The size and shape of voids in three-dimensional galaxy surveys

The sizes and shapes of voids in a galaxy survey depend not only on the physics of structure formation, but also on the sampling density of the survey and on the algorithm used to define voids. Using an N-body simulation with a tau CDM power spectrum, we study the properties of voids in samples with different number densities of galaxies, in both redshift space and real space. When voids are defined as totally empty regions of space, their characteristic volume is strongly dependent on sampling density; when they are defined as regions whose density is 0.2 times the mean galaxy density, the dependence is less strong. We compare two void-finding algorithms, one in which voids are nonoverlapping spheres, and one, based on the algorithm of Aikio & Mahonen, that does not predefine the shape of a void. Regardless of the algorithm chosen, the characteristic void size is larger in redshift space than in real space, and is larger for low sampling densities than for high sampling densities. We define an elongation statistic Q that measures the tendency of voids to be stretched or squashed along the line of sight. Using this statistic, we find that at sufficiently high sampling densities (comparable to the number density of L > L-* galaxies), large voids tend to be slightly elongated along the line of sight in redshift space.