Under the standard model of hierarchical structure formation, the overall geometry of galaxy clusters is better described by a triaxial ellipse than by a sphere. As a result, the application of spherically symmetric models can result in significant biases, with masses derived from weak-lensing observations being particularly sensitive. These biases can be mitigated by fitting a triaxial model, but this requires deep multi-probe data along with a set of physically motivated models to describe them. We present a multi-probe triaxial analysis method based on the data available for galaxy clusters in the Cluster Heritage project with XMM-Newton - Mass Assembly and Thermodynamics at Endpoint of structure formation (CHEX-MATE), which includes X-ray data from XMM-Newton, Sunyaev-Zel'dovich effect maps from Planck and ACT, and weak-lensing data from Subaru. This work builds upon our previous development of a gas-only X-ray and Sunyaev-Zel'dovich triaxial fitting formalism in Paper I. After verifying our approach using mock observations of model clusters with known properties, we applied it to the CHEX-MATE galaxy cluster PSZ2 G313.33+61.13 (Abell 1689). We found that the cluster is elongated along the line of sight relative to the plane of sky by a factor of & Rscr;(LP) = 1.20 +/- 0.04. As a result, the weak-lensing mass obtained from our triaxial fit, M-200c = (13.88(-1.43)(+1.73)) & times; 10(14)M(circle dot ) , is significantly lower than the value of (17.77(-1.75)(+2.00))& times;10(14)M(circle dot )obtained from a spherically symmetric fit that otherwise employed the same method. Our triaxial fit finds a concentration ofc(200c)=8.66(-1.70)(+2.08), consistent with the spherically symmetric value of 9.99+2.26-1.78, which suggests that the unexpectedly high concentration in Abell 1689 is not due to triaxiality and orientation. We also measured the nonthermal pressure fraction at radii between 0.18-1.37 Mpc and found a minimum of approximately 20% at intermediate radii, increasing to near 30% at the smallest and largest radii, and with a typical measurement precision of +/- 5%.

We present a weak-lensing shear analysis of 41 Planck SZ-selected galaxy clusters at 0.11≤ z≤ 0.55 from the CHEX-MATE sample, using wide-field Subaru/Suprime-Cam and CFHT/MegaPrime imaging from the AMALGAM project. We detect the azimuthally averaged weak-lensing signal around the X-ray peak of each cluster, achieving a median S/N of 6.5 per cluster. The 45^∘-rotated component has a median S/N of -0.1 and ranges from -1.8 to +1.8, consistent with zero. We model the excess surface mass density profile of each cluster with an NFW profile to infer weak-lensing mass and concentration constraints. The total systematic uncertainty in the weak-lensing mass calibration is assessed to be 8%. Using a hierarchical Bayesian framework, we then derive weak-lensing-calibrated scaling relations for the halo concentration, c_200, as a function of M_200 and redshift, and for the Planck SZ mass proxy, M_SZ, as a function of M_500 and redshift, while accounting for sample selection effects, weak-lensing modelling biases, and residual calibration uncertainty. At M_200=10^15M_⊙ and z=0.25, we find c_200=3.53±0.71 with an intrinsic scatter of 0.22±0.04 dex. The inferred normalisation and scatter are consistent with recent ΛCDM predictions for massive haloes, with no significant mass or redshift dependence over the probed range. For the Planck mass proxy, our baseline regression yields M_SZ/M_500=0.83±0.09 at M_500=7×10^14M_⊙ and z=0.25, with an intrinsic scatter of 0.10±0.02 dex. A restricted model with fixed unit mass slope and no redshift evolution gives 1-b=0.72±0.11. We also provide weak-lensing-calibrated posterior estimates of M_500 for the sample based on the baseline M_SZ–M_500–z relation. These results provide an initial weak-lensing mass calibration for CHEX-MATE multi-probe cluster studies.

The Cluster HEritage project with XMM-Newton - Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE) is a programme to study a minimally biased sample of 118 galaxy clusters detected by Planck through the Sunyaev-Zeldovich effect. Accurate and precise mass measurements are required to exploit CHEX-MATE as an astrophysical laboratory and a calibration sample for cosmological probes in the era of large surveys. We measured masses based on the galaxy dynamics, which are highly complementary to weak-lensing or X-ray estimates. We analysed the sample with a uniform pipeline that is stable both for poorly sampled or rich clusters -using spectroscopic redshifts from public (NED, SDSS, and DESI) or private archives and dedicated observational programmes. We modelled the halo mass density and the anisotropy profile. Membership is confirmed with a cleaning procedure in phase space. We derived masses from measured velocity dispersions under the assumed model. We measured dynamical masses for 101 CHEX-MATE clusters with at least ten confirmed members within the virial radius r200c. Estimated redshifts and velocity dispersions agree with literature values when available. Validation with weak-lensing masses shows agreement within 8 +/- 16 (stat.) +/- 5 (sys.)%, and confirms dynamical masses as an unbiased proxy. Comparison with Planck masses shows them to be biased low by 34 +/- 3 (stat.) +/- 5 (sys.)%. A follow-up spectroscopic campaign is underway to cover the full CHEX-MATE sample.

Context. X-ray observations of galaxy clusters are routinely used to derive radial distributions of intracluster medium (ICM) thermodynamical properties, such as density and temperature. However, observations only allow access to quantities projected on the celestial sphere, so an assumption on the three-dimensional distribution of the ICM is necessary. Usually, spherical geometry is assumed. Aims. The aim of this paper is to determine the bias due to this approximation on the reconstruction of the ICM density radial profile of a cluster sample and on the intrinsic scatter of the density profiles' distribution, particularly when the substructures of clusters are not masked. Methods. We used simulated clusters for which we can access the three-dimensional ICM distribution. In particular, we considered a sample of 98 simulated clusters drawn from THE THREE HUNDRED project. For each cluster, we simulated 40 different observations by projecting the cluster along 40 different lines of sight. We extracted the ICM density profile from each observation, assuming the ICM to be spherically distributed. For each line of sight, we then considered the mean density profile over the sample and compared it with the three-dimensional density profile given by the simulations. We thus derived the spherical bias in the density profile by considering the ratio between the observed and the input quantities. We also studied the bias in the intrinsic scatter of the density profile distribution by performing the same procedure. Results. We find a bias in the density profile, b(n), smaller than 10% for R less than or similar to R-500, and it increases up to approximate to 50% for larger radii. The bias in the intrinsic scatter profile, b(s), is higher, reaching a value of approximate to 100% for R approximate to R-500. We find that the bias for both of the analyzed quantities strongly depends on the morphology composition of the objects in the sample. For clusters that do not show large-scale substructures, both b(n) and b(s) are reduced by a factor of two. Conversely, for systems that do show large-scale substructures, both b(n) and b(s) increase significantly.

The AXIS Community Science Book represents the collective effort of 592 scientists worldwide to define the transformative science enabled by the Advanced X-ray Imaging Satellite (AXIS), a next-generation X-ray mission selected by NASA's Astrophysics Probe Program for Phase A study. AXIS will advance the legacy of high-angular-resolution X-ray astronomy with 1.5” imaging over a wide 24' field of view and an order of magnitude greater collecting area than Chandra in the 0.3-12 keV band. Combining sharp imaging, high throughput, and rapid response capabilities, AXIS will open new windows on virtually every aspect of modern astrophysics, exploring the birth and growth of supermassive black holes, the feedback processes that shape galaxies, the life cycles of stars and exoplanet environments, and the nature of compact stellar remnants, supernova remnants, and explosive transients. This book compiles 138 community-contributed science cases developed by five Science Working Groups focused on AGN and supermassive black holes, galaxy evolution and feedback, compact objects and supernova remnants, stellar physics and exoplanets, and time-domain and multi-messenger astrophysics. Together, these studies establish the scientific foundation for next-generation X-ray exploration in the 2030s and highlight strong synergies with facilities of the 2030s, such as JWST, Roman, Rubin/LSST, SKA, ALMA, ngVLA, and next-generation gravitational-wave and neutrino networks.

The intra-cluster medium is prone to turbulent motion that will contribute to the non-thermal heating of the gas, complicating the use of galaxy clusters as cosmological probes. Indirect approaches can estimate the intensity and structure of turbulent motions by studying the associated fluctuations in gas density and X-ray surface brightness. In this work, we want to constrain the gas density fluctuations at work in the CHEX-MATE sample to obtain a detailed view of their properties in a large population of clusters. We use a simulation-based approach to constrain the parameters of the power spectrum of density fluctuations, assuming a Kolmogorov-like spectrum and including the sample variance, further providing an approximate likelihood for each cluster. This method requires clusters to be not too disturbed, as fluctuations can originate from dynamic processes such as merging. Accordingly, we remove the less relaxed clusters (centroid shift $w>0.02$) from our sample, resulting in a sample of 64 clusters. We define different subsets of CHEX-MATE to determine properties of density fluctuations as a function of dynamical state, mass and redshift, and investigate the correlation with the presence or not of a radio halo. We found a positive correlation between the dynamical state and density fluctuation variance, a non-trivial behaviour with mass and no specific trend with redshift or the presence/absence of a radio halo. The injection scale is mostly constrained by the core region. The slope in the inertial range is consistent with Kolmogorov theory. When interpreted as originating from turbulent motion, the density fluctuations in $R_{500}$ yield an average Mach number of $M_{3D}\simeq 0.4\pm 0.2$, an associated non-thermal pressure support of $ P_{turb}/P_{tot}\simeq (9\pm 6) \%$ or a hydrostatic mass bias $b_{turb}\simeq 0.09\pm 0.06$, in line with what is expected from the literature.

The relation between giant radio halos and mini-halos in galaxy clusters is not understood. The former are usually associated with merging clusters, the latter are found in relaxed systems. In the last years, the advent of low-frequency radio observations has challenged this dichotomy, finding intermediate objects with a hybrid radio morphology. We aim to investigate the presence of diffuse radio emission in the cluster Abell 1413 and determine its dynamical status. We used LOFAR HBA observations centred at 144 MHz to study the diffuse emission hosted by this cluster.To investigate the dynamical state of the system, we complete our study with newly analysed XMM-Newton archival data. A1413 shows features that are typically present in both relaxed (e.g., peaked x-ray surface brightness distribution and little large-scale inhomogeneities) and disturbed (e.g., flatter temperature and metallicity profiles) clusters.This evidence supports the scenario that A1413 is neither a disturbed nor fully relaxed object. We argue that it is an intermediate-phase cluster.Using radio observations at 144 MHz, we discover the presence of a wider diffuse component surrounding the previously reported mini-halo at the cluster centre. By fitting the radio surface brightness profile with a double-exponential model, we can disentangle the two components. We find an inner mini-halo with an e-folding radius r_e1=28 kpc and the extended component with r_e2 = 290 kpc. We also performed point-to-point correlations between radio and X-ray surface brightness, finding a sub-linear relation for the outer emission and a super-linear relation for the mini-halo.The mini-halo and the diffuse emission extend over different scales and show different features, confirming the double nature of the radio emission and suggesting that the mechanisms responsible for the re-acceleration of the radio-emitting particle might be different.

The “Cluster HEritage project with XMM-Newton: Mass Assembly and Thermodynamics at the End point of structure formation” (CHEX-MATE) is a multi-year heritage program to obtain homogeneous XMM-Newton observations of a representative sample of 118 galaxy clusters. The observations are tuned to reconstruct the distribution of the main thermodynamic quantities of the intra-cluster medium up to R500 and to obtain individual mass measurements, via the hydrostatic-equilibrium equation, with a precision of 15−20%. Temperature profiles are a necessary ingredient for the scientific goals of the project and it is thus crucial to derive the best possible temperature measurements from our data. This is why we have built a new pipeline for spectral extraction and analysis of XMM-Newton data, based on a new physically motivated background model and on a Bayesian approach with Markov chain Monte Carlo methods, which we present in this paper for the first time. We applied this new method to a subset of 30 galaxy clusters representative of the CHEX-MATE sample and show that we can obtain reliable temperature measurements up to regions where the source intensity is as low as 20% of the background, keeping systematic errors below 10%. We compare the median profile of our sample and the best-fit slope at large radii with literature results and we find a good agreement with other measurements based on XMM-Newton data. Conversely, when we exclude the most contaminated regions, where the source intensity is below 20% of the background, we find significantly flatter profiles, in agreement with predictions from numerical simulations and independent measurements with a combination of Sunyaev–Zeldovich and X-ray imaging data.

The connection between the thermal and non-thermal properties in galaxy clusters hosting radio halos seems fairly well established. However, a comprehensive analysis of such a connection has only been done for integrated quantities (e.g. L X − P radio relation). In recent years, new-generation radio telescopes have enabled the unprecedented possibility to study the non-thermal properties of galaxy clusters on a spatially resolved basis. In this work, we performed a pilot study to investigate the mentioned properties on five targets by combining X-ray data from the CHEX-MATE project with the second data release from the LOFAR Two meter Sky survey. We find a strong correlation ( r s ∼ 0.7) with a slope less than unity between the radio and X-ray surface brightness. We also report differences in the spatially resolved properties of the radio emission in clusters that show different levels of dynamical disturbance. In particular, less perturbed clusters (according to X-ray parameters) show peaked radio profiles in the centre, with a flattening in the outer regions, while the three dynamically disturbed clusters have steeper profiles in the outer regions. We fitted a model to the radio emission in the context of turbulent re-acceleration with a constant ratio between thermal and non-thermal particles’ energy densities and a magnetic field profile linked to the thermal gas density as B ( r ) ∝ n th 0.5 . We found that this simple model cannot reproduce the behaviour of the observed radio emission.

Clusters of galaxies are turbulent environments, whether merging systems with a turbulent intracluster medium (ICM) or relaxed systems sloshing within the potential well. In many such clusters, diffuse radio sources associated with the ICM are found: radio haloes and mini-haloes. Abell 2142 is a rich cluster undergoing extreme core sloshing, generating four cold fronts and a complex multi-component radio halo. Recent work revealed three halo components which span 2.4 Mpc. Particle acceleration on such scales is poorly understood, and requires high-quality multi-frequency data to understand. We use new deep MeerKAT L-band (1283 MHz) observations, combined with LOFAR HBA (143 MHz) data and X-ray data from XMM-Newton and Chandra to study the spectrum of the halo and the connection between the thermal and non-thermal components of the ICM. We detect the third halo component for the first time at 1283 MHz and confirm its ultra-steep spectrum nature, recovering $\alpha_{\rm H3, total} = -1.68 \pm 0.10$. All components follow power-law spectra which steepen toward the cluster outskirts. We profile the halo along three directions, finding evidence of asymmetry and spectral steepening perpendicular to the main axis of the cluster. Our thermal/non-thermal investigation shows sub-linear correlations that are steeper at 1283 MHz than 143 MHz, and we find different connections in different components of the halo. We find both a moderate anti-correlation (H1, the core) and positive correlation (H2, the ridge) between radio spectral index and X-ray temperature. Our results are broadly consistent with an interpretation of inhomogeneous turbulent (re-)acceleration. However, the anti-correlation between radio spectral index and X- ray temperature in the cluster core is challenging to explain; the presence of three cold fronts and a generally lower temperature may provide the foundations of an explanation.

We characterise the entropy profiles of 32 very high mass (M_500>7.75×10^14 M_⊙) galaxy clusters (HIGHMz), selected from the CHEX-MATE sample, to study the intracluster medium (ICM) entropy distribution in a regime where non-gravitational effects are minimised. Using XMM-Newton measurements, we measure the entropy profiles up to R_500 for all objects. The scaled profiles exhibit large dispersion in the central regions, but converge rapidly to the expectation from pure gravitational collapse beyond the core. We quantify the correlation between the ICM morphological parameters and scaled entropy as a function of radius, showing that morphologically relaxed (disturbed) objects have low (high) central entropy. We compare our data to other observational samples, finding differences in normalisation which are linked to the average mass of the samples in question. We find that a weaker mass dependence than self-similar in the scaling (Am -0.25) allows us to minimise the dispersion in the radial range [0.3-0.8]R_500 for clusters spanning over a decade in mass. The deviation from self-similarity is radially dependent and is more pronounced at small and intermediate radii than at R_500. We also investigate the distribution of central entropy K_0, finding no evidence for bimodality, and outer slopes α, which peaks at 1.1. Using weak lensing masses, we find indication for a small suppression of the scatter ( 30 using masses derived from Yx in the rescaling. Finally, we compare to recent cosmological numerical simulations from THE THREE HUNDRED and MACSIS, finding good agreement with our observational data. These results provide a robust observational benchmark in the gravity-dominated regime and will serve as a future reference for samples at lower mass, higher redshifts, and for ongoing work using cosmological numerical simulations.

We present a detailed study of the gas and galaxy properties of the cluster PSZ2 G282.28+49.94 detected in the Planck all-sky survey. The intracluster medium (ICM) of this object at z=0.56 exhibits a cometary-like shape. Combining Chandra and TNG observations, we characterised the spatially resolved thermodynamical properties of the gas and the spatial and velocity distribution of 73 galaxy members. The cluster structure is quite complex with an elongated core region containing the two brightest cluster galaxies and one dense group to the south-east. Since there is no velocity difference between the core and the south-east group, we suggest the presence of a merger along the plane of the sky. This structure is related to complex X-ray and radio features, and thus the merger has likely been caught during the post-merger phase. Comparing the distribution of the ICM and of member galaxies, we find a large offset of similar to 50 kpc between the position of the X-ray peak and the centre of a concentration of galaxies, preceding it in the likely direction of motion. This configuration is similar to the famous Bullet Cluster, leading us to dub PSZ2 G282.28+49.94 the 'Planck bullet', and represents an ideal situation to provide astrophysical constraints to the self-interaction cross-section (sigma/m) of dark matter particles. These results illustrate the power of a multi-wavelength approach to probe the merging scenario of such complex and distant systems.

Context. Galaxy clusters grow through the accretion of mass over cosmic time. Their observed properties are then shaped by how baryons distribute and energy is diffused. Thus, a better understanding of spatially resolved, projected thermodynamic properties of the intra-cluster medium (ICM) may provide a more consistent picture of how mass and energy act locally in shaping the X-ray observed quantities of these massive virialized or still collapsing structures. Aims. We study the perturbations in the temperature (and density) distribution to evaluate and characterize the level of inhomogeneities and the related dynamical state of the ICM. Methods. We obtain and analyze the temperature and density distribution for 28 clusters (2.4 × 1014 M⊙ < M500 < 1.2 × 1015 M⊙; 0.07 < z < 0.45) selected from the CHEX-MATE sample. We use these spatially resolved two-dimensional distributions to measure the global and radial scatter and identify the regions that deviate the most from the average distribution. During this process, we introduce three dynamical state estimators and produce “clean” temperature profiles after removing the most deviant regions. Results. We find that the temperature distribution of most of the clusters is skewed towards high temperatures and is well described by a log-normal function. There is no indication that the number of regions deviating more than 1σ from the azimuthal value is correlated with the dynamical state inferred from morphological estimators. The removal of these regions leads to local temperature variations up to 10–20% and an average increase of ∼5% in the overall cluster temperatures. The measured relative intrinsic scatter within R500, σT, int/T, has values of 0.17−0.05+0.08, and is almost independent of the cluster mass and dynamical state. Comparing the scatter of temperature and density profiles to hydrodynamic simulations, we constrain the average Mach number regime of the sample to Ṁ3D = 0.36−0.09+0.16. We infer the ratio between the energy in turbulence and the thermal energy, and translate this ratio in terms of a predicted hydrostatic mass bias b, estimating an average value of b ∼ 0.11 (covering a range between 0 and 0.37) within R500. Conclusions. This study provides detailed temperature fluctuation measurements for 28 CHEX-MATE clusters which can be used to study turbulence, derive the mass bias, and make predictions on the scaling relation properties.

We characterise the intracluster gas entropy profiles of 32 very high-mass (M-500 > 7.75 x 10(14) M-circle dot) Planck SZ-detected galaxy clusters (HIGHMz), selected from the CHEX-MATE sample, allowing us to study the intracluster medium (ICM) entropy distribution in a regime where non-gravitational effects are expected to be minimised. Using XMM-Newton measurements, we determined the entropy profiles up to similar to R-500 for all objects. We assessed the relative role of gas density and temperature measurements on the uncertainty in entropy reconstruction, showing that in the outer regions the largest contribution comes from the temperature. The scaled profiles exhibit a large dispersion in the central regions, but converge rapidly to the value expected from simple gravitational collapse beyond the core regions. We quantified the correlation between the ICM morphological parameters and scaled entropy as a function of radius, showing that centrally peaked objects have low central entropy, while morphologically disturbed objects have high central entropy. We compared the scaled HIGHMz entropy profiles to results from other observational samples, finding differences in normalisation, which appear linked to the average mass of the samples in question. Combining HIGHMz with other samples, we found that a weaker mass dependence than self-similar in the scaling (A(m) similar to -0.25) allows us to minimise the dispersion in the radial range [0.3 - 0.8] R-500 for clusters spanning over a decade in mass. The deviation from self-similar predictions is radially dependent and is more pronounced at small and intermediate radii than at R-500. We also investigated the distribution of central entropy K-0, finding no evidence for bimodality in the data and outer slope alpha, which peaks at alpha similar to 1.1 with tails at both low and high alpha that correlate with dynamical state. Using weak-lensing masses for half of the sample, we found an indication for a small suppression of the scatter (similar to 30%) beyond the core when using masses derived from Y-X in the rescaling. Finally, we compared our results to recent cosmological numerical simulations from THE THREE HUNDRED and MACSIS, finding good agreement with the observational data in this mass regime. These results provide a robust observational benchmark in the gravity-dominated regime, and will serve as a future reference for samples at lower masses, higher redshifts, and for ongoing work using cosmological numerical simulations.

Aims. The goal of this work is to devise a description of the enrichment process in large-scale structure that explains the available observations and makes predictions for future measurements. Methods. We took a spartan approach to this study, employing observational results and algebra to connect stellar assembly in star-forming halos with metal enrichment of the intra-cluster and group medium. Results. On one hand, our construct is the first to provide an explanation for much of the phenomenology of metal enrichment in clusters and groups. It sheds light on the lack of redshift evolution in metal abundance, as well as the small scatter of metal abundance profiles, the entropy versus abundance anti-correlation found in cool core clusters, and the so-called Fe conundrum, along with several other aspects of cluster enrichment. On the other hand, it also allows us to infer the properties of other constituents of large-scale structure. We find that gas that is not bound to halos must have a metal abundance similar to that of the ICM and only about one-seventh to one-third of the Fe in the Universe is locked in stars. A comparable amount is found in gas in groups and clusters and, lastly and most importantly, about three-fifths of the total Fe is contained in a tenuous warm or hot gaseous medium in or between galaxies. We point out that several of our results follow from two critical but well motivated assumptions: 1) the stellar mass in massive halos is currently underestimated and 2) the adopted Fe yield is only marginally consistent with predictions from synthesis models and SN rates. Conclusions. One of the most appealing features of the work presented here is that it provides an observationally grounded construct where vital questions on chemical enrichment in the large-scale structure can be addressed. We hope that it may serve as a useful baseline for future works.

Context. Tailed radio galaxies are shaped by ram pressure that is due to the high-velocity motion of their host through the intracluster medium (ICM). Recent works have reported on the increasing complexity of the phenomenology of tailed galaxies, with departures from theoretical ageing models and novel evidence of re-energising mechanisms that are nonetheless unclear. Aims. The nearby (z = 0.0894) galaxy cluster Abell 2142 hosts two tailed galaxies, namely T1 and T2, which exhibit peculiar morphological features. We aim to investigate the properties of T1 and T2 and constrain their spectral evolution, dynamics, and interactions with the ICM. Methods. We combined data from LOw Frequency Array (LOFAR), upgraded Giant Metrewave Radio Telescope (uGMRT), Very Large Array (VLA), and MeerKAT (from 30 MHz to 6.5 GHz) to carry out a detailed spectral analysis of T1 and T2. We analysed the surface brightness profiles, measured integrated and spatially resolved spectral indices. We performed a comparison with single injection ageing models. The Chandra X-ray data were used to search for discontinuities in the ICM properties in the direction of the targets. Results. The spectral properties of T1 at low frequencies can be predicted by ageing models and provide constraints on the 3D dynamics of the host by assuming a constant velocity. However, a more complex scenario is suggested by the sharp transitions along sub-regions of the tail, local surface brightness enhancements, and a spectral shape at high frequencies that is not predicted by any of the models. This scenario may plausibly involve hydrodynamical instabilities and particle mixing. T2 exhibits unusual morphological and surface brightness features, and its spectral behaviour is not predicted by standard models. The effects of two active galactic nucleus (AGN) outburst events during the infall of T2 towards the cluster centre could potentially explain its characteristic properties.

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 to investigate the 3D triaxial shapes of galaxy clusters from the Cluster HEritage project with XMM-Newton -- Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE). In this work, the first paper of a CHEX-MATE triaxial analysis series, we focus on utilizing X-ray data from XMM and Sunyaev-Zel'dovich (SZ) effect maps from Planck and ACT 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 compare 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 apply the analysis to reconstruct the gas shape from the observed data of one CHEX-MATE galaxy cluster, Abell 1689, to illustrate the technique. The inferred parameters are in agreement with previous analyses for that 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 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.

In this work, we investigate the interplay between the X-ray and radio emission of the cluster PSZ2G113.91-37.01 ( z = 0.371) using the high-quality XMM-Newton observations of the Cluster HEritage project with XMM-Newton – Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE), and the images from the second data release of the LOFAR Two-meter Sky Survey (LoTSS-DR2). The cluster is undergoing a merger along the north-south axis and shows a central radio halo and two radio relics, one in the southern region and one in the northern one. Analysis of the intracluster medium (ICM) distribution revealed the presence of a northern surface brightness (SB) jump associated with the merger event. By extracting spectra across this discontinuity, we classified the edge as a cold front. Furthermore, we made use of upgraded Giant Metrewave Radio Telescope observations that allowed us to perform a spectral analysis of the G113 radio emission. We found evidence for the re-acceleration of particles in the northern relic, and we measured an associated Mach number of ℳ = 1.95 ± 0.01, as inferred from radio observations. We then performed a point-to-point analysis of the X-ray and radio emission, both in the halo and in the northern relic regions. We found a strong correlation for the halo and an anti-correlation for the relic. The former behaviour is in agreement with previous studies. The relic anti-correlation is likely related to the reverse radial distribution of the X-ray (increasing towards the cluster centre) and radio (decreasing towards the cluster centre) emissions. Finally, we performed a point-to-point analysis of the radio emission and the residuals obtained by subtracting a double β model from the X-ray emission. We found a strong correlation between the two quantities. This behaviour suggests the presence of a connection between the process responsible for the radio emission and the one that leaves fluctuations in the X-ray observations.

Radio observations of a few cool-core galaxy clusters have revealed the presence of diffuse emission on cluster scales, similar to what was found in merging clusters in the form of radio halos. These sources might suggest that a minor merger, while not sufficiently energetic to disrupt the cool core, could still trigger particle acceleration in the intracluster medium on scales of hundreds of kpc. We observed with LOFAR at 144 MHz a sample of twelve cool-core galaxy clusters presenting some level of dynamical disturbances, according to X-ray data. We also performed a systematic search of cold fronts in these clusters, re-analysing archival Chandra data. The clusters PSZ1G139.61+24, A1068 (new detection), MS 1455.0+2232, and RX J1720.1+2638 present diffuse radio emission on a cluster scale. This emission is characterised by a double component: a central mini-halo confined by cold fronts and diffuse emission on larger scales, whose radio power at 144 MHz is comparable to that of radio halos detected in merging systems. The cold fronts in A1068 are a new detection. We also found a candidate plasma depletion layer in this cluster. No sloshing features are found in the other eight clusters. Two of them present a mini-halo, with diffuse radio emission confined to the cluster core. We also found a new candidate mini-halo. Whereas, for the remaining five clusters, we did not detect halo-like emission. For clusters without cluster-scale halos, we derived upper limits to the radio halo power. We found that cluster-scale diffuse radio emission is not present in all cool-core clusters when observed at a low frequency, but it is correlated to the presence of cold fronts. This morphology requires a specific configuration of the merger and so it puts some constraints on the turbulence, which deserves to be investigated in the future with theoretical works.

Context.Many galaxy clusters show diffuse cluster-scale emission in the form of radio halos, showing that magnetic fields and relativistic electrons are mixed in with the intracluster medium. There is in general agreement with the idea that the origin of radio halos is connected to turbulence generated during cluster mergers. Statistical studies of large samples of galaxy clusters in the radio band have the potential to unveil the connection between the properties of radio halos and the mass and dynamics of the host clusters.Aims.Previous studies were limited to massive clusters and were based on a small number of radio halos. The aim of this paper is to investigate the scaling relation between the radio power of radio halos and the mass of the host clusters at low frequencies and down to lower cluster masses.Methods.We analysed the clusters from the second catalogue ofPlanckSunyaev–Zel’dovich sources that lie within the 5634 deg2covered by the second Data Release of the LOFAR Two-meter Sky Survey. We derived the correlation between radio power and host cluster mass, and investigated the distribution of clusters without radio halos with respect to this correlation. We used X-ray observations to classify the dynamical state of clusters and investigated its effect on the power of radio halos.Results.Using different fitting methods, we found a correlation between the power of a radio halo at 150 MHz and the mass of its host cluster down to 3 × 1014 M⊙. For comparison with previous works, with the Bivariate Correlated Errors and intrinsic Scatter (BCES)Y|Xmethod, we obtained the slope of the correlationB = 3.55 ± 0.60 and the normalisationA = 1.1 ± 0.1. This correlation has a large scatter, part of which can be attributed to the different dynamical states of host clusters. We used two statistical tests to show that the distribution of clusters with and without (upper limits) radio halos in the mass–radio power diagram is not compatible with a single correlation and that it is also not compatible with clusters being uniformly distributed below the correlation.