The sparkling Universe: Clustering of voids and void clumps
  We analyse the clustering of cosmic voids using a numerical simulation and
the main galaxy sample from the Sloan Digital Sky Survey. We take into account
the classification of voids into two types that resemble different evolutionary
modes: those with a rising integrated density profile (void-in-void mode, or
R-type) and voids with shells (void-in-cloud mode, or S-type). The results show
that voids of the same type have stronger clustering than the full sample. We
use the correlation analysis to define void clumps, associations with at least
two voids separated by a distance of at most the mean void separation. In order
to study the spatial configuration of void clumps, we compute the minimal
spanning tree and analyse their multiplicity, maximum length and elongation
parameter. We further study the dynamics of the smaller sphere that encloses
all the voids in each clump. Although the global densities of void clumps are
different according to their member-void types, the bulk motions of these
spheres are remarkably lower than those of randomly placed spheres with the
same radii distribution. In addition, the coherence of pairwise void motions
does not strongly depend on whether voids belong to the same clump. Void clumps
are useful to analyse the large-scale flows around voids, since voids embedded
in large underdense regions are mostly in the void-in-void regime, were the
expansion of the larger region produces the separation of voids. Similarly,
voids around overdense regions form clumps that are in collapse, as reflected
in the relative velocities of voids that are mostly approaching.
