Spatial and dynamical properties of voids in a Λ cold dark matter universe

We study the statistical properties of voids in the distribution of mass, dark-matter haloes and galaxies (BJ 1011.5 h−1 M⊙, similar to the median halo mass, Mmed= 1011.3 h−1 M⊙. We also find that the number density of galaxy- and halo-defined voids can be up to two orders of magnitude higher than mass-defined voids for large void radii, however, we observe that this difference is reduced to about half an order of magnitude when the positions are considered in redshift space. As expected, there are outflow velocities that show their maximum at larger void-centric distances for larger voids. We find a linear relation for the maximum outflow velocity, vmax=v0rvoid. The void-centric distance where this maximum occurs follows a suitable power-law fit of the form log(d)=(rvoid/A)B. At sufficiently large distances, we find mild infall motions on to the subdense regions. The galaxy velocity field around galaxy-defined voids is consistent with the results of haloes with masses above the median, showing milder outflows than the mass around mass-defined voids. We find that a similar analysis in redshift space would make both outflows and infalls appear with a lower amplitude. We also find that the velocity dispersion of galaxies and haloes is larger in the direction parallel to the void walls by ≃10–20 per cent. Given that voids are by definition subdense regions, the cross-correlation function between galaxy-defined voids and galaxies is close to ξ=−1 out to separations comparable to the void size, and at larger separations the correlation function level increases, approaching the values of the auto-correlation function of galaxies. The cross-correlation amplitude of mass-defined voids versus mass has a more gentle behaviour remaining negative at larger distances. The cross- to auto-correlation function ratio as a function of the distance normalized to the void radius shows a small scatter around a relation that depends only on the object used to define the voids (galaxies or haloes for instance). The distortion pattern observed in ξ(σ, π) is that of an elongation along the line of sight that extends out to large separations. Positive ξ contours evidence finger-of-god motions at the void walls. Elongations along the line of sight are roughly comparable between galaxy-, halo- and mass-defined voids.