The DEEP2 Galaxy Redshift Survey: The Evolution of Void Statistics fromz∼ 1 toz∼ 0

We present measurements of the void probability function (VPF) at z~1 usingdata from the DEEP2 Redshift Survey and its evolution to z~0 using data fromthe Sloan Digital Sky Survey (SDSS). We measure the VPF as a function of galaxycolor and luminosity in both surveys and find that it mimics trends displayedin the two-point correlation function, $\xi$; namely that samples of brighter,red galaxies have larger voids (i.e. are more strongly clustered) than fainter,blue galaxies. We also clearly detect evolution in the VPF with cosmic time,with voids being larger in comoving units at z~0. We find that the reduced VPFmatches the predictions of a `negative binomial' model for galaxies of allcolors, luminosities, and redshifts studied. This model lacks a physicalmotivation, but produces a simple analytic prediction for sources of any numberdensity and integrated two-point correlation function, \bar{\xi}. This impliesthat differences in the VPF across different galaxy populations are consistentwith being due entirely to differences in the population number density and\bar{\xi}. The robust result that all galaxy populations follow the negativebinomial model appears to be due to primarily to the clustering of dark matterhalos. The reduced VPF is insensitive to changes in the parameters of the halooccupation distribution, in the sense that halo models with the same \bar{\xi}will produce the same VPF. For the wide range of galaxies studied, the VPFtherefore does not appear to provide useful constraints on galaxy evolutionmodels that cannot be gleaned from studies of \bar{\xi} alone. (abridged)Comment: 17 pages, 15 figures, ApJ accepte