Unveiling the Coma Cluster Structure: From the Core to the Hubble Flow

TL;DR

This work maps the Coma cluster from its virial core to the surrounding Hubble flow using a data-driven, cosmology-agnostic pipeline that combines SDSS DR17 galaxy data with Cosmicflows-4 distances. A DBSCAN-based member selection, anchored in line-of-sight velocities and sky density, yields a robust Coma membership (core, full, outskirts) and enables a velocity-distance analysis through radial-infall models and CF4 calibrations. The study derives a Coma centre distance of $r_c=(69.959\pm0.012)\,h^{-1}$ Mpc, a virial radius $r_{\rm vir}=(1.95\pm0.12)\,h^{-1}$ Mpc, and a turnaround radius $r_{\rm ta}\geq4.87\,h^{-1}$ Mpc, with a Hubble constant $H_0=(73.10\pm0.92)$ km s$^{-1}$ Mpc$^{-1}$ and a mass range $M=[0.77,2.0]\times10^{15}\,h^{-1}\,M_\odot$ subject to methodological degeneracies. Mass estimates from caustics, virial theorem, and Hubble-flow approaches are broadly consistent with prior results, while relying on fewer model assumptions for member selection. The work highlights the degeneracies between $H_0$, $r_{\rm vir}$, and $M$, and demonstrates a principled pathway to integrate cluster dynamics with the local Hubble flow, laying groundwork for improved constraints with future datasets such as DESI.

Abstract

The Coma cluster, embedded in a cosmic filament, is a complex and dynamically active structure in the local Universe. Applying a density-based member selection (\texttt{dbscan}) to data from the Sloan Digital Sky Survey (SDSS), we identify its virialised core and zero-velocity boundary. Cross-correlating with the Cosmicflows-4 (CF4) catalogue enables a velocity-distance analysis, incorporating radial infall models and redshift-independent distance estimators. This reveals, for the first time, the Hubble flow surrounding Coma, a first step to investigate the entanglement between Coma's dark matter halo and the dark energy driving the expansion of the surroundings. The distance to the Coma centre is determined as $(69.959 \pm 0.012) \, h^{-1}~\text{Mpc}$. From \texttt{dbscan}, we infer a virial radius of $r_{\rm vir} = \left(1.95 \pm 0.12\right)\,h^{-1}~\text{Mpc}$ and a turnaround of $r_{\rm ta} \geq 4.87~{h}^{-1}~\mbox{Mpc}$. Combining the SDSS redshifts with the CF4 distances, we estimate the Hubble constant to be $H_0 = (73.10 \pm 0.92)~\mbox{km}/\mbox{s}/\mbox{Mpc}$, which varies between $[72, 80]$~km/s/Mpc with different calibrations for the distance moduli. Mass estimates via caustics, the virial theorem and the Hubble-flow method yield $M = [0.77, 2.0] \times 10^{15}\,h^{-1}\,M_{\odot}$, consistent with prior mass estimates. However, our mass estimates are based on fewer model assumptions in the member selection and require fewer members to attain the same precision. Our systematic approach maps the structure of Coma into the local Hubble flow and shows the degeneracies between dynamical parameters such as the Hubble constant, the virial radius, and the total mass.

Figures (15)

• Figure 1: Constraining the Coma cluster member galaxies along the line of sight to $z\in \left[0.0177, 0.0297 \right]$ by finding local maxima and minima in a smoothed version (black line) of a redshift histogram (gray bars in the background). Vertical red lines delimit structures according to the minima. The peak position for Coma is found at $z=0.0232$ ($\pm 0.00025$ due to the chosen resolution), indicated by a vertical black line according to the global maximum. Other local maxima are marked with gray vertical lines, denoting peaks of other structures.
• Figure 2: Average distance for all $k$-nearest neighbors of all 2744 galaxies in the Coma field (left) and average number of galaxies in a circle of radius eps around all galaxies (right). Any $\langle n_\mathrm{gal} \rangle < 0$ is nonphysical but plotted to show the change in the lower 1$-\sigma$ bound in $\emph{eps}\in \left[0,2\right]^\circ$.
• Figure 3: Results for dbscan clustering on the Coma dataset for a parameter space of $\emph{eps} \in \left[0.1, 3.5\right]^\circ$ in steps of $0.1^\circ$ and $\emph{min\_samples} \in \left[2, 1050 \right]$ in steps of 1 sample: number of clusters found (left), ratio of galaxies in the largest cluster to the total number of galaxies in the dataset (centre), ratio of galaxies in the background field to the total number of galaxies (right). The parameter combination with maximum curvature in the number of clusters (left) is marked in all three plots (black dashed lines): $\emph{eps}=(1.6\pm 0.1)^\circ$ and $\emph{min\_samples}=716 \pm 1$.
• Figure 4: Quality of fit criteria for the parameter combinations shown in Fig. \ref{['fig:dbscan_scan']}: normalised mean distance (top), normalised number of members in the largest cluster (centre), and the silhouette score (bottom) over min_samples for selected eps-values. The min_samples-values with maximum curvature are also added (vertical dotted lines for least dense stable clustering, vertical dashed lines for most dense stable clustering).
• Figure 5: Coma dbscan clustering results for different parameter-value combinations: least-dense robust clustering from $\overline{n}_\mathrm{mem}$ (left column), densest robust clustering from $\overline{n}_\mathrm{mem}$ (centre column), and maximum possible clustering (right column). The least-dense clustering may include structures accreted from the outskirts, while the maximum clustering under-estimates the number of members even for large eps.