  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
CDM power spectrum, we study the properties of voids in samples with different
number densities of galaxies, both in redshift space and in real space. When
voids are defined as regions totally empty of galaxies, 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 and Mahonen,
which 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 which 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 densities of galaxies brighter than L_*), large voids tend to be
slightly elongated along the line of sight in redshift space.

Astrophysics