The challenge of large and empty voids in the SDSS DR7 redshift survey

We present catalogues of voids for the SDSS DR7 redshift survey and for Millennium I simulation mock data. We aim to compare the observations with simulations based on a $\Lambda$CDM model and a semi-analytic galaxy formation model. We use the void statistics as a test for these models. We assembled a mock catalogue that closely resembles the SDSS DR7 catalogue and carried out a parallel statistical analysis of the observed and simulated catalogue. We find that in the observation and the simulation, voids tend to be equally spherical. The total volume occupied by the voids and their total number are slightly larger in the simulation than in the observation. We find that large voids are less abundant in the simulation and the total luminosity of the galaxies contained in a void with a given radius is higher on average than observed by SDSS DR7 survey. We expect these discrepancies to be even more significant in reality than found here since the present value of $\sigma_8$ given by WMAP7 is lower than the value of 0.9 used in the Millennium I simulation. The reason why the simulation fails to produce enough large and dark voids might be the failure of certain semi-analytic galaxy formation models to reduce the small-scale power of $\Lambda$CDM and to produce sufficient power on large scales.