Morphological Properties of Superclusters of Galaxies
  We studied superclusters of galaxies in a volume-limited sample extracted
from the Sloan Digital Sky Survey Data Release 7 (SDSS/DR7) and from mock
catalogues based on a semi-analytical model of galaxy evolution in the
Millenium Simulation. A density field method was applied to a sample of
galaxies brighter than $M_r= -21+5 \log h_{100}$ to identify superclusters,
taking into account selection and boundary effects. In order to evaluate the
influence of threshold density, we have chosen two thresholds: the first
maximizes the number of objects (D1), and the second constrains the maximum
supercluster size to $\sim$120~h$^{-1}$Mpc (D2). We have performed a
morphological analysis, using Minkowski Functionals, based on a parameter which
increases monotonically from filaments to pancakes. An anti-correlation was
found between supercluster richness (and total luminosity or size) and the
morphological parameter, indicating that filamentary structures tend to be
richer, larger and more luminous than pancakes in both observed and mock
catalogues. We have also used the mock samples to compare supercluster
morphologies identified in position and velocity spaces, concluding that our
morphological classification is not biased by the peculiar velocities. Monte
Carlo simulations designed to investigate the reliability of our results with
respect to random fluctuations show that these results are robust. Our analysis
indicates that filaments and pancakes present different luminosity and size
distributions.
