Numerical Estimator for Large-Scale Cosmic Structures
  Components of large-scale structure (LSS) of Universe includes galaxy
clusters, walls, filaments, groups and field galaxies. The question of spatial
organization of all these components remains open despite of a number of
recently developed methods of LSS analysis. In this paper we introduce new
continuous structural parameter of galaxy distribution for the determinig of
the type of LSS surrounding. This parameter is based on comparison of the
radial distribution of galaxies around the certain point with the uniform one.
Our method for structure parameter calculation is based on the distribution of
1000 closets galaxies to the selected one. Such number was selected because
most galaxy clusters contains up to 1000 galaxies. When we exceed 1000th
closest galaxy we will leave possible cluster or filament and will pass to
another type of LSS. We suppose that in uniform distribution of galaxies their
number should increase as third power a distance, similar to luminosity.
Therefore the inverse dependence of galaxy distance from number should be cubic
root. New structural parameter was introduced as the difference of this
dependence of cubic root. The main type of cosmic surrounding for a galaxy is
defined by the value and the sign of such structural parameter. If a galaxy lie
in a cluster the distances of nearby galaxies will be less than cubic root. We
integrated distance difference for all 1000 galaxies and get negative stuctural
parameter in this case. In the case of void the structural parameter will be
positive. New parameter was calculated for sky distribution of SDSS galaxies at
distances from 50 to 150 Mpc. Analysing obtained values, we come to conclusion
that our structural parameter can be used for the division of LSS components
and extragalactic filament detection.
