Shape Of Galaxy Clusters Research Articles

CHEX-MATE: CLUster Multi-Probes in Three Dimensions (CLUMP-3D). I. Gas analysis method using X-ray and Sunyaev–Zel’dovich effect data

Galaxy clusters are the products of structure formation through myriad physical processes that affect their growth and evolution throughout cosmic history. As a result, the matter distribution within galaxy clusters, or their shape, is influenced by cosmology and astrophysical processes, in particular the accretion of new material due to gravity. We introduce an analysis method for investigating the three-dimensional triaxial shapes of galaxy clusters from the Cluster HEritage project with -- Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE). In this paper, the first in a CHEX-MATE triaxial analysis series, we focus on utilizing X-ray data from and Sunyaev-Zel'dovich (SZ) effect maps from and the Atacama Cosmology Telescope to obtain a three-dimensional triaxial description of the intracluster medium (ICM) gas. We present the forward modeling formalism of our technique, which projects a triaxial ellipsoidal model for the gas density and pressure, to be compared directly with the observed two-dimensional distributions in X-rays and the SZ effect. A Markov chain Monte Carlo is used to estimate the posterior distributions of the model parameters. Using mock X-ray and SZ observations of a smooth model, we demonstrate that the method can reliably recover the true parameter values. In addition, we applied the analysis to reconstruct the gas shape from the observed data of one CHEX-MATE galaxy cluster, PSZ2 G313.33+61.13 (Abell 1689), to illustrate the technique. The inferred parameters are in agreement with previous analyses for the cluster, and our results indicate that the geometrical properties, including the axial ratios of the ICM distribution, are constrained to within a few percent. With a much better precision than previous studies, we thus further establish that Abell 1689 is significantly elongated along the line of sight, resulting in its exceptional gravitational lensing properties.

Why weak lensing cluster shapes are insensitive to self-interacting dark matter

ABSTRACT We investigate whether the shapes of galaxy clusters inferred from weak gravitational lensing can be used as a test of the nature of dark matter. We analyse mock weak lensing data, with gravitational lenses extracted from cosmological simulations run with two different dark matter models: cold dark matter (CDM) and self-interacting dark matter (SIDM). We fit elliptical Navarro–Frenk–White profiles to the shear fields of the simulated clusters. Despite large differences in the distribution of 3D shapes between CDM and SIDM, we find that the distributions of weak-lensing-inferred cluster shapes are almost indistinguishable. We trace this information loss to two causes. First, weak lensing measures the shape of the projected mass distribution, not the underlying 3D shape, and projection effects wash out some of the difference. Secondly, weak lensing is most sensitive to the projected shape of clusters, on a scale approaching the virial radius ($\sim\! 1.5 \mathrm{\, Mpc}$), whereas SIDM shapes differ most from CDM in the inner halo. We introduce a model for the mass distribution of galaxy clusters where the ellipticity of the mass distribution can vary with distance to the centre of the cluster. While this mass distribution does not enable weak lensing data to distinguish between CDM and SIDM with cluster shapes (the ellipticity at small radii is poorly constrained by weak lensing), it could be useful when modelling combined strong and weak gravitational lensing of clusters.

Accurate dark-matter halo elongation from weak-lensing stacking analysis

ABSTRACT Shape estimates that quantifying the halo anisotropic mass distribution are valuable parameters that provide information on their assembly process and evolution. Measurements of the mean shape estimates for a sample of cluster-sized haloes can be used to test halo formation scenarios, as well as improving the modelling of potential biases in constraining cosmological parameters using these systems. In this work, we test the recovery of halo cluster shapes and masses applying weak-lensing stacking techniques. To this end, we use lensing shear and a new dark-matter halo catalogue, derived from the light-cone output of the cosmological simulation MICE-GC. We perform this study by combining the lensing signals obtained for several samples of haloes, selected according to their mass and redshift, taking into account the main directions of the dark-matter distributions. In the analysis, we test the impact of several potential introduced systematics, such as the adopted modelling, the contribution of the neighbouring mass distribution, miscentring, and misalignment effects. Our results show that when some considerations regarding the halo relaxation state are taken into account, the lensing semi-axial ratio estimates are in agreement within a 5 per cent with the mean shapes of the projected dark-matter particle distribution of the stacked haloes. The presented methodology provides a useful tool to derive reliable shapes of galaxy clusters and to contrast them with those expected from numerical simulations. Furthermore, our proposed modelling, that takes into account the contribution of neighbouring haloes, allows to constraint the elongation of the surrounding mass distribution.

Triaxiality in galaxy clusters: Mass versus potential reconstructions

Context. Accounting for the triaxial shapes of galaxy clusters will become important in the context of upcoming cosmological surveys. This will provide a challenge given that the density distribution of gas cannot be described by simple geometrical models without loss of information. Aims. We investigate the effects of simple 3D models on cluster gravitational potentials and gas density distribution to determine which of these quantities is most suitable and appropriate for characterising galaxy clusters in cosmological studies. Methods. We use a statistical sample of 85 galaxy clusters from a large cosmological N-body + hydrodynamical simulation to investigate cluster shapes as a function of radius for both gas density and potential. We examine how the resulting parameters are affected by the substructure removal (for the gas density) and by the definition of the computation volume (interior vs. shells). Results. We find that the orientation and axis ratio of gas isodensity contours are degenerate with the presence of substructures and are unstable against fluctuations. Moreover, as the derived cluster shape depends on the method used for removing the substructures, thermodynamic properties extracted from the X-ray emissivity profile, for example, suffer from this additional and often underestimated bias. In contrast, the shapes of the smooth cluster potentials are less affected by fluctuations and converge towards simple geometrical models, both in the case of relaxed and dynamically active clusters. Conclusions. The observation that cluster potentials can be represented better by simple geometrical models and reconstructed with a lower level of systematic error for both dynamically active and relaxed clusters suggests that characterising galaxy clusters by their potential is a promising alternative to using cluster masses in cluster cosmology. With this approach, dynamically active and relaxed clusters could be combined in cosmological studies, improving statistics and lowering scatter.

Halo cluster shapes: insights from simulated galaxies and ICL with prospects for weak lensing applications

ABSTRACT We present a detailed study of the shapes and alignments of different galaxy cluster components using hydrodynamical simulations. We compute shape parameters from the dark matter (DM) distribution, the galaxy members and the intracluster light (ICL). We assess how well the DM cluster shape can be constrained by means of the identified galaxy member positions and the ICL. Further, we address the dilution factor introduced when estimating the cluster elongation using weak-lensing stacking techniques, which arises due to the misalignment between the total surface mass distribution and the distribution of luminous tracers. The dilution is computed considering the alignment between the DM and the brightest cluster galaxy, the galaxy members and the ICL. Our study shows that distributions of galaxy members and ICL are less spherical than the DM component, although both are well aligned with the semimajor axis of the latter. We find that the distribution of galaxy members hosted in more concentrated subhaloes is more elongated than the distribution of the DM. Moreover, these galaxies are better aligned with the DM component compared to the distribution of galaxies hosted in less concentrated subhaloes. We conclude that the positions of galaxy members can be used as suitable tracers to estimate the cluster surface density orientation, even when a low number of members is considered. Our results provide useful information for interpreting the constraints on the shapes of galaxy clusters in observational studies.

The probability distribution of 3D shapes of galaxy clusters from 2D X-ray images

ABSTRACT We present a new method to determine the probability distribution of the 3D shapes of galaxy clusters from the 2D images using stereology. In contrast to the conventional approach of combining different data sets (such as X-rays, Sunyaev–Zeldovich effect, and lensing) to fit a 3D model of a galaxy cluster for each cluster, our method requires only a single data set, such as X-ray observations or Sunyaev–Zeldovich effect observations, consisting of sufficiently large number of clusters. Instead of reconstructing the 3D shape of an individual object, we recover the probability distribution function (PDF) of the 3D shapes of the observed galaxy clusters. The shape PDF is the relevant statistical quantity, which can be compared with the theory and used to test the cosmological models. We apply this method to publicly available Chandra X-ray data of 89 well-resolved galaxy clusters. Assuming ellipsoidal shapes, we find that our sample of galaxy clusters is a mixture of prolate and oblate shapes, with a preference for oblateness with the most probable ratio of principle axes 1.4 : 1.3 : 1. The ellipsoidal assumption is not essential to our approach and our method is directly applicable to non-ellipsoidal shapes. Our method is insensitive to the radial density and temperature profiles of the cluster. Our method is sensitive to the changes in shape of the X-ray emitting gas from inner to outer regions and we find evidence for variation in the 3D shape of the X-ray emitting gas with distance from the centre.

Reconciling galaxy cluster shapes, measured by theorists versus observers

ABSTRACT If properly calibrated, the shapes of galaxy clusters can be used to investigate many physical processes: from feedback and quenching of star formation, to the nature of dark matter. Theorists frequently measure shapes using moments of inertia of simulated particles’. We instead create mock (optical, X-ray, strong-, and weak-lensing) observations of the 22 most massive ($\sim 10^{14.7}\, \mathrm{ M}_\odot$) relaxed clusters in the BAHAMAS simulations. We find that observable measures of shape are rounder. Even when moments of inertia are projected into 2D and evaluated at matched radius, they overestimate ellipticity by 56 per cent (compared to observable strong lensing) and 430 per cent (compared to observable weak lensing). Therefore, we propose matchable quantities and test them using observations of eight relaxed clusters from the Hubble Space Telescope (HST) and Chandra X-Ray Observatory. We also release our HST data reduction and lensing analysis software to the community. In real clusters, the ellipticity and orientation angle at all radii are strongly correlated. In simulated clusters, the ellipticity of inner (<rvir/20) regions becomes decoupled: for example, with greater misalignment of the central cluster galaxy. This may indicate overly efficient implementation of feedback from active galactic nuclei. Future exploitation of cluster shapes as a function of radii will require better understanding of core baryonic processes. Exploitation of shapes on any scale will require calibration on simulations extended all the way to mock observations.

Deep learning for Sunyaev–Zel’dovich detection in Planck

The Planck collaboration has extensively used the six Planck HFI frequency maps to detect the Sunyaev–Zel’dovich (SZ) effect with dedicated methods, for example by applying (i) component separation to construct a full-sky map of the y parameter or (ii) matched multi-filters to detect galaxy clusters via their hot gas. Although powerful, these methods may still introduce biases in the detection of the sources or in the reconstruction of the SZ signal due to prior knowledge (e.g. the use of the generalised Navarro, Frenk, and White profile model as a proxy for the shape of galaxy clusters, which is accurate on average but not for individual clusters). In this study, we use deep learning algorithms, more specifically, a U-net architecture network, to detect the SZ signal from the Planck HFI frequency maps. The U-net shows very good performance, recovering the Planck clusters in a test area. In the full sky, Planck clusters are also recovered, together with more than 18 000 other potential SZ sources for which we have statistical indications of galaxy cluster signatures, by stacking at their positions several full-sky maps at different wavelengths (i.e. the cosmic microwave background lensing map from Planck, maps of galaxy over-densities, and the ROSAT X-ray map). The diffuse SZ emission is also recovered around known large-scale structures such as Shapley, A399–A401, Coma, and Leo. Results shown in this proof-of-concept study are promising for potential future detection of galaxy clusters with low SZ pressure with this kind of approach, and more generally, for potential identification and characterisation of large-scale structures of the Universe via their hot gas.

Intrinsic alignment of redMaPPer clusters: cluster shape–matter density correlation

We measure the alignment of the shapes of galaxy clusters, as traced by their satellite distributions, with the matter density field using the public redMaPPer catalogue based on SDSS-DR8, which contains 26 111 clusters up to z~0.6. The clusters are split into nine redshift and richness samples; in each of them we detect a positive alignment, showing that clusters point towards density peaks. We interpret the measurements within the tidal alignment paradigm, allowing for a richness and redshift dependence. The intrinsic alignment (IA) amplitude at the pivot redshift z=0.3 and pivot richness \lambda=30 is A_{IA}^{gen}=12.6_{-1.2}^{+1.5}. We obtain tentative evidence that the signal increases towards higher richness and lower redshift. Our measurements agree well with results of maxBCG clusters and with dark-matter-only simulations. Comparing our results to IA measurements of luminous red galaxies, we find that the IA amplitude of galaxy clusters forms a smooth extension towards higher mass. This suggests that these systems share a common alignment mechanism, which can be exploited to improve our physical understanding of IA.

The Evolving Shape of Galaxy Clusters

AbstractWe present the first measurement of the evolution of the apparent projected shape of galaxy clusters from 0.2≲ z≲2. We measure the ellipticities (εcl) of homogeneously selected galaxy clusters over this wide redshift range. We confirm the predictions of N-body simulations that clusters are more elongated at higher redshift, finding the mean projected ellipticity changes linearly from 0.36±0.01 to 0.25±0.01 over that range. The fraction of relaxed clusters (defined as having εcl<0.2) is 9+5-3% at z∼1.8, steadily increasing to 42+7-6% by z∼0.3. Because more spherical clusters have a higher degree of virialization, our result shows significant evolution in the degree of cluster virialization over cosmic time.

AN IMPROVED METHOD TO TEST THE DISTANCE-DUALITY RELATION

Many researchers have performed cosmological-model-independent tests for the distance duality (DD) relation. Theoretical work has been conducted based on the results of these tests. However, we find that almost all of these tests were perhaps not cosmological-model-independent after all, because the distance moduli taken from a given type Ia supernovae (SNe Ia) compilation are dependent on a given cosmological model and Hubble constant. In this Letter, we overcome these defects and by creating a new cosmological-model-independent test for the DD relation. We use the original data from the Union2 SNe Ia compilation and the angular diameter distances from two galaxy cluster samples compiled by De Filippis et al. and Bonamente et al. to test the DD relation. Our results suggest that the DD relation is compatible with observations, and the spherical model is slightly better than the elliptical model at describing the intrinsic shape of galaxy clusters if the DD relation is valid. However, these results are different from those of previous work.

The Three-Dimensional Shapes of Galaxy Clusters

While clusters of galaxies are considered one of the most important cosmological probes, the standard spherical modelling of the dark matter and the intracluster medium is only a rough approximation. Indeed, it is well established both theoretically and observationally that galaxy clusters are much better approximated as triaxial objects. However, investigating the asphericity of galaxy clusters is still in its infancy. We review here this topic which is currently gathering a growing interest from the cluster community. We begin by introducing the triaxial geometry. Then we discuss the topic of deprojection and demonstrate the need for combining different probes of the cluster's potential. We discuss the different works that have been addressing these issues. We present a general parametric framework intended to simultaneously fit complementary data sets (X-ray, Sunyaev Zel'dovich and lensing data). We discuss in details the case of Abell 1689 to show how different models/data sets lead to different haloe parameters. We present the results obtained from fitting a 3D NFW model to X-ray, SZ, and lensing data for 4 strong lensing clusters. We argue that a triaxial model generally allows to lower the inferred value of the concentration parameter compared to a spherical analysis. This may alleviate tensions regarding, e.g. the over-concentration problem. However, we stress that predictions from numerical simulations rely on a spherical analysis of triaxial halos. Given that triaxial analysis will have a growing importance in the observational side, we advocate the need for simulations to be analysed in the very same way, allowing reliable and meaningful comparisons. Besides, methods intended to derive the three dimensional shape of galaxy clusters should be extensively tested on simulated multi-wavelength observations.

On mass and shape of galaxy clusters by comparison of X‐ray, Sunyaev‐Zel'dovich effect, and gravitational lensing observations

AbstractThe accurate determination of the mass of galaxy clusters is crucial to precision astronomy. We have often to deal with either biased measurements or precise determinations of peculiar quantities. A better understanding of intrinsic shapes plays a major role. We consider how the shape of the intracluster medium (ICM) can be inferred by combining X‐ray photometry and spectroscopy with the measurement of the Sunyaev‐Zel'dovich effect (SZe). Together with gravitational lensing (GL), we can get unbiased estimates of mass and concentration and probe the hydrodynamical properties of the cluster. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Cosmic distance duality relation and the shape of galaxy clusters

Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, D_L(z) (1 + z)^{2}/D_{A}(z) = 1, an exact result required by the Etherington reciprocity theorem where D_L(z) and D_A(z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts D_A(z) = D_L(z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine D_A(z)from galaxy clusters. This combination offers the possibility of testing the validity of the DD relation, as well as determining which physical processes occur in galaxy clusters via their shapes. We use WMAP (7 years) results by fixing the conventional LCDM model to verify the consistence between the validity of DD relation and different assumptions about galaxy cluster geometries usually adopted in the literature. We assume that $\eta$ is a function of the redshift parametrized by two different relations: \eta(z) = 1 + \eta_{0}z, and \eta(z)=1 + \eta_{0}z/(1+z), where \eta_0 is a constant parameter quantifying the possible departure from the strict validity of the DD relation. In order to determine the probability density function (PDF) of \eta_{0}, we consider the angular diameter distances from galaxy clusters recently studied by two different groups by assuming elliptical (isothermal) and spherical (non-isothermal) $\beta$ models. The strict validity of the DD relation will occur only if the maximum value of \eta_{0} PDF is centered on \eta_{0}=0. It was found that the elliptical $\beta$ model is in good agreement with the data, showing no violation of the DD relation (PDF peaked close to \eta_0=0 at 1-sigma), while the spherical (non-isothermal) one is only marginally compatible at 3-sigma.

On the deprojection of clusters of galaxies combining X-ray, Sunyaev-Zeldovich temperature decrement and gravitational lensing maps

Knowledge of the intrinsic shape of galaxy clusters is very important in investigating cosmic structure formation and astrophysical processes. The reconstruction of the 3D structure usually relies on deprojecting 2D X-ray, Sunyaev-Zeldovich (SZ) and/or gravitational lensing observations. As known, a joint analysis of these data sets can provide the elongation of the cluster along the line of sight together with its length and width in the plane of the sky. An unbiased measurement of the Hubble constant can be also inferred. Due to some intrinsic degeneracies, the observational constraints obtained from such projected data sets are not enough to allow an unique inversion. In general, the projected maps can be at the same time compatible with prolate, oblate and with many triaxial configurations. Even a prolate cluster might be interpreted as an oblate system and vice versa. Assuming that the cluster is axially symmetric is likely to overestimate the intrinsic ellipticity, whereas the system always looks rounder performing the inversion under the hypothesis of a triaxial cluster aligned with the line of sight. In general, analysing triaxial clusters under the prolate or oblate assumption may introduce strong biases even when the clusters are actually near to axial symmetry whereas the systematics introduced assuming the cluster to be aligned with the line of sight are more under control.

ON THE DETERMINATION OF GALAXY STRUCTURE ELLIPTICITY

We discuss factors influencing the determination of the observed shape of galaxy clusters when the covariance ellipse method is involved. The analysis of 377 Abell clusters show that at greater distances from the cluster center the ellipticity is rather smooth. There were no statistical differences among ellipticities when the cluster center was located at the brightest cluster member, the third brightest galaxy, the mean as well as the median values of galaxy coordinates. Moreover, we show that for rich galaxy clusters the distribution of ellipticities is the same for two totally different cluster samples.

Measuring the Three‐dimensional Structure of Galaxy Clusters. II. Are Clusters of Galaxies Oblate or Prolate?

The intrinsic shape of galaxy clusters can be obtained through a combination of X-ray and Sunyaev-Zeldovich effect observations once cosmological parameters are assumed to be known. In this paper we discuss the feasibility of modeling galaxy clusters as either prolate or oblate ellipsoids. We analyze the intracluster medium distribution for a sample of 25 X-ray-selected clusters, with measured Sunyaev-Zeldovich temperature decrements. A mixed population of prolate and oblate ellipsoids of revolution fits the data well, with prolate shapes preferred by ~60%-76%. We observe an excess of clusters nearly aligned along the line of sight, with respect to what is expected from a randomly oriented cluster population, which might imply the presence of a selection bias in our sample. We also find signs that a more general triaxial morphology might better describe the morphology of galaxy clusters. Additional constraints from gravitational lensing could disentangle the degeneracy between an ellipsoidal and a triaxial morphology, and could also allow an unbiased determination of the Hubble constant.

Characterizing the shapes of galaxy clusters using moments of the gravitational lensing shear

We explore the use of the tangential component of weak lensing shear to characterize the ellipticity of clusters of galaxies. We introduce an ellipticity estimator, and quantify its properties for isolated clusters from ΛCDM N-body simulations. We compare the N-body results to results from smooth analytic models. The expected distribution of the estimator for mock observations is presented, and we show how this distribution is impacted by contaminants such as noise, line of sight projections, and misalignment of the central galaxy used to determine the orientation of the triaxial halo. We examine the radial profile of the estimator and discuss tradeoffs in the observational strategy to determine cluster shape.

Measuring the Three‐dimensional Structure of Galaxy Clusters. I. Application to a Sample of 25 Clusters

We discuss a method to constrain the intrinsic three-dimensionale shapes of galaxy clusters by combining X-Ray and Sunyaev-Zeldovich observations. The method is applied to a sample of 25 X-Ray selected clusters, with measured Sunyaev-Zeldovich temperature decrements. The sample turns out to be slightly biased, with strongly elongated clusters preferentially aligned along the line of sight. This result demonstrates that X-Ray selected cluster samples may be affected by morphological and orientation effects even if a relatively high threshold signal-to-noise ratio is used to select the sample. A large majority of the clusters in our sample exhibit a marked triaxial structure, with prolate-like shapes being slightly more likely than oblate-like ones; the spherical hypothesis is strongly rejected for most sample members. Cooling flow clusters do not show preferentially regular morphologies.

Abell 370: A cluster with a pronounced triaxial morphology

We have developed a new method to constrain the intrinsic three-dimensional shape of galaxy clusters using combined Sunyaev–Zel’dovich effect and X-ray observations. We here present a first empirical implementation of this tool to an extremely intriguing distant galaxy cluster: Abell 370.