Discriminating Topology in Galaxy Distributions using Network Analysis

TL;DR

This paper introduces a network analysis approach to distinguish topologically different galaxy distributions that appear similar under traditional two-point correlation analysis, revealing structures like filaments missed by simpler statistics.

Contribution

The study demonstrates that network analysis metrics can effectively discriminate between galaxy distributions with identical two-point correlations but different topologies, such as filamentary structures.

Findings

Network metrics distinguish simulated galaxy distributions from Lévy fractals.

Filamentary structures are identified in cosmological simulations but absent in Lévy models.

Network analysis provides a new tool for comparing observed and theoretical galaxy distributions.

Abstract

(abridged) The large-scale distribution of galaxies is generally analyzed using the two-point correlation function. However, this statistic does not capture the topology of the distribution, and it is necessary to resort to higher order correlations to break degeneracies. We demonstrate that an alternate approach using network analysis can discriminate between topologically different distributions that have similar two-point correlations. We investigate two galaxy point distributions, one produced by a cosmological simulation and the other by a L\'evy walk. For the cosmological simulation, we adopt the redshift $z = 0.58$ slice from Illustris (Vogelsberger et al. 2014A) and select galaxies with stellar masses greater than $10^8$$M_\odot$. The two point correlation function of these simulated galaxies follows a single power-law, $\xi(r) \sim r^{-1.5}$. Then, we generate L\'evy walks matching the correlation function and abundance with the simulated galaxies. We find that, while the two simulated galaxy point distributions have the same abundance and two point correlation function, their spatial distributions are very different; most prominently, \emph{filamentary structures}, absent in L\'evy fractals. To quantify these missing topologies, we adopt network analysis tools and measure diameter, giant component, and transitivity from networks built by a conventional friends-of-friends recipe with various linking lengths. Unlike the abundance and two point correlation function, these network quantities reveal a clear separation between the two simulated distributions; therefore, the galaxy distribution simulated by Illustris is not a L\'evy fractal quantitatively. We find that the described network quantities offer an efficient tool for discriminating topologies and for comparing observed and theoretical distributions.