly steeper profiles. When a proper lower mass threshold is chosen, voids in halo distributions largely mimic those found in galaxy populations, except for ellipticities, where galaxy bias leads to higher values. We use the void density profile of Hamaus et al. to show that voids follow a self-similar and universal trend, allowing simple translations between voids studied in dark matter and voids identified in galaxy surveys. We have added the mock void catalogues used in this work to the Public Cosmic Void Catalog at http://www.cosmicvoids.net.