The nature of voids - I. Watershed void finders and their connection with theoretical models

The statistical study of voids in the matter distribution promises to be an important tool for precision cosmology, but there are known discrepancies between theoretical models of voids and the voids actually found in large simulations or galaxy surveys. The empirical properties of observed voids are also not well understood. In this paper, we study voids in an N-body simulation, using the ZOBOV watershed algorithm. As in other studies, we use sets of subsampled dark matter particles as tracers to identify voids, but we use the full-resolution simulation output to measure dark matter densities at the identified locations. Voids span a wide range of sizes and densities, but there is a clear trend towards larger voids containing deeper density minima, a trend which is expected for all watershed void finders. We also find that the tracer density at void locations is usually smaller than the true density, and that this relationship depends on the sampling density of tracers. We show that fits given in the literature fail to match the observed density profiles of voids. The average enclosed density contrast within watershed voids varies widely with both the size of the void and the minimum density within it, but is always far from the shell-crossing threshold expected from theoretical models. Voids with deeper density minima also show much broader density profiles. We discuss the implications of these results for the excursion set approach to modelling such voids.