Self-similarity and universality of void density profiles in simulation
  and SDSS data
  The stacked density profile of cosmic voids in the galaxy distribution
provides an important tool for the use of voids for precision cosmology. We
study the density profiles of voids identified using the ZOBOV watershed
transform algorithm in realistic mock luminous red galaxy (LRG) catalogues from
the Jubilee simulation, as well as in void catalogues constructed from the SDSS
LRG and Main Galaxy samples. We compare different methods for reconstructing
density profiles scaled by the void radius and show that the most commonly used
method based on counts in shells and simple averaging is statistically flawed
as it underestimates the density in void interiors. We provide two alternative
methods that do not suffer from this effect; one based on Voronoi tessellations
is also easily able to account from artefacts due to finite survey boundaries
and so is more suitable when comparing simulation data to observation. Using
this method we show that voids in simulation are exactly self-similar, meaning
that their average rescaled profile does not depend on the void size. Within
the range of our simulation we also find no redshift dependence of the profile.
Comparison of the profiles obtained from simulated and real voids shows an
excellent match. The profiles of real voids also show a universal behaviour
over a wide range of galaxy luminosities, number densities and redshifts. This
points to a fundamental property of the voids found by the watershed algorithm,
which can be exploited in future studies of voids.
