Network Theory in Galaxy Distributions: The Coma Supercluster Neighborhood

TL;DR

The paper addresses how to characterize the large-scale structure of the galaxy distribution using spatial networks rather than solely two-point statistics. It builds 3D networks from the Tempel 2014 flux catalog, varies the connection radius $r$, and compares to Random Geometric Graphs and Segment Cox processes to identify percolation- and diameter-driven structures. Key findings include a strong link between mean degree and environmental density, a density-morphology relation with high-degree galaxies more likely to be elliptical, and the utility of betweenness and closeness centralities to trace filaments and superclusters, with the correlation dimension defined as $D_2(r)=\frac{d \ln \mathcal{N}(<r)}{d \ln r}+3$. Overall, the work demonstrates that a network-theory toolbox provides complementary methods for mapping clusters, filaments and percolation scales in the cosmic web.

Abstract

In this work, we use the theory of spatial networks to analyze galaxy distributions. The aim is to develop new approaches to study the spatial galaxy environment properties by means of the network parameters. We investigate how each of the network parameters (degree, closeness and betweeness centrality; diameter; giant component; transitivity) map the cluster structure and properties. We measure the network parameters of galaxy samples comprising the Coma Supercluster and 4 regions in their neighborhood ($z<0.0674$) using the catalog produced by \citet{tempel2014flux}. For comparison we repeat the same procedures for Random Geometric Graphs and Segment Cox process, generated with the same dimensions and mean density of nodes. We found that there is a strong correlation between degree centrality and the normalized environmental density. Also, at high degrees there are more elliptical than spiral galaxies, which confirms the density-morphology relation. The mean degree as a function of the connection radius is an estimator of the count-of-spheres and consequently provides the correlation dimension as a function of the connection radius. The correlation dimension indicates high clustering at scales indicated by the network diameter. Further, at this scales, high values of betweeness centrality characterize galaxy bridges connecting dense regions, tracing very well the filamentary structures. Then, since galaxies with the highest closeness centrality belongs to the largest components of the network, associated to supercluster regions, we can produce a catalog of superclusters only by extracting the largest connected components of the network. Establishing the correlation between the well-studied normalized environmental densities and the parameters of the network theory allows us to develop alternative tools to the study of the large-scale structures.

Figures (23)

• Figure 1: Data sample composed by Super Coma Region in red points; Region 1 in blue points; Region 2 in green points; Region 3 in yellow points and Region 4 in magenta points.
• Figure 2: Network diameter, as well as APL, normalized giant component and transitivity, versus$r$ for Coma, Super Coma, Regions 1, 2, 3, 4 and the respective RGG sample (for each dataset -- rows 1 and 3 -- the corresponding random dataset is presented below -- rows 2 and 4.) The network diameter increases to a maximum value, then the graph tends to a complete graph and the network diameter tends to one hong2016discriminating. The APL follows a similar behavior. The giant component emerges on steps due to density variations on the sample.
• Figure 3: Network diameter, as well as APL, normalized giant component and transitivity, versus$r$ for Segment Cox process 1 and 2, for a mean of ten realizations. The right plot shows the behavior of Segment Cox process for one realization.
• Figure 4: The LS two-point correlation $\xi_{LS}(r)$ for Region 1 and 4 calculated with eight times more random points than the data sample. The dashed red line is the power-law fit to the LS correlation function $\xi_{LS}(r) = \left( r/r_0 \right)^{\gamma}$ calculated via non-linear least squares.
• Figure 5: The scaled counts-in-spheres estimator $\mathcal{N}_k(<r) = \langle \mathcal{K} \rangle_r$ from Equation \ref{['eq:scaled_meandeg']} for Region 1, Region 4 and Cox Process 2 calculated until $r= 20 h^{-1}$Mpc with $\Delta r = 0.5 h^{-1}$Mpc. The dashed red line is the power-law fit to the scaled counts-of-spheres $\langle \mathcal{K} \rangle_r = \left( r/r_{0\mathcal{K}} \right)^{\gamma}$ calculated via non-linear least squares.