The Effect of Nearby Voids on Galaxy Number Counts

The size, shape and degree of emptiness of void interiors sheds light on the details of galaxy formation. A particularly interesting question is whether void interiors are completely empty or contain a dwarf population. However the nearby voids that are most conducive for dwarf searches have large angular diameters, on the order of a steradian, making it difficult to redshift-map a statistically significant portion of their volume to the magnitude limit of dwarf galaxies. As part of addressing this problem, we investigate here the usefulness of number counts in establishing the best locations to search inside nearby (d < 300 Mpc) galaxy voids, utilizing Wolf plots of log(n < m) vs. m as the basic diagnostic. To illustrate expected signatures, we consider the signature of three void profiles, "cut out", "built up", and "universal profile" carved into Monte-Carlo Schechter function models. We then investigate the signatures of voids in the Millennium Run dark matter simulation and the Sloan Digital Sky Survey. We find in all of these the evidence for cut-out and built-up voids is most discernible when the void diameter is similar to the distance to its center. However the density distribution of the universal profile that is characteristic of actual voids is essentially undetectable at any distance. A useful corollary of this finding is that galaxy counts are a reliable measure of survey completeness and stellar contamination even when sampling through significant voids.