The Cosmic Dance: Observational Detection of Coherent Spin in Galaxy Clusters

TL;DR

This study delivers the first observational, statistical detection of coherent spin in galaxy clusters by applying a novel spin metric that maximizes the projected redshift difference $\Delta Z_{\max}$ across a trial rotation axis to two large SDSS-based cluster samples. Using $10^4$ Monte Carlo realizations, the authors demonstrate a significant excess of rotational signal relative to random controls, with peak rotation speeds around $\sim380\ \mathrm{km\,s^{-1}}$ (Sample-1) and $\sim300\ \mathrm{km\,s^{-1}}$ (Sample-2), strengthening in richer clusters. They find that the rotational velocity grows with cluster mass ($M_{\rm vir}$), from about $360\ \mathrm{km\,s^{-1}}$ at $10^{14}\,M_\odot$ to $\sim693\ \mathrm{km\,s^{-1}}$ at $10^{15}\,M_\odot$, and that cluster spins tend to align parallel to central-galaxy spins while being perpendicular to the nearest cosmic filament. These results link cluster-scale angular momentum to both internal dynamics and the surrounding cosmic web, offering a new window into angular-momentum transfer in hierarchical structure formation and a potential new avenue for cross-checking mass and dynamical state with multi-wavelength probes.

Abstract

The spin of galaxy clusters encodes key information about their formation, dynamics, and the influence of large-scale structure. However, whether clusters possess statistically significant spin and how to measure it observationally remain open questions. Here, we present the first observational, statistical detection of coherent spin in galaxy clusters, using two samples of 2,170 and 1,329 systems with $M > 10^{14}\,M_\odot$, selected from two publicly available group catalogs (\citet{2017A&A...602A.100T} and \citet{2012ApJ...752...41Y}) constructed with two different algorithms and but both based primarily on SDSS galaxies. Cluster spin is quantified by identifying the orientation in the projected plane that maximizes the redshift difference ($ΔZ_{\rm max}$) between member galaxies in two regions divided by a trial axis. We find compelling statistical evidence for coherent rotation, as the observed $ΔZ_{\rm max}$ distribution departs markedly from the randomized controls, exhibiting pronounced deviations near $380\,\mathrm{km\,s^{-1}}$. Stacked visualizations confirm the spatial segregation of redshifted and blueshifted galaxies across the rotation axis. The radial profile of the rotational velocity indicates that it increases as a function of radius. The cluster rotation speed increases with mass, from $\sim360~\mathrm{km\,s}^{-1}$ at $10^{14} M_\odot$ to $\sim693~\mathrm{km\,s}^{-1}$ at $10^{15} M_\odot$. Additionally, cluster spin tends to align parallel with the central galaxy spin and perpendicular to the nearest cosmic filament, particularly in richer systems. These results reveal significant coherent spin in galaxy clusters, shaped by both internal dynamics and large-scale structure.

Figures (7)

• Figure 1: A schematic illustration of the method for identifying the projected rotation axis of a galaxy cluster. Star symbols represent the the geometrical centre of all galaxies in the group(black) and the member galaxies (red and blue). The dashed line marks the projected rotation axis, which divides the projected plane into two regions: Region A (red) and Region B (blue). If the cluster is rotating in the direction indicated by the blue arrow, member galaxies in Region A are expected to predominantly exhibit red-shifted velocities, while those in Region B are expected to appear mostly blue-shifted.In this illustration, the projected rotation axis is rotated by an angle $\theta_{\rm max}$ from the reference axis (the x-axis, dotted line); see the main text for further details.
• Figure 2: Distributions of the basic properties of the galaxy clusters used in this study for both Sample-1 (blue line) and Sample-2 (orange line). From left to right, the panels show: (1) cluster mass $\log(M_{\mathrm{cl}}/M_\odot)$; (2) cluster radius $R_{\mathrm{cl}}$ (in Mpc); (3) number of member galaxies $N_{\mathrm{gal}}$ (richness); (4) cluster redshift $Z_{\mathrm{cl}}$; and (5) spectroscopic redshift error $Z_{\mathrm{error}}$.
• Figure 3: The global detection of cluster spin for Sample-1 (top row) and Sample-2 (bottom row). Left: The cumulative distribution of the redshift difference, $\Delta Z_{\rm max}$, between galaxies in region A and region B. The solid red lines in the bottom panel represent the distribution of the measured cluster spin signal, while the 10,000 gray lines correspond to randomized trials. The black solid lines indicate the median values of the random samples. The top panels display the sample-to-sample distance between the real clusters in the observation and the random samples, expressed in units of the standard deviation of the random trials. The upper x-axes show the rotation speed of the filaments, calculated as $\mu=\frac{1}{2}c\times\,{\rm \Delta Z_{Max}}$. Middle: Similar to the left panel, but show clusters with member galaxies more than 10 ($N_{gal}>10$). Right: The significance of the cluster spin signal as a function of the ratio $Z_{\mathrm{rms}}/\Delta Z_{\rm max}$. Each point represents a cluster, colored by the number of member galaxies in regions A and B ($N_{\mathrm{gal}}^{A,B}$). The vertical dashed line marks $Z_{\mathrm{rms}}/\Delta Z_{\rm max} = 1$.
• Figure 4: Left: Projected distribution of galaxies within clusters, where the $x$- and $y$-axes represent normalized coordinates ($\Delta x/d_{\mathrm{max}}$, $\Delta y/d_{\mathrm{max}}$) centered on the cluster center, with $d_{\mathrm{max}}$ defined as the distance to the most distant member galaxy in each cluster. Each point is color-coded by its redshift deviation $\Delta z$ from the cluster mean; redder (bluer) points indicate galaxies moving away (approaching). The black vertical line marks the rotation axis, and the arrow shows the inferred spin direction. All clusters are rotated to align their spin axes vertically. Middle: Cluster rotation speed as a function of normalized distance to the center. Each point shows the measured rotation speed of a member galaxy, with blue and red points for galaxies on opposite sides of the rotation axis. Distances in the receding (approaching) region are shown in red (blue) and assigned positive (negative) values. Right: The relation between circular velocity $\log \mu$ (km s$^{-1}$) and cluster mass, $\log(M_{\rm 200}/M_\odot)$. Each data point represents a single cluster, color-coded by its richness, $N_{gal}$, as indicated by the colorbar. The black solid line shows the median relation, while the grey dashed lines represent the $1\sigma$ scatter in each mass bin.
• Figure 5: Left: Distribution of the angle between the cluster spin axis and the spin of the central galaxy. The blue and red histograms represent all clusters and clusters with more than 10 member galaxies ($N_{\mathrm{gal}} > 10$), respectively. Right: Distribution of the angle between the cluster spin axis and the orientation of the nearest cosmic filament. The blue and red histograms represent the same samples as in the left panel.