VOIDS IN REAL-SPACE AND IN REDSHIFT SPACE

Before using void statistics to compare simulations with redshift surv eys, it is best to understand the behavior of the statistics as a func tion of the density fluctuation power spectrum and in the transformati on from real space to redshift space. This is most efficiently accompl ished by using two-dimensional numerical simulations of gravitational clustering, with initial power spectra of the form P(k) proportional t o k(n). We compare the properties of voids in real space to their prop erties in redshift space. Both the void probability function (VPF) and the underdense probability function (UPF) are enhanced in redshift sp ace. The enhancement is greatest in the limit n = -2. The VPF and UPF treat voids statistically and assume that two-dimensional voids are ci rcular; we present an algorithm that detects individual voids. Voids f ound 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 larg est voids in the n = 2 and n = 0 simulations show a statistically sign ificant tendency (at the 95% confidence level) to be distributed aniso tropically, relative to the line of sight from the origin to the void center.