Voids in real space and in redshift space

Before using void statistics to compare simulations with redshift surveys, it is best to understand the behavior of the statistics as a function of the density fluctuation power spectrum and in the transformation from real space to redshift space. This is most efficiently accomplished by using two-dimensional numerical simulations of gravitational clustering, with initial power spectra of the form P(k) proportional to k(n). We compare the properties of voids in real space to their properties in redshift space. Both the void probability function (VPF) and the underdense probability function (UPF) are enhanced in redshift space. The enhancement is greatest in the limit n = -2. The VPF and UPF treat voids statistically and assume that two-dimensional voids are circular; we present an algorithm that detects individual voids. Voids found by this algorithm are ellipses whose enclosed density of galaxies falls below a threshold density. When voids are identified using this algorithm, the mean void size and the maximum void size both increase in going from real space to redshift space. The increase is greatest in the limit n = -2. In redshift space, the principal axes of the largest voids in the n = 2 and n = 0 simulations show a statistically significant tendency (at the 95% confidence level) to be distributed anisotropically, relative to the line of sight from the origin to the void center.