# Numerical Estimator for Large-Scale Cosmic Structures

## TL;DR

This paper introduces a new continuous structural parameter based on galaxy distance distributions to classify large-scale cosmic structures, aiding in distinguishing clusters, filaments, and voids.

## Contribution

A novel structural parameter derived from galaxy distance distributions that helps identify and classify large-scale structures in the universe.

## Key findings

- Parameter effectively distinguishes clusters from voids.
- Application to SDSS data demonstrates practical utility.
- Potential to improve LSS component analysis.

## Abstract

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.