The 2dF galaxy redshift survey: Voids and hierarchical scaling models

We measure the redshift-space reduced void probability function (VPF) for 2dFGRS volume-limited galaxy samples covering the absolute magnitude range MbJ -5log10 h = -18 to -22. Theoretically, the VPF connects the distribution of voids to the moments of galaxy clustering of all orders, and can be used to discriminate clustering models in the weakly nonlinear regime. The reduced VPF measured from the 2dFGRS is in excellent agreement with the paradigm of hierarchical scaling of the galaxy clustering moments. The accuracy of our measurement is such that we can rule out, at a very high significance, popular models for galaxy clustering, including the lognormal distribution. We demonstrate that the negative binomial model gives a very good approximation to the 2dFGRS data over a wide range of scales, out to at least 20 h-1 Mpc. Conversely, the reduced VPF for dark matter in a A cold dark matter ( ACDM) universe does appear to be lognormal on small scales but deviates significantly beyond ∼4 h-1 Mpc. We find little dependence of the 2dFGRS reduced VPF on galaxy luminosity. Our results hold independently in both the North and South Galactic Pole survey regions.