The Blooming Tree Algorithm at Work: Clusters, Filaments and Superclusters in the Field of A2029

TL;DR

The Blooming Tree (BT) algorithm provides a unified, non-parametric hierarchical clustering framework to identify galaxy clusters, groups, filaments, and superclusters from spectroscopic redshift surveys. By building a binary tree from pairwise binding energies and using the density-contrast threshold $\Delta\eta$, BT detects structures without assuming spherical symmetry or hydrostatic equilibrium and yields memberships plus a hierarchical view of assembly. Applied to a $10\times10$ deg$^2$ field around the massive cluster A2029, BT recovers all X-ray luminous clusters, many optical clusters, and traces surrounding filaments and three superclusters, offering insights into accretion histories and evolution on non-linear scales. The results demonstrate BT's utility for current and upcoming large-scale surveys (e.g., DESI, Roman) and enable robust cross-wavelength comparisons (eROSITA) to advance understanding of baryons and dark matter in the cosmic web.

Abstract

The Blooming Tree (BT) algorithm, based on the hierarchical clustering method, is designed to identify clusters, groups, and substructures from galaxy redshift surveys. We apply the BT algorithm to a wide-field ($10\times 10$ deg$^2$) spectroscopic dataset centered on the galaxy cluster A2029. The BT algorithm effectively identifies all the X-ray luminous clusters and most of the optical clusters known in the literature, numerous groups, and the filaments surrounding the clusters, associating a list of galaxy members to each structure. By lowering the detection threshold, the BT algorithm also identifies the three superclusters in the field. The BT algorithm arranges the clusters and groups that make up the superclusters in a hierarchical tree according to their pairwise binding energy: the algorithm thus unveils the possible accretion history of each supercluster and their future evolution. These results show how the BT algorithm can represent a crucial tool to investigate the formation and evolution of cosmic structures on non-linear and mildly non-linear scales.

Figures (10)

• Figure 1: The top panel is the spectroscopic completeness as a function of the r-band magnitude. The solid vertical line indicates $m_{\rm r,Petro,0} = 17.77$. The bottom panel is the two-dimensional completeness map of the A2029 field.
• Figure 2: The redshift distribution of the galaxies in our sample (solid histogram). The galaxy number density in each redshift bin is represented by the red curve. The two dashed vertical lines indicate redshifts 0.02 and 0.13. The horizontal dashed line indicates the galaxy number density 0.003 Mpc$^{-3}$.
• Figure 3: Distribution of the BT structures on the sky. Different structures are shown with different colors. However, some colors are reused. The identification numbers of the BT structures are placed near their centroids. The grey points, the red circles and the blue circles show the galaxies, the Abell clusters, and the MCXC clusters, respectively.
• Figure 6: Central density against velocity dispersion of the 87 BT structures. The size of each circle is proportional to the number of clusters associated to the structure as listed in Table \ref{['tab:x']}. BT structures with X-ray emission are indicated by cyan dots. The 26 low-density structures that are missing from the sample of 72 high-density structures are marked with an additional red cross.
• Figure 7: The redshift distribution of the structures with at least 20 members and velocity dispersion larger than 200 km s$^{-1}$. The grey points, the blue circles, and the red circles show the galaxies, the MCXC clusters, and the Abell clusters, respectively.