Voids in the Two-Degree Field Galaxy Redshift Survey

We present an analysis of voids in the 2dF Galaxy Redshift Survey (2dFGRS). This analysis includes identification of void regions and measurement of void statistics. The 2dFGRS is the largest completed redshift survey to date, including a total of 245,591 galaxies covering 1500 deg² to a median depth of z_med ~ 0.11. We use the voidfinder algorithm to identify a total of 289 voids in the 2dFGRS with radius larger than 10 h^-1 Mpc. These voids have an average effective radius, the radius of a sphere with the same volume as the void, of h^-1 Mpc in the North Galactic Pole region (NGP) and h^-1 Mpc in the South Galactic Pole region (SGP). These voids are extremely underdense, with average density contrast of δρ/ρ = -0.94 ± 0.02. The centers of voids are even emptier, because the few galaxies within the voids typically lie close to the edges. The total volume of the universe filled by these void regions is approximately 40%. These results are very similar to results found from our analysis of the PSCz survey and the Updated Zwicky Catalog; here we detect almost a factor of 10 more voids. We measure the void probability function (VPF) of the 2dFGRS for volume-limited samples with limiting absolute magnitudes, M_lim - 5 log h, from -16 to -21 in b_J. We measure the underdensity probability function (with density contrast threshold δρ/ρ = -0.8) for samples with limiting absolute magnitudes, M_lim - 5 log h, from -18 to -21. We find that the SGP is more underdense than the NGP for all but the brightest sample under consideration. There is good agreement between the VPFs of the Center for Astrophysics survey and the 2dFGRS. Comparison of VPFs measured for the 2dFGRS with the distribution of simulated dark matter halos of similar number density indicates that voids in the matter distribution in ΛCDM simulations are not empty enough. However, semianalytic models of galaxy formation that include feedback effects yield VPFs that show excellent agreement with the data.