The emptiness of voids: yet another overabundance problem for the Λ cold dark matter model

Abstract

We study the luminosity function, the peculiar velocities and the sizes of voids in the Local Volume (LV) in observational samples of galaxies which contain galaxies down to M B = ― 10 and to M B = ―12 within the distance 4-8 Mpc. When we compare the results with the predictions of the standard cosmological λ cold dark matter (ACDM) model, we find that the theory faces a sever problem: it predicts a factor of 10 more dwarf haloes as compared with the observed number of dwarf galaxies. In the LV, we identify voids with sizes ranging from 1 to 4.5 Mpc and compare the observational distribution of void sizes with the voids in very high-resolution simulations of the ACDM model with Wilkinson Microwave Anisotropy Probe 1(WMAP1) and WMAP3 parameters. The theoretical void function matches the observations remarkably well only if we use haloes with circular velocities V c larger than 40-45 km s -1 [M vir = (1-2) x 10 10 M ⊙ ] for models with σ 8 = 0.9 and V c > 35 km s -1 [M vir = (6-8) × 10 9 M ⊙ ] for σ 8 = 0.75. We exclude the possibility that in the ACDM model haloes with circular velocities <35 km s -1 can host galaxies as bright as M B = -12: there are too many small haloes in the ACDM model resulting in voids being too small as compared with the observations. The problem is that many of the observed dwarf galaxies have H I rotational velocities below 25 km s ―1 that strictly contradicts the ACDM predictions. Thus, the ACDM model faces the same overabundance problem, which it had with the number of satellites in the Local Group (LG). We also estimate the rms deviations from the Hubble flow σ H for galaxies at different distances from the LG and find that in most of our model LV candidates the rms peculiar velocities are consistent with observational values: σ H = 50 km s ―1 for distances less than 3 Mpc and σ H = 80 km s ―1 for distances less than 8 Mpc. At distances 4 (8) Mpc, the observed overdensities of galaxies are 3.5-5.5 (1.3-1.6) - significantly larger than typically assumed.