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 phy sics 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 sp ace. When voids are defined as totally empty regions of space, their charac teristic volume is strongly dependent on sampling density; when they are de fined as regions whose density is 0.2 times the mean galaxy density, the de pendence is less strong. We compare two void-finding algorithms, one in whi ch voids are nonoverlapping spheres, and one, based on the algorithm of Aik io & Mahonen, that does not predefine the shape of a void. Regardless of th e algorithm chosen, the characteristic void size is larger in redshift spac e than in real space, and is larger for low sampling densities than for hig h sampling densities. We define an elongation statistic Q that measures the tendency of voids to be stretched or squashed along the line of sight. Usi ng this statistic, we find that at sufficiently high sampling densities (co mparable to the number density of L > L-* galaxies), large voids tend to be slightly elongated along the line of sight in redshift space.