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

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 (ΛCDM) 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 4.5Mpc and compare the observational distribution of void sizes with the voids in very high-resolution simulations of the ΛCDM 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 40-45km s^-1 [M_vir = (1-2) × 10¹⁰M_solar] for models with σ₈ = 0.9 and V_c > 35kms^-1 [M_vir = (6-8) × 10⁹M_solar] for σ₈ = 0.75. We exclude the possibility that in the ΛCDM model haloes with circular velocities <35kms^-1 can host galaxies as bright as M_B = -12: there are too many small haloes in the ΛCDM model resulting in voids being too small as compared with the observations. The problem is that many of the observed dwarf galaxies have HI rotational velocities below 25km s^-1 that strictly contradicts the ΛCDM predictions. Thus, the ΛCDM 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 = 50kms^-1 for distances less than 3Mpc and σ_H = 80kms^-1 for distances less than 8Mpc. At distances 4 (8) Mpc, the observed overdensities of galaxies are 3.5-5.5 (1.3-1.6) - significantly larger than typically assumed.