SDSS DR7 superclusters. Morphology
  We study the morphology of a set of superclusters drawn from the SDSS DR7. We
calculate the luminosity density field to determine superclusters from a flux-
limited sample of galaxies from SDSS DR7, and select superclusters with 300 and
more galaxies for our study. The morphology of superclusters is described with
the fourth Minkowski functional V3, the morphological signature (the curve in
the shapefinder's K1-K2 plane) and the shape parameter (the ratio of the
shapefinders K1/K2). We investigate the supercluster sample using
multidimensional normal mixture modelling, and use Abell clusters to identify
our superclusters with known superclusters and to study the large-scale
distribution of superclusters. The superclusters in our sample form three
chains of superclusters; one of them is the Sloan Great Wall. Most
superclusters have filament-like overall shapes. Superclusters can be divided
into two sets; more elongated superclusters are more luminous, richer, have
larger diameters, and a more complex fine structure than less elongated
superclusters. The fine structure of superclusters can be divided into four
main morphological types: spiders, multispiders, filaments, and multibranching
filaments. We present the 2D and 3D distribution of galaxies and rich groups,
the fourth Minkowski functional, and the morphological signature for all
superclusters. Widely different morphologies of superclusters show that their
evolution has been dissimilar. A study of a larger sample of superclusters from
observations and simulations is needed to understand the morphological variety
of superclusters and the possible connection between the morphology of
superclusters and their large-scale environment.
