Multimodality of rich clusters from the SDSS DR8 within the
  supercluster-void network
  We study the relations between the multimodality of galaxy clusters drawn
from the SDSS DR8 and the environment where they reside. As cluster environment
we consider the global luminosity density field, supercluster membership, and
supercluster morphology. We use 3D normal mixture modelling, the
Dressler-Shectman test, and the peculiar velocity of cluster main galaxies as
signatures of multimodality of clusters. We calculate the luminosity density
field to study the environmental densities around clusters, and to find
superclusters where clusters reside. We determine the morphology of
superclusters with the Minkowski functionals and compare the properties of
clusters in superclusters of different morphology. We apply principal component
analysis to study the relations between the multimodality parametres of
clusters and their environment simultaneously. We find that multimodal clusters
reside in higher density environment than unimodal clusters. Clusters in
superclusters have higher probability to have substructure than isolated
clusters. The superclusters can be divided into two main morphological types,
spiders and filaments. Clusters in superclusters of spider morphology have
higher probabilities to have substructure and larger peculiar velocities of
their main galaxies than clusters in superclusters of filament morphology. The
most luminous clusters are located in the high-density cores of rich
superclusters. Five of seven most luminous clusters, and five of seven most
multimodal clusters reside in spider-type superclusters; four of seven most
unimodal clusters reside in filament-type superclusters. Our study shows the
importance of the role of superclusters as high density environment which
affects the properties of galaxy systems in them.
