Distribution Of Galaxy Clusters Research Articles

The abundance and spatial distribution of ultra-diffuse galaxies in nearby galaxy clusters

Recent observations have highlighted a significant population of faint but large (r_eff>1.5 kpc) galaxies in the Coma cluster. The origin of these Ultra Diffuse Galaxies (UDGs) remains puzzling, as the interpretation of the observational results has been hindered by the subjective selection of UDGs, and the limited study of only the Coma (and some examples in the Virgo-) cluster. We extend the study of UDGs using 8 clusters in the redshift range 0.044<z<0.063 with deep g- and r-band imaging data taken with MegaCam at the CFHT. We describe an automatic selection pipeline for quantitative identification, tested for completeness using image simulations of these galaxies. We find that the abundance of the UDGs we can detect increases with cluster mass, reaching ~200 in typical haloes of M200~10^15 Msun. The cluster UDGs have colours consistent with the cluster red sequence, and have a steep size distribution that declines as n~r_eff^-3.4. Their radial distribution is significantly steeper than NFW in the outskirts, and is significantly shallower in the inner parts. They follow the same radial distribution as the more massive quiescent galaxies in the clusters, except within the core region of r<0.15XR200 (or <300 kpc). Within this region the number density of UDGs drops and is consistent with zero. These diffuse galaxies can only resist tidal forces down to this cluster-centric distance if they are highly centrally dark-matter dominated. The observation that the radial distribution of more compact dwarf galaxies (r_eff<1.0 kpc) with similar luminosities follows the same distribution as the UDGs, but exist down to a smaller distance of 100kpc from the cluster centres, indicates that they may have similarly massive sub-haloes as the UDGs. Although several scenarios can give rise to the UDG population, our results point to differences in the formation history as the most plausible explanation.

Redshifts distribution in A262

Galaxy clusters are the largest virialized systems in the Universe containing a collection of galaxies of dierent redshifts. The redshift distribution of galaxies in galaxy clusters is concentrated at a certain redshift range which remarkably tells us that only the galaxies in a certain radial range belong to the galaxy cluster. This leads to a boundary estimation of the cluster. Background and foreground systems are represented by a histogram that determines whether some of the galaxies are too far or too high in redshift to be counted as the member of the cluster. With the recent advances in multibre spectroscopy it has become possible to perform detailed analysis of the redshift distribution of several galaxy clusters in the Abell Catalogue. This has given rise to signicantly improved estimates of cluster membership, extent and dynamical history. Here we present a spectroscopic analysis of the galaxy cluster A262. We nd 55 galaxies fall within z = 0.0143 and 0.0183 with velocity range 4450 { 5300 km/s, and are therefore members of the cluster. We derived a new mean redshift of z = 0:016173 0:000074 (4852 22 km/s) for the system of which we compare with our neutral hydrogen (HI) detection which peaks at 4970 0:5 km/s. It is found that the distribution of HI tends to be located at the edge of the cluster since most of spiral rich galaxies were away from cluster center.

Galaxy sizes as a function of environment at intermediate redshift from the ESO Distant Cluster Survey

In order to assess whether the environment has a significant effect on galaxy sizes, we compare the mass--size relations of cluster and field galaxies in the $0.4 < z < 0.8$ redshift range from the ESO Distant Cluster Survey (EDisCS) using HST images. We analyse two mass-selected samples, one defined using photometric redshifts ($10.2 \le \log M_\ast/M_{\odot} \le 12.0$), and a smaller more robust subsample using spectroscopic redshifts ($10.6 \le \log M_\ast/M_{\odot} \le 11.8$). We find no significant difference in the size distributions of cluster and field galaxies of a given morphology. Similarly, we find no significant difference in the size distributions of cluster and field galaxies of similar rest-frame $B-V$ colours. We rule out average size differences larger than $10$--$20$\% in both cases. Consistent conclusions are found with the spectroscopic and photometric samples. These results have important consequences for the physical process(es) responsible for the size evolution of galaxies, and in particular the effect of the environment. The remarkable growth in galaxy size observed from $z\sim2.5$ has been reported to depend on the environment at higher redshifts ($z>1$), with early-type/passive galaxies in higher density environments growing earlier. Such dependence disappears at lower redshifts. Therefore, if the reported difference at higher-$z$ is real, the growth of field galaxies has caught up with that of cluster galaxies by $z\sim1$. Any putative mechanism responsible for galaxy growth has to account for the existence of environmental differences at high redshift and their absence (or weakening) at lower redshifts.

Mass and galaxy distributions of four massive galaxy clusters from Dark Energy Survey Science Verification data

We measure the weak-lensing masses and galaxy distributions of four massive galaxy clusters observed during the Science Verification phase of the Dark Energy Survey. This pathfinder study is meant to 1) validate the DECam imager for the task of measuring weak-lensing shapes, and 2) utilize DECam's large field of view to map out the clusters and their environments over 90 arcmin. We conduct a series of rigorous tests on astrometry, photometry, image quality, PSF modeling, and shear measurement accuracy to single out flaws in the data and also to identify the optimal data processing steps and parameters. We find Science Verification data from DECam to be suitable for the lensing analysis described in this paper. The PSF is generally well-behaved, but the modeling is rendered difficult by a flux-dependent PSF width and ellipticity. We employ photometric redshifts to distinguish between foreground and background galaxies, and a red-sequence cluster finder to provide cluster richness estimates and cluster-galaxy distributions. By fitting NFW profiles to the clusters in this study, we determine weak-lensing masses that are in agreement with previous work. For Abell 3261, we provide the first estimates of redshift, weak-lensing mass, and richness. In addition, the cluster-galaxy distributions indicate the presence of filamentary structures attached to 1E 0657-56 and RXC J2248.7-4431, stretching out as far as 1 degree (approximately 20 Mpc), showcasing the potential of DECam and DES for detailed studies of degree-scale features on the sky.

MC2: CONSTRAINING THE DARK MATTER DISTRIBUTION OF THE VIOLENT MERGING GALAXY CLUSTER CIZA J2242.8+5301 BY PIERCING THROUGH THE MILKY WAY

CIZA J2242.8+5301 is a merging system with a prominent (~2 Mpc long) radio relic, which together with the morphology of the X-ray emission provides strong evidence for a violent collision along the N-S axis. We present our constraints on the dark matter distribution of this unusual system using Subaru and CFHT imaging data. Measuring a high S/N lensing signal from this cluster is potentially a challenging task because of its proximity to the Milky Way plane (|b|~5 deg). We overcome this challenge with careful observation planning and systematics control, which enables us to successfully map the dark matter distribution of the cluster with high fidelity. The resulting mass map shows that the mass distribution is highly elongated along the N-S merger axis inferred from the orientation of the radio relics. Based on our mass reconstruction, we identify two sub-clusters, which coincide with the cluster galaxy distributions. We determine their masses using MCMC analysis by simultaneously fitting two NFW halos without fixing their centroids. The resulting masses of the northern and southern systems are $M_{200}=11.0_{-3.2}^{+3.7}\times10^{14} M_{\sun}$ and $9.8_{-2.5}^{+3.8}\times10^{14} M_{\sun}$, respectively, indicating that we are witnessing a post-collision of two giant systems of nearly equal mass. When the mass and galaxy centroids are compared in detail, we detect ~ 1' (~190 kpc) offsets in both northern and southern sub-clusters. We find that the galaxy luminosity-mass offset for the northern clump is statistically significant at the ~2 sigma level whereas the detection is only marginal for the southern sub-cluster in part because of a relatively large mass centroid error. We conclude that it is yet premature to uniquely attribute the galaxy-mass misalignment to SIDM and discuss caveats.

Hubble Frontier Fields: the geometry and dynamics of the massive galaxy cluster merger MACSJ0416.1-2403

We use a joint optical/X-ray analysis to constrain the geometry and history of the ongoing merging event in the massive galaxy cluster MACSJ0416.1−2403 (z = 0.397). Our investigation of cluster substructure rests primarily on a combined strong- and weak-lensing mass reconstruction based on the deep, high-resolution images obtained for the Hubble Frontier Fields initiative. To reveal the system's dynamics, we complement this lensing analysis with a study of the intracluster gas using shallow Chandra data, and a three-dimensional model of the distribution and motions of cluster galaxies derived from over 100 spectroscopic redshifts. The multiscale grid model obtained from our combined lensing analysis extends the high-precision strong-lensing mass reconstruction recently performed to cluster-centric distances of almost 1 Mpc. Our analysis detects the two well-known mass concentrations in the cluster core. A pronounced offset between collisional and collisionless matter is only observed for the SW cluster component, while excellent alignment is found for the NE cluster. Both the lensing analysis and the distribution of cluster light strongly suggest the presence of a third massive structure, almost 2 arcmin SW of the cluster centre. Since no X-ray emission is detected in this region, we conclude that this structure is non-virialized and speculate that it might be part of a large-scale filament almost aligned with our line of sight. Combining all evidence from the distribution of dark and luminous matter, we propose two alternative scenarios for the trajectories of the components of MACSJ0416.1−2403. Upcoming deep X-ray observations that allow the detection of shock fronts, cold cores, and sloshing gas (all key diagnostics for studies of cluster collisions) will allow us to test, and distinguish between these two scenarios.

Characterising superclusters with the galaxy cluster distribution

Superclusters are the largest, observed matter density structures in the Universe. Recently Chon et al.(2013) presented the first supercluster catalogue constructed with a well-defined selection function based on the X-ray flux-limited cluster survey, REFLEX II. For the construction of the sample we proposed a concept to find the large objects with a minimum overdensity such that most of their mass will collapse in the future. The main goal of the paper is to provide support for our concept using simulations that we can, on the basis of our observational sample of X-ray clusters, construct a supercluster sample defined by a certain minimum overdensity, and to test how superclusters trace the underlying dark matter distribution. Our results confirm that an overdensity in the number of clusters is tightly correlated with an overdensity of the dark matter distribution. This enables us to define superclusters such that most of the mass will collapse in the future and to get first-order mass estimates of superclusters on the basis of the properties of the member clusters. We also show that in this context the ratio of the cluster number density and dark matter mass density is consistent with the theoretically expected cluster bias. Our previous work provided evidence that superclusters are a special environment for density structures of the dark matter to grow differently from the field as characterised by the X-ray luminosity function. Here we confirm for the first time that this originates from a top-heavy mass function at high statistical significance provided by a Kolmogorov-Smirnov test. We also find in close agreement with observations that the superclusters occupy only a small volume of few percent while they contain more than half of the clusters in the present day Universe.

Constraining galaxy cluster temperatures and redshifts with eROSITA survey data

Context. The nature of dark energy is imprinted in the large-scale structure of the Universe and thus in the mass and redshift distribution of galaxy clusters. The upcoming eROSITA instrument will exploit this method of probing dark energy by detecting ~100 000 clusters of galaxies in X-rays.

Bayesian Cosmic Web Reconstruction: BARCODE for Clusters

AbstractWe describe the Bayesian \barcode\ formalism that has been designed towards the reconstruction of the Cosmic Web in a given volume on the basis of the sampled galaxy cluster distribution. Based on the realization that the massive compact clusters are responsible for the major share of the large scale tidal force field shaping the anisotropic and in particular filamentary features in the Cosmic Web. Given the nonlinearity of the constraints imposed by the cluster configurations, we resort to a state-of-the-art constrained reconstruction technique to find a proper statistically sampled realization of the original initial density and velocity field in the same cosmic region. Ultimately, the subsequent gravitational evolution of these initial conditions towards the implied Cosmic Web configuration can be followed on the basis of a proper analytical model or an N-body computer simulation. The BARCODE formalism includes an implicit treatment for redshift space distortions. This enables a direct reconstruction on the basis of observational data, without the need for a correction of redshift space artifacts. In this contribution we provide a general overview of the the Cosmic Web connection with clusters and a description of the Bayesian BARCODE formalism. We conclude with a presentation of its successful workings with respect to test runs based on a simulated large scale matter distribution, in physical space as well as in redshift space.

Properties of galaxies reproduced by a hydrodynamic simulation.

Previous simulations of the growth of cosmic structures have broadly reproduced the 'cosmic web' of galaxies that we see in the Universe, but failed to create a mixed population of elliptical and spiral galaxies, because of numerical inaccuracies and incomplete physical models. Moreover, they were unable to track the small-scale evolution of gas and stars to the present epoch within a representative portion of the Universe. Here we report a simulation that starts 12 million years after the Big Bang, and traces 13 billion years of cosmic evolution with 12 billion resolution elements in a cube of 106.5 megaparsecs a side. It yields a reasonable population of ellipticals and spirals, reproduces the observed distribution of galaxies in clusters and characteristics of hydrogen on large scales, and at the same time matches the 'metal' and hydrogen content of galaxies on small scales.

WEIGHING “EL GORDO” WITH A PRECISION SCALE:HUBBLE SPACE TELESCOPEWEAK-LENSING ANALYSIS OF THE MERGING GALAXY CLUSTER ACT-CL J0102–4915 ATz= 0.87

(Abridged) We present a HST weak-lensing study of the merging galaxy cluster "El Gordo" (ACT-CL J0102-4915) at z=0.87 discovered by the Atacama Cosmology Telescope collaboration as the strongest SZ decrement in its ~1000 sq. deg survey. Our weak-lensing analysis confirms that ACT-CL J0102-4915 is indeed an extreme system consisting of two massive (~10^15 Msun each) subclusters with a projected separation of ~0.7 Mpc. This binary mass structure revealed by our lensing study is consistent with the cluster galaxy distribution and the dynamical study carried out with 89 spectroscopic members. We estimate the mass of ACT-CL J0102-4915 by simultaneously fitting two axisymmetric NFW profiles allowing their centers to vary. Our MCMC analysis shows that the masses of the northwestern (NW) and the southeastern (SE) components are M200c=(1.38+-0.22) x 10^15 Msun and (0.78+-0.20) x 10^15 Msun, respectively. The lensing-based velocity dispersions are consistent with their spectroscopic measurements. The centroids of both components are tightly constrained (~4") and close to the optical luminosity centers. The X-ray and mass peaks are spatially offset by ~8" (~62 kpc), which is significant at the ~2 sigma confidence level and confirms that the baryonic and dark matter in this cluster are disassociated. The dark matter peak, however, does not lead the gas peak in the direction expected if we are viewing the cluster soon after first core passage during a high speed merger. Under the assumption that the merger is happening in the plane of the sky, extrapolation of the two NFW halos to a radius r200a=2.4 Mpc yields a combined mass of M200a=(3.13+-0.56) x 10^15 Msun. This extrapolated total mass is consistent with our two-component-based dynamical analysis and previous X-ray measurements, projecting ACT-CL J0102-4915 to be the most massive cluster at z>0.6 known to date.

What can the spatial distribution of galaxy clusters tell about their scaling relations?

We aim to quantify the capability of the inhomogeneous distribution of galaxy clusters, represented by the two-point statistics in Fourier space, to retrieve information on the underlying scaling relations. We make a case study using the mass X-ray luminosity scaling relation for galaxy clusters and study its impact on the clustering pattern of these objects. We define the luminosity-weighted power spectrum and introduce the luminosity power spectrum as direct assessment of the clustering of the property of interest, in our case, the cluster X-ray luminosity. Using a suite of halo catalogs extracted from N-body simulations and realistic estimates of the mass X-ray luminosity relation, we measured these statistics with their corresponding covariance matrices. By carrying out a Fisher matrix analysis, we quantified the content of information (by means of a figure-of merit) encoded in the amplitude, shape, and full shape of our probes for two-point statistics. The full shape of the luminosity power spectrum, when analyzed up to scales of k~0.2 h/Mpc, yields a figure of merit which is two orders of magnitude above the figure obtained from the unweighted power spectrum, and only one order of magnitude below the value encoded in X-ray luminosity function estimated from the same sample. This is a significant improvement over the analysis developed with the standard (i.e., unweighted) clustering probes. The measurements of the clustering of galaxy clusters and its explicit dependence on the cluster intrinsic properties can contribute to improving the degree of knowledge regarding the underlying links between cluster observables and the cluster masses (Abridged).

Photometric studies of Abell 1664: the subtle effect a minor merger has on cluster galaxies

A combination of $BRI$ photometry and archival Chandra X-ray data have been used to analyse the effects a minor merger has on the galaxy population of A1664. We utilise adaptive smoothing techniques in the 2D spatial distribution of cluster galaxies to reveal substructure $\sim$ 800 kpc South of the cluster core. We identify this substructure as most likely the remnant core of a merging group which has passed pericentre and responsible for triggering a cold front in the cluster core. We define two samples to represent two different environments within A1664 in accordance with the location of the substructure. We apply a morphological analysis using CAS, M$_{20}$ and Gini to these samples to deduce if there has been any significant effect on the cluster galaxies due to this interaction. We find there are more asymmetric galaxies found in the inner sample (at the 3.7$\sigma$ level) which is likely due to galaxy-galaxy interactions as the merging group passed through core passage. No other differences were found between the inner and outer cluster in our morphological analysis, which we attribute to the limited resolution of our imagery. The colour profiles of the galaxies are found to be consistent with the morphology-density relation suggesting there is no unique environmental effect in A1664 that has enhanced galaxy transformations. This study favours the star formation of cluster galaxies being quenched well before it is able to interact with the merging group and demonstrates that a minor cluster merger has little effect on the observable parameters of cluster galaxies such as morphology and colour.

HUBBLE SPACE TELESCOPE/ADVANCED CAMERA FOR SURVEYS CONFIRMATION OF THE DARK SUBSTRUCTURE IN A520

We present the results from a weak gravitational lensing study of the merging cluster A520 based on the analysis of Hubble Space Telescope/Advanced Camera for Surveys (ACS) data. The excellent data quality allows us to reach a mean number density of source galaxies of ~109 per sq. arcmin, which improves both resolution and significance of the mass reconstruction compared to a previous study based on Wide Field Planetary Camera 2 (WFPC2) images. We take care in removing instrumental effects such as the trailing of charge due to radiation damage of the ACS detector and the position-dependent point spread function (PSF). This new ACS analysis confirms the previous claims that a substantial amount of dark mass is present between two luminous subclusters. We examine the distribution of cluster galaxies and observe very little light at this location. We find that the centroid of the dark peak in the current ACS analysis is offset to the southwest by ~1 arcmin with respect to the centroid from the WFPC2 analysis. Interestingly, this new centroid is in better spatial agreement with the location where the X-ray emission is strongest, and the mass-to-light ratio estimated with this centroid is much higher 813+-78 M_sun/L_Rsun than the previous value; the aperture mass based on the WFPC2 centroid provides a slightly lower, but consistent mass. Although we cannot provide a definite explanation for the presence of the dark peak, we discuss a revised scenario, wherein dark matter with a more conventional range sigma_DM/m_DM < 1 cm^2/g of self-interacting cross-section can lead to the detection of this dark substructure. If supported by detailed numerical simulations, this hypothesis opens up the possibility that the A520 system can be used to establish a lower limit of the self-interacting cross-section of dark matter.

NoSOCS in SDSS

We investigate relations between the color and luminosity distributions of cluster galaxies and the evolutionary state of their host clusters. Our aim is to explore some aspects of cluster galaxy evolution and the dynamical state of clusters as two sides of the same process. We used 10,721 member galaxies of 183 clusters extracted from the Sloan Digital Sky Survey using a list of NoSOCS and CIRS targets. First, we classified the clusters into two categories, Gaussian and non-Gaussian, according to their velocity distribution measurements, which we used as an indicator of their dynamical state. We then used objective criteria to split up galaxies according to their luminosities, colors, and photometric mean stellar age. This information was then used to evaluate how galaxies evolve in their host clusters. Meaningful color gradients, i.e., the fraction of red galaxies as a function of radius from the center, are observed for both the Gaussian velocity distribution and the non-Gaussian velocity distribution cluster subsamples, which suggests that member galaxy colors change on a shorter timescale than the time needed for the cluster to reach dynamical equilibrium. We also found that larger portions of fainter red galaxies are found, on average, in smaller radii. The luminosity function in Gaussian clusters has a brighter characteristic absolute magnitude and a steeper faint-end slope than it does in the non-Gaussian velocity distribution clusters. Our findings suggest that cluster galaxies experience intense color evolution before virialization, while the formation of faint galaxies through dynamical interactions probably takes place on a longer timescale, possibly longer than the virialization time.

AN EXAMINATION OF THE OPTICAL SUBSTRUCTURE OF GALAXY CLUSTERS HOSTING RADIO SOURCES

Using radio sources from the Faint Images of the Radio Sky at Twenty-cm (FIRST) survey, and optical counterparts in the Sloan Digital Sky Survey (SDSS), we have identified a large number of galaxy clusters. The radio sources within these clusters are driven by active galactic nuclei, and our cluster samples include clusters with bent, and straight, double-lobed radio sources. We also included a single-radio-component comparison sample. We examine these galaxy clusters for evidence of optical substructure, testing the possibility that bent double-lobed radio sources are formed as a result of large-scale cluster mergers. We use a suite of substructure analysis tools to determine the location and extent of substructure visible in the optical distribution of cluster galaxies, and compare the rates of substructure in clusters with different types of radio sources. We found no preference for significant substructure in clusters hosting bent double-lobed radio sources compared to those with other types of radio sources.

A MULTI-WAVELENGTH STUDY OF LOW-REDSHIFT CLUSTERS OF GALAXIES. II. ENVIRONMENTAL IMPACT ON GALAXY GROWTH

Galaxy clusters provide powerful laboratories for the study of galaxy evolution, particularly the origin of correlations of morphology and star formation rate (SFR) with density. We construct visible to MIR spectral energy distributions (SEDs) of cluster galaxies and use them to measure stellar masses and SFRs in eight low redshift clusters, which we examine as a function of environment. A partial correlation analysis indicates that SFR depends strongly on R/R200 (>99.9% confidence) and is independent of projected local density at fixed radius. SFR also shows no residual dependence on stellar mass. We therefore conclude that interactions with the intra-cluster medium drive the evolution of SFRs in cluster galaxies. A merged sample of galaxies from the five most complete clusters shows <SFR>\propto(R/R200)^(1.3+/-0.7) for galaxies with R/R200<0.4. A decline in the fraction of SFGs toward the cluster center contributes most of this effect, but it is accompanied by a reduction in SFRs among star-forming galaxies (SFGs) near the cluster center. The increase in the fraction of SFGs toward larger R/R200 and the isolation of SFGs with reduced SFRs near the cluster center are consistent with ram pressure stripping as the mechanism to truncate star formation in galaxy clusters. We conclude that stripping drives the properties of SFGs over the range of radii we examine. We also find that galaxies near the cluster center are more massive than galaxies farther out in the cluster at ~3.5\sigma, which suggests that cluster galaxies experience dynamical relaxation during the course of their evolution.

The radial distribution of galaxies in groups and clusters

We present a new catalogue of 55,121 groups and clusters centred on Luminous Red Galaxies from SDSS DR7 in the redshift range 0.15<z<0.4. We provide halo mass estimates for each of these groups derived from a calibration between the optical richness of bright galaxies (M_r<-20.5) within 1 Mpc, and X-ray-derived mass for a small subset of 129 groups and clusters with X-ray measurements. We derive the mean (stacked) surface number density profiles of galaxies as a function of total halo mass in different mass bins. We find that derived profiles can be well-described by a projected NFW profile with a concentration parameter (<c>~2.6) that is approximately a factor of two lower than that of the dark matter (as predicted by N-body cosmological simulations) and nearly independent of halo mass. Interestingly, in spite of the difference in shape between the galaxy and dark matter radial distributions, both exhibit a high degree of self-similarity. A self-consistent comparison to several recent semi-analytic models of galaxy formation indicates that: (1) beyond ~0.3 r_500 current models are able to reproduce both the shape and normalisation of the satellite profiles; and (2) within ~0.3 r_500 the predicted profiles are sensitive to the details of the satellite-BCG merger timescale calculation. The former is a direct result of the models being tuned to match the global galaxy luminosity function combined with the assumption that the satellite galaxies do not suffer significant tidal stripping, even though their surrounding dark matter haloes can be removed through this process. Combining our results with measurements of the intracluster light should provide a way to inform theoretical models on the efficacy of the tidal stripping and merging processes.

Multimodality in galaxy clusters from SDSS DR8: substructure and velocity distribution

We search for the presence of substructure, a non-Gaussian, asymmetrical velocity distribution of galaxies, and large peculiar velocities of the main galaxies in galaxy clusters with at least 50 member galaxies, drawn from the SDSS DR8. We employ a number of 3D, 2D, and 1D tests to analyse the distribution of galaxies in clusters: 3D normal mixture modelling, the Dressler-Shectman test, the Anderson-Darling and Shapiro-Wilk tests and others. We find the peculiar velocities of the main galaxies, and use principal component analysis to characterise our results. More than 80% of the clusters in our sample have substructure according to 3D normal mixture modelling, the Dressler-Shectman (DS) test shows substructure in about 70% of the clusters. The median value of the peculiar velocities of the main galaxies in clusters is 206 km/s (41% of the rms velocity). The velocities of galaxies in more than 20% of the clusters show significant non-Gaussianity. While multidimensional normal mixture modelling is more sensitive than the DS test in resolving substructure in the sky distribution of cluster galaxies, the DS test determines better substructure expressed as tails in the velocity distribution of galaxies. Richer, larger, and more luminous clusters have larger amount of substructure and larger (compared to the rms velocity) peculiar velocities of the main galaxies. Principal component analysis of both the substructure indicators and the physical parameters of clusters shows that galaxy clusters are complicated objects, the properties of which cannot be explained with a small number of parameters or delimited by one single test. The presence of substructure, the non-Gaussian velocity distributions, as well as the large peculiar velocities of the main galaxies, shows that most of the clusters in our sample are dynamically young.

Cross-correlating the thermal Sunyaev-Zel’dovich effect and the distribution of galaxy clusters

We present the analytical formulas, derived based on the halo model, to compute the cross-correlation between the thermal Sunyaev-Zel'dovich (SZ) effect and the distribution of galaxy clusters. By binning the clusters according to their redshifts and masses, this cross-correlation, the so-called stacked SZ signal, reveals the average SZ profile around the clusters. The stacked SZ signal is obtainable from a joint analysis of an arcminute-resolution cosmic microwave background (CMB) experiment and an overlapping optical survey, which allows for detection of the SZ signals for clusters whose masses are below the individual cluster detection threshold. We derive the error covariance matrix for measuring the stacked SZ signal, and then forecast for its detection from ongoing and forthcoming combined CMB-optical surveys. We find that, over a wide range of mass and redshift, the stacked SZ signal can be detected with a significant signal to noise ratio (total S/N \gsim 10), whose value peaks for the clusters with intermediate masses and redshifts. Our calculation also shows that the stacking method allows for probing the clusters' SZ profiles over a wide range of scales, even out to projected radii as large as the virial radius, thereby providing a promising way to study gas physics at the outskirts of galaxy clusters.