Sizes of voids as a test for dark matter models

Abstract

We use the void probability function (VPF) to study the distribution of galaxies in a volume{limited subsample of the Perseus{Pisces survey. We compare observational results with theoretical predictions based on high{resolution N{body simulations for two realizations of the Cold+Hot Dark Matter (CHDM) model and for unbiased (b = 1) and biased (b = 1:5) CDM models in a 50 h 1Mpc box. We identify galaxies as peaks of the evolved density eld. Overmerged structures are fragmented into individual galaxies so as to reproduce both the correct luminosity function (after assuming M=L values for the resulting galaxy groups) and the two{point correlation function. We also try to reproduce the observational biases of the observational data as best as we can. Our main result is that on intermediate 2 8h 1Mpc scales the void{probability function for the standard CHDM model with cold= hot= bar = 0:6=0:3=0:1 exceeds the observational VPF with a high con dence level. CDM models produce smaller VPF, whose shape is independent of the biasing parameter. We verify the robustness of this result against changing the observer position in the simulations and the threshold for galaxy identi cation.