A catalogue of merging clusters of galaxies: cluster partners, merging subclusters, and post-collision clusters

The hierarchical formation scenario of the large-scale structure suggests that larger structures are formed through the continuous merging of smaller structures (Springel et al., 2005). As the largest virialized systems in the Universe, clusters of galaxies were formed at the epoch of $z\sim 2$ and grew through merging smaller clusters (Kravtsov & Borgani, 2012). The merging process results in obvious substructures or the non-spherical distribution of member galaxies and/or hot gas inside a cluster of galaxies, which can be used to reveal the dynamical state of clusters (Wen & Han, 2013) and test models for the structure formation of the Universe (West et al., 1988; Jing et al., 1995).

The merging process of galaxy clusters usually experiences several stages. Before the merger, two or more clusters have a large separation with only very weak gravitational interaction. These clusters may be located in a cosmological filament as suggested by the distribution of galaxies or diffuse gas (Porter et al., 2008; Zhang et al., 2013), which are good targets to reveal the missing baryon in the form of warm-hot intergalactic medium (Werner et al., 2008; Tejos et al., 2016; Mirakhor et al., 2022), and to study star formation history of galaxies around clusters (Gray et al., 2004; Porter et al., 2008; Piraino-Cerda et al., 2024). As two clusters approach but are not connected at the early stage of mergers, they have a stronger interaction with some gas partly mixed. Merging clusters at this stage generally have not yet produced shocks shown in X-ray images (e.g. Belsole et al., 2004; Kato et al., 2015) except few cases (e.g. Akamatsu et al., 2016; Gu et al., 2019). Afterward, two clusters experience mergers with an enormous amount of energy released. Strong shocks of intracluster hot gas are usually generated, which can transfer the dynamical energy in the intracluster medium (ICM) into non-thermal component (van Weeren et al., 2010; van Weeren et al., 2012; Macario et al., 2011; Russell et al., 2010). Radio observations reveal radio relics which are produced by particles accelerated to relativistic velocity in merging shock fronts, or radio halo by re-accelerated particles in the turbulence in the ICM (Feretti et al., 2012). The ICM in some merging subclusters can be stripped by the ram pressure. The extreme case of cluster merger, e.g. 1E 0657$-$558 (the Bullet cluster, Markevitch et al., 2002), shows the significant offset between the matter and the ICM, which provides direct evidence of dark matter and constraint on the properties of dark matter (Markevitch et al., 2004; Clowe et al., 2006). After merging, the hot gas and member galaxies may experience long post-merging phase and gradually slow down towards a final relaxed state which is shown by a bright cool core in X-ray and a dominated brightest cluster galaxy (BCG) in optical (Vikhlinin et al., 2005; Wen & Han, 2015a; Lopes et al., 2018).

Merging clusters are indicated by substructures inside a cluster. About 40% – 70% of clusters show an obvious signature of recent mergers (Schuecker et al., 2001; Smith et al., 2005; Wen & Han, 2013). The dynamical states of galaxy clusters are direct indications of merging processes inside clusters and be quantified by the concentration index, the centroid shift, the power ratio, and the morphology index in X-ray images (Buote & Tsai, 1995; Mohr et al., 1995; Santos et al., 2008; Yuan & Han, 2020). In optical, it also can be diagnosed by the 3-D distribution of member galaxies (Dressler & Shectman, 1988; Yu et al., 2018) and the relaxation parameters based on the 2-D distribution of member galaxies (Wen & Han, 2013). The above measurements merely give the amount of the substructure for clusters without the information of merging stages, and hence are insufficient to describe the dynamical states of clusters.

Cluster mergers at different stages have been explored previously. A few tens of paired clusters and pre-merger systems have been individually studied by optical and X-ray data (e.g. Belsole et al., 2004; Sakelliou & Ponman, 2004; Planck Collaboration et al., 2013; Molino et al., 2019). Ongoing mergers have been identified for more than one hundred clusters through X-ray images (e.g. Kempner & David, 2004; Markevitch et al., 2005; Sakelliou & Ponman, 2006; Giacintucci et al., 2009; Boschin et al., 2012a) or observations of radio diffuse halos and relics (e.g. Feretti et al., 2012; van Weeren et al., 2019). Mann & Ebeling (2012) identified 10 clusters that likely have undergone recent multiple merger events and also 11 systems that are likely the post-collision of head-on mergers based on the projected offset between the BCG and the peak of X-ray emission, and also a visual assessment of the cluster morphology in optical and X-ray. By using Sloan Digital Sky Survey (SDSS) spectroscopic data release 12 (DR12), Tempel et al. (2017) found 498 potential partner systems for the galaxy groups in the redshift range of $z<0.17$. Recently Oak & Paul (2024) presented an improved search algorithm for interacting galaxy clusters from the SDSS DR17 and published 160 merging systems and 21 pre-merging/post-merging systems at $z\leq 0.2$.

In recent years, a large number of galaxy clusters up to $z>1$ have been identified from the optical survey data, e.g. SDSS (Koester et al., 2007; Wen et al., 2009, 2012; Wen & Han, 2015b; Rykoff et al., 2014; Oguri, 2014; Banerjee et al., 2018), Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys (Yang et al., 2021; Zou et al., 2022; Wen & Han, 2024) and Dark Energy Survey (DES; Rykoff et al., 2016; Wen & Han, 2022). These cluster samples, supplemented with spectroscopic or photometric data of galaxies in optical surveys, provide an unprecedentedly large database to reveal cluster mergers.

Optical imaging data can show cluster mergers projected on the sky plane and trace the mass distribution inside merging clusters since galaxies are essentially collisionless during mergers (e.g. Jee et al., 2015; Golovich et al., 2016; Finner et al., 2017). In this paper, we identify a large sample of merging clusters at different stages by using the large optical cluster sample from the DESI Legacy Surveys. In Section 2, we describe the cluster sample and the member galaxies. In Section 3, we obtain a large sample of pre-merger cluster partner systems. In section 4, we analyze the subclusters within the region of $r_{500}$ for rich clusters and quantify the merging process via a coupling factor. In section 5, we identify post-collision mergers from rich clusters according to the deviations of the BCGs from the distribution of other member galaxies. A summary is presented in Section 6.

Throughout this paper, we assume a flat Lambda cold dark matter ($\Lambda$CDM) cosmology taking $H_{0}=70$ km s^-1 Mpc^-1, $\Omega_{m}=0.3$ and $\Omega_{\Lambda}=0.7$.

This study uses the catalogue of 1.58 million galaxy clusters in the redshift range of $z<1.5$ identified by Wen & Han (2024) from the DESI Legacy Imaging Surveys (Dey et al., 2019) DR9 and new data from DR10, covering a total sky area of $\sim$24,000 deg². Our algorithm first selects a sample of massive BCG-like galaxies with a stellar mass of $M_{\star}\geq 10^{11}M_{\odot}$, a high optical/infrared luminosity and a red colour defined by known BCGs. Then clusters are searched as being the overdensity peaks of galaxy stellar masses in the redshift slices around the massive BCG-like galaxies. The galaxies within a given redshift slice and a given projected separation from the BCG-like galaxies were taken as member galaxy candidates of clusters to-be-identified. The cluster redshifts were then determined from the photometric redshifts and available spectroscopic redshifts of member galaxy candidates. The cluster center is defined as being the position of the BCGs. The cluster radius ($r_{500}$, the radius within which the mean density of a cluster is 500 times the critical density of the universe) and mass ($M_{500}$, the cluster mass within $r_{500}$) were estimated from the total stellar masses of member galaxy candidates via the calibrated scaling relations. The clusters have a mass $M_{500}$ in the range of $(0.47-12)\times 10^{14}~{}M_{\odot}$ with an uncertainty of 0.2 dex. Among the 1.58 million clusters of galaxies, 338 841 clusters have spectroscopic redshifts, and the others have photometric redshifts with an uncertainty of about 0.01. Cross-matching with known clusters suggests that our cluster catalogue has a high purity of $\sim$97% at $z<0.9$ and contains $\sim$90% of X-ray clusters with $M_{500}>0.5\times 10^{14}~{}M_{\odot}$. See details in Wen & Han (2024).

In this paper, we use the 338 841 clusters that have spectroscopic redshifts among the 1.58 million clusters for finding cluster partner systems at the pre-merger stage. The spectroscopic redshifts are mostly taken for the member galaxies from the 2MASS Redshift Survey at low redshifts and from the SDSS up to the intermediate redshifts.

From 27 685 rich clusters in the catalogue of 1.58 million clusters, which have more than 30 member galaxy candidates within $r_{500}$, we find merging subclusters and post-collision mergers. These clusters have a mass $M_{500}$ in the range of $(1.2-12)\times 10^{14}~{}M_{\odot}$ with the median mass of $2.87\times 10^{14}~{}M_{\odot}$. For this work, only massive galaxies with a stellar mass of $M_{\star}\geq 10^{10}~{}M_{\odot}$ within a projected radius of 3 Mpc are taken as member galaxy (candidates), if they have spectroscopic redshifts within a velocity difference of $\Delta v<2500$ km s^-1 from the cluster redshifts or in a photometric redshift slice according to the uncertainty of their photometric redshifts (Wen & Han, 2021). The spectroscopic data from the GAMA survey (Driver et al., 2022) have been used to test the accuracy and completeness of so-detected bright member galaxies. We found that 83% of the member galaxy candidates from photometric redshifts can be verified well by spectroscopic redshifts, and only about 8% of true members are missing by our algorithm.

We first find cluster partner systems before merging, which contain two or more nearby clusters that are probably gravitationally bound together. The more massive one is called the main cluster, and the other(s) with a less mass are partners. To avoid any misidentifications, we find the cluster partner systems from the 338 841 clusters with spectroscopic redshifts.

Clusters in the partnership are identified with criteria of a small separation on the sky plane and a small velocity difference indicated by spectroscopic redshifts. We set a maximum projected separation of 5 $r_{500}$ of the main cluster, which is about the half turn-around radius of a cluster (Regos & Geller, 1989; Rines & Diaferio, 2006; Hansen et al., 2020). The velocity difference between the two partners is temporarily set to be less than 1500 km s^-1, and then we use the two-body model for gravitational binding (Beers et al., 1982) to further constrain the velocity difference by,

where $v_{r}$ is the relative velocity along the line of sight, $r_{p}$ is the projected separation, $M$ is the total virial mass of the system, and $\alpha$ is the angle between the line connecting two clusters and the plane of the sky. The right term of Eq. 1 has a maximum value of $4\sqrt{3}GM/9$, hence the partners with $v^{2}_{r}r_{p}>4\sqrt{3}GM/9$ are discarded.

From the 338 841 clusters, we find 39 382 partners for 33 126 main clusters as listed in Table 1, which satisfy the criteria for the partnership. Among them, 28 041, 4161, 737, 146, 29, 7, 4, and 1 main clusters have one, two, three, four, five, six, seven, and even nine partners, respectively. The projected distributions of member galaxies for three examples of partnerships with one, two, and three partners, respectively, are shown in Fig. 1. Not surprisingly, galaxies are concentrated inside each cluster or in the region between clusters. The distributions for the projected separation and the velocity difference of 39 382 partners from the main clusters are shown in Fig. 2, together with the histogram number distributions. Under the gravitational binding condition, most ($\sim$97%) systems have a velocity difference of less than 1000 km s^-1, and a smaller velocity difference is desired at a larger projected separation.

The sample of our identified partner systems includes the previously well-known double clusters, such as A21 – IVZw015 (Planck Collaboration et al., 2013; Piffaretti et al., 2011), A1095W – A1095E (Ge et al., 2016), A1560A – A1560B (Ulmer & Cruddace, 1982), 400dJ1359 – ZwCl1358.1 (Planck Collaboration et al., 2013; Piffaretti et al., 2011), A1882A – A1882B (Owers et al., 2013), and A2029 – A2033 (Gonzalez et al., 2018). However, some previously proposed double clusters, such as A2061 – 2067 (Pearson et al., 2014) and A1758N – A1758S (David & Kempner, 2004), cannot satisfy the criterion for the velocity difference for the gravitation binding (Eq. 1), and therefore are not listed in Table 1 as being cluster partner systems. Some close double clusters, e.g. A98N – A98S (Paterno-Mahler et al., 2014) and A1750N – A1750C (Bulbul et al., 2016), are not in our sample since they have a projected separation smaller than $r_{500}$. They are considered as merging subclusters inside massive clusters in this work (see Section 4).

Clusters of galaxies are preferably located at the knots of filamentary large-scale structures in the Universe, and are preferably aligned together (Altay et al., 2006; Smargon et al., 2012). Here we investigate the alignment of the partner positions to the main clusters using the 4161 clusters with two partners, and find the preferential alignment. The distribution of the angles of two partners to the main cluster is shown in Fig. 3, showing peaks at about 20 – 30 degrees for similar directions of two partners and at 170 – 180 degrees for the opposite. The partners at around 70-80 degrees are 30% below the average.

We noticed that more massive clusters have a higher fraction with partners (see Fig. 4). Considering the completeness of cluster spectroscopic redshifts, for statistics, we use only these clusters in the region of SDSS Baryon Oscillation Spectroscopic Survey with a redshift of $z<0.5$ and a mass $M_{500}\geq 1\times 10^{14}~{}M_{\odot}$ for this statistics because about 90% of such clusters in the catalogue of 1.58 million clusters have spectroscopic redshifts. Among the 338 841 clusters with spectroscopic redshifts in this specific region, we get 20 145 clusters in the partner systems and 40 038 isolated clusters. It is understandable that in the hierarchical cluster formation scenario massive clusters are preferably formed in a denser environment and are experiencing more merging processes than isolated clusters.

Clusters of galaxies in merging processing usually contain distinct subclusters, which are not dynamically relaxed. Here we work on 27 685 rich clusters with more than 30 member galaxies, decompose the subclusters, and finally obtain a coupling factor for overlapping subclusters in 7845 rich clusters.

Cluster merging at the post-collision stage is most intriguing for many aspects, e.g. dark matter distribution, electron acceleration, synchrotron radiation and the ICM heating (Markevitch et al., 2004; Feretti et al., 2012). Some post-collision clusters have been recognized previously from X-ray images based on highly elongated features, the shock front with a sharp edge of X-ray surface brightness, and the stripped gas tails (Markevitch & Vikhlinin, 2007; Russell et al., 2010; Menanteau et al., 2012; Jee et al., 2015). Here we identify post-collision merging clusters based on the two-dimensional distribution of member galaxies on the sky plane.

We present large samples of cluster mergers according to the optical properties of a large sample of galaxy clusters identified from the DESI Legacy Surveys data. By searching nearby clusters, we identify a sample of 39 382 partner clusters for 33 126 main clusters within a projected distance of 5 $r_{500}$. About 97% partners have a velocity difference of 1000 km s^-1 from the main clusters. For rich clusters with more than 30 member galaxies, we analyze the subclusters by smoothing the optical stellar mass distribution and then fit them with the dual-King model. We define the coupling factor to quantify the merging status for 7845 rich clusters. Based on the projected distribution of member galaxies, we further develop a new approach to recognize 3446 rich clusters with post-collision features, some of which have been validated by using X-ray images.

Such large samples of merging clusters of galaxies are important databases for studying the hierarchical structure formation, cluster evolution, and the physics of intergalactic medium. The partner systems are objects for the study of the process in the pre-merger stage, the material between clusters, and the structure formation. The mergers in the rich clusters can help to understand the violent process of cluster formation, diffuse radio emission, and properties of dark matter.

We thank the referee for valuable comments that helped to improve the paper. The authors are supported by the National Natural Science Foundation of China (Grant Numbers 11988101, 11833009 and 12073036), the Key Research Program of the Chinese Academy of Sciences (Grant Number QYZDJ-SSW-SLH021). We also acknowledge the support by the science research grants from the China Manned Space Project with Numbers CMS-CSST-2021-A01 and CMS-CSST-2021-B01.

The DESI Legacy Imaging Surveys consist of three individual and complementary projects: the Dark Energy Camera Legacy Survey (DECaLS), the Beijing-Arizona Sky Survey (BASS), and the Mayall z-band Legacy Survey (MzLS). DECaLS, BASS and MzLS together include data obtained, respectively, at the Blanco telescope, Cerro Tololo Inter-American Observatory, NSF’s NOIRLab; the Bok telescope, Steward Observatory, University of Arizona; and the Mayall telescope, Kitt Peak National Observatory, NOIRLab. NOIRLab is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. Pipeline processing and analyses of the data were supported by NOIRLab and the Lawrence Berkeley National Laboratory (LBNL). Legacy Surveys also uses data products from the Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE), a project of the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. Legacy Surveys was supported by: the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy; the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility; the U.S. National Science Foundation, Division of Astronomical Sciences; the National Astronomical Observatories of China, the Chinese Academy of Sciences and the Chinese National Natural Science Foundation. LBNL is managed by the Regents of the University of California under contract to the U.S. Department of Energy. The complete acknowledgments can be found at https://www.legacysurvey.org/acknowledgment/.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss4.org. SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, Center for Astrophysics — Harvard & Smithsonian (CfA), the Chilean Participation Group, the French Participation Group, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, the Korean Participation Group, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatório Nacional / MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

This work also uses observations obtained with XMM–Newton, an ESA science mission with instruments and contributions directly fundedby the ESA Member States and the National Aeronautics and Space Administration (NASA). This research has used data obtained from the Chandra Data Archive and the Chandra Source Catalogue, and software provided by the Chandra X-ray Center (CXC) in the application packages CIAO, CHIPS and SHERPA.

We publish the full tables for 33 126 cluster partner systems, 7845 clusters with distinct subclusters and 3446 post-collision mergers. They are also publicly available at http://zmtt.bao.ac.cn/galaxy_clusters/.