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.
