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The stacked density profile of cosmic voids in the galaxy distributionprovides an important tool for the use of voids for precision cosmology. Westudy the density profiles of voids identified using the ZOBOV watershedtransform algorithm in realistic mock luminous red galaxy (LRG) catalogues fromthe Jubilee simulation, as well as in void catalogues constructed from the SDSSLRG and Main Galaxy samples. We compare different methods for reconstructingdensity profiles scaled by the void radius and show that the most commonly usedmethod based on counts in shells and simple averaging is statistically flawedas it underestimates the density in void interiors. We provide two alternativemethods that do not suffer from this effect; one based on Voronoi tessellationsis also easily able to account from artefacts due to finite survey boundariesand so is more suitable when comparing simulation data to observation. Usingthis method we show that voids in simulation are exactly self-similar, meaningthat their average rescaled profile does not depend on the void size. Withinthe range of our simulation we also find no redshift dependence of the profile.Comparison of the profiles obtained from simulated and real voids shows anexcellent match. The profiles of real voids also show a universal behaviourover a wide range of galaxy luminosities, number densities and redshifts. Thispoints to a fundamental property of the voids found by the watershed algorithm,which can be exploited in future studies of voids.

Self-similarity and universality of void density profiles in simulation and SDSS data