We study the statistical properties of voids in the distribution of mass, dark‐matter haloes and galaxies (BJ < −16) in a Λ cold dark matter (ΛCDM) numerical simulation populated with galaxies using a semi‐analytic galaxy formation model (GALFORM, Cole et al.). We find that the properties of voids selected from GALFORM galaxies are compatible with those of voids identified from a population of haloes with mass M > 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 v max)=(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.

Using the redshift-space distortions of void-galaxy cross-correlation function we analyse the dynamics of voids embedded in different environments. We compute the void-galaxy crosscorrelation function in the Sloan Digital Sky Survey (SDSS) in terms of distances taken along the line of sight and projected into the sky. We analyse the distortions on the cross-correlation isodensity levels and we find anisotropic isocontours consistent with expansion for large voids with smoothly rising density profiles and collapse for small voids with overdense shells surrounding them. Based on the linear approach of gravitational collapse theory we developed a parametric model of the void-galaxy redshift space cross-correlation function. We show that this model can be used to successfully recover the underlying velocity and density profiles of voids from redshift space samples. By applying this technique to real data, we confirm the twofold nature of void dynamics: large voids typically are in an expansion phase whereas small voids tend to be surrounded by overdense and collapsing regions. These results are obtained from the SDSS spectroscopic galaxy catalogue and also from semi-analytic mock galaxy catalogues, thus supporting the viability of the standard ΛCDM model to reproduce large scale structure and dynamics.

We perform a statistical study focused on void environments. We examine galaxy density profiles around voids in the SDSS, finding a correlation between void-centric distance to the shell of maximum density and void radius when a maximum in overdensity exists. We analyze voids with and without a surrounding over-dense shell in the SDSS. We find that small voids are more frequently surrounded by over-dense shells whereas the radial galaxy density profile of large voids tends to rise smoothly towards the mean galaxy density. We analyse the fraction of voids surrounded by overdense shells finding a continuous trend with void radius. The differences between voids with and without an overdense shell around them can be understood in terms of whether the voids are, on average, in the process of collapsing or continuing their expansion, respectively, in agreement with previous theoretical expectations. We use numerical simulations coupled to semi-analytic models of galaxy formation in order to test and interpret our results. The very good agreement between the mock catalog results and the observations provides additional support to the viability of a ΛCDM model to reproduce the large scale structure of the universe as defined by the void network, in a way which has not been analysed previously.

We perform a statistical study on the distribution and dynamics of voids in the 2dF Galaxy Redshift Survey (2dFGRS). Our statistics are tested and calibrated using mock 2dFGRS catalogues. We analyse the dynamics around voids in mock and real 2dFGRS surveys. The void–galaxy cross‐correlation redshift‐space distortions show evidence of the continuing growth of voids, confirming another prediction of the hierarchical clustering scenario. A non‐linear outflow model can be used to provide quantitative estimates of the outflow velocities around 2dFGRS voids. These results are consistent with maximum outflows of 110, 210 and 270 km s−1 for voids of 〈rvoid〉= 7.5, 12.5 and 17.5 Mpc h−1, assuming a galaxy bias of b= 1. As an application for future surveys, our study of the mock catalogues shows that direct measurements of the expansion of voids can be obtained using peculiar velocity data. We find that it would also be possible to detect differences in the velocity dispersion of galaxies in the directions parallel and perpendicular to the void walls.

We perform a statistical study of the characteristics of galaxies in voids and void walls in the SDSS and 2dFGRS catalogues. We investigate dependencies of the distribution of galaxy spectral types and colours as a function of the relative position to the void centres for different luminosity and local density ranges. We find a trend towards bluer, star forming galaxies in void walls beyond the local density dependence. These results indicate that luminosity and local density do not entirely determine the distribution of galaxy properties such as colours and spectral types, and point towards a large scale modulation of star formation. We argue that this effect is due to the lower accretion and merger history of galaxies arriving at void walls from the emptier inner void regions.Comment: 5 pages, 6 figures, submitted to MRNAS Letter

Inspired on the well known dynamical dichotomy predicted in voids, where some underdense regions expand whereas others collapse due to overdense surrounding regions, we explored the interplay between the void inner dynamics and its large scale environment. The environment is classified depending on its density as in previous works. We analyse the dynamical properties of void-centered spherical shells at different void-centric distances depending on this classification. The above dynamical properties are given by the angular distribution of the radial velocity field, its smoothness, the field dependence on the tracer density and shape, and the field departures from linear theory. We found that the velocity field in expanding voids follows more closely the linear prediction, with a more smooth velocity field. However when using velocity tracers with large densities such deviations increase. Voids with sizes around 18hMpc are in a transition regime between regions with expansion overpredicted and underpredicted from linear theory. We also found that velocity smoothness increases as the void radius, indicating the laminar flow dominates the expansion of larger voids (more than 18hMpc). The correlations observed suggest that nonlinear dynamics of the inner regions of voids could be dependent on the evolution of the surrounding structures. These also indicate possible scale couplings between the void inner expansion and the large scale regions where voids are embedded. These results shed some light to the origin of nonlinearities in voids, going beyond the fact that voids just quickly becomes nonlinear as they become emptier.

We compute the bulk motions of cosmic voids, using a ΛCDM numerical simulation considering the mean velocities of the dark matter inside the void itself and that of the haloes in the surrounding shell. We find coincident values of these two measures in the range ∼ 300-400 km s −1 , not far from the expected mean peculiar velocities of groups and galaxy clusters. When analysing the distribution of the pairwise relative velocities of voids, we find a remarkable bimodal behaviour consistent with an excess of both systematically approaching and receding voids. We determine that the origin of this bimodality resides in the void large scale environment, since once voids are classified into void-in-void (R-type) or void-in-cloud (S-type), R-types are found mutually receding away, while S-types approach each other. The magnitude of these systematic relative velocities account for more than 100 km s −1 , reaching large coherence lengths of up to 200 h −1 Mpc . We have used samples of voids from the Sloan Digital Sky Survey Data Release 7 (SDSS-DR7) and the peculiar velocity field inferred from linear theory, finding fully consistent results with the simulation predictions. Thus, their relative motion suggests a scenario of a sparkling Universe, with approaching and receding voids according to their local environment.

Cosmic voids are prominent features of the Universe, encoding relevant information of the growth and evolution of structure through their dynamics. Here, we perform a statistical study of the global motion of cosmic voids using both a numerical simulation and observational data. Their relation to large-scale mass flows and the physical effects that drive those motions. We analyse the bulk motions of voids, finding void mean bulk velocities in the range 300 to 400 km s −1 , depending on void size and the large-scale environment. Statistically, small voids move faster, and voids in relatively higher density environments have higher bulk velocities. Also, we find large-scale overdensities (underdensities) along (opposite to) the void motion direction, suggesting that void motions respond to a pull-push mechanism. Our analysis suggests that their relative motions are generated by large-scale density fluctuations. In agreement with linear theory, voids embedded in low (high) density regions mutually recede (attract) each other, providing the general mechanism to understand the bimodal behavior of void motions. We have also inferred void motions in the Sloan Digital Sky Survey using linear theory, finding that their estimated motions are in qualitatively agreement with the results of the simulation. Our results suggest a scenario of galaxies and galaxy systems flowing away from void centers with the additional, and more relevant, contribution of the void bulk motion to the total velocity.