Void scaling and void profiles in cold dark matter models

An analysis of voids using cosmological N-body simulations of cold dark matter (CDM) models is presented. We use a robust void statistic, that was recently applied to discriminate between data from the Las Campanas Redshift Survey (LCRS) and different cosmological models. Here we extend the analysis to three dimensions and show that typical void sizes D in the simulated galaxy samples obey a linear scaling relation with the mean galaxy separation λ:D=D0+ν×λ. It has the same slope ν as in two dimensions, but with lower absolute void sizes. The scaling relation is able to discriminate between different cosmologies. For the best standard ΛCDM model, the slope of the scaling relation for voids in the dark matter haloes is too steep compared with the LCRS, with too small void sizes for well-sampled data sets. By considering a range of CDM simulations we further investigate the scaling relation for voids within the distribution of dark matter haloes and other properties of underdense regions. The scaling relation of voids for dark matter haloes with increasing mass thresholds is even steeper than that for samples of galaxy-mass haloes where we sparsely sample the data. This shows the stronger clustering of more massive haloes. Further, we find a correlation of the void size to its central and environmental average density. We study the evolution of the void size distribution of dark matter haloes at redshifts up to z=3 measuring the sizes in comoving coordinates. While there is little sign of evolution in samples of small DM haloes with vcirc≈90 km s−1, voids in haloes with circular velocity over vcirc=200 km s−1 are larger at redshift z=3 owing to the smaller halo number density. The flow of dark matter from the underdense to overdense regions in an early established network of large-scale structure is also imprinted in the evolution of the density profiles with a relative density decrease in void centres by Δ(ρ/ρ)≃0.18 per redshift unit between z=3 and 0.