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.

We present a joint millimetric and X-ray analysis of hot gas properties in the distant galaxy cluster SPT-CLJ0615-5746 (z = 0.972). Combining Chandra observations with the South Pole Telescope (SPT) and Planck data, we performed radial measurements of thermodynamical quantities up to a characteristic radius of 1.2 R-500. We exploited the high angular resolution of Chandra and SPT to map the innermost region of the cluster and the high sensitivity to the larger angular scales of Planck to constrain the outskirts and improve the estimation of the cosmic microwave background and the galactic thermal dust emissions. In addition to maximizing the accuracy of radial temperature measurements, our joint analysis allows us to test the consistency between X-ray and millimetric derivations of thermodynamic quantities via the introduction of a normalization parameter (eta(T)) between X-ray and millimetric temperature profiles. This approach reveals a substantial high value of the normalization parameter, eta(T) = 1.45(-0.18)(+0.17), suggesting that the gas halo is aspherical. Assuming hot gas hydrostatic equilibrium within complementary angular sectors that intercept the major and minor elongation of the X-ray image, we infer a halo mass profile that results from an effective compensation of azimuthal variations of gas densities by variations in the eta(T) parameter. Consistent with earlier integrated X-ray and millimetric measurements, we infer a cluster mass of M-500(HE) = 10.67(-0.50)(+0.62) 10(14) M-circle dot.

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.

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.

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.

We present the first detailed analysis of the ultra-steep spectrum radio halo in the merging galaxy cluster A521, based on upgraded Giant Metrewave Radio telescope observations. The combination of radio observations (300–850 MHz) and archival X-ray data provides a new window into the complex physics occurring in this system. When compared to all previous analyses, our sensitive radio images detected the centrally located radio halo emission to a greater extent of ∼1.3 Mpc. A faint extension of the southeastern radio relic has been discovered. We detected another relic, recently discovered by MeerKAT, and coincident with a possible shock front in the X-rays, at the northwest position of the center. We find that the integrated spectrum of the radio halo is well-fitted with a spectral index of −1.86 ± 0.12. A spatially resolved spectral index map revealed the spectral index fluctuations, as well as an outward radial steepening of the average spectral index. The radio and X-ray surface brightness is well correlated for the entire and different subparts of the halo, with sublinear correlation slopes (0.50–0.65). We also found a mild anticorrelation between the spectral index and X-ray surface brightness. Newly detected extensions of the SE relic and the counter relic are consistent with the merger in the plane of the sky.

We investigate the statistical properties and the origin of the scatter within the spatially resolved surface brightness profiles of the CHEX-MATE sample, formed by 118 galaxy clusters selected via the SZ effect. These objects have been drawn from the Planck SZ catalogue and cover a wide range of masses, M$_{500}=[2-15] \times 10^{14} $M$_{\odot}$, and redshift, z=[0.05,0.6]. We derived the surface brightness and emission measure profiles and determined the statistical properties of the full sample. We found that there is a critical scale, R$\sim 0.4 R_{500}$, within which morphologically relaxed and disturbed object profiles diverge. The median of each sub-sample differs by a factor of $\sim 10$ at $0.05\,R_{500}$. There are no significant differences between mass- and redshift-selected sub-samples once proper scaling is applied. We compare CHEX-MATE with a sample of 115 clusters drawn from the The Three Hundred suite of cosmological simulations. We found that simulated emission measure profiles are systematically steeper than those of observations. For the first time, the simulations were used to break down the components causing the scatter between the profiles. We investigated the behaviour of the scatter due to object-by-object variation. We found that the high scatter, approximately 110%, at $R<0.4R_{500}$ is due to a genuine difference between the distribution of the gas in the core. The intermediate scale, $R_{500} =[0.4-0.8]$, is characterised by the minimum value of the scatter on the order of 0.56, indicating a region where cluster profiles are the closest to the self-similar regime. Larger scales are characterised by increasing scatter due to the complex spatial distribution of the gas. Also for the first time, we verify that the scatter due to projection effects is smaller than the scatter due to genuine object-by-object variation in all the considered scales. [abridged]

Pressure profiles are sensitive probes of the thermodynamic conditions and the internal structure of galaxy clusters. The intra-cluster gas resides in hydrostatic equilibrium within the Dark Matter gravitational potential. However, this equilibrium may be perturbed, e.g. as a consequence of thermal energy losses, feedback and non-thermal pressure supports. Accurate measures of the gas pressure over the cosmic times are crucial to constrain the cluster evolution as well as the contribution of astrophysical processes. In this work we presented a novel algorithm to derive the pressure profiles of galaxy clusters from the Sunyaev-Zeldovich (SZ) signal measured on a combination of Planck and South Pole Telescope (SPT) observations. The synergy of the two instruments made it possible to track the profiles on a wide range of spatial scales. We exploited the sensitivity to the larger scales of the Planck High-Frequency Instrument to observe the faint peripheries, and the higher spatial resolution of SPT to solve the innermost regions. We developed a two-step pipeline to take advantage of the specifications of each instrument. We first performed a component separation on the two data-sets separately to remove the background (CMB) and foreground (galactic emission) contaminants. Then we jointly fitted a parametric pressure profile model on a combination of Planck and SPT data. We validated our technique on a sample of 6 CHEX-MATE clusters detected by SPT. We compare the results of the SZ analysis with profiles derived from X-ray observations with XMM-Newton. We find an excellent agreement between these two independent probes of the gas pressure structure.

The X-ray spectrum of extragalactic sources, such as galaxy clusters, is affected by the photo-absorption of various components of the Galactic interstellar medium (ISM). The resulting spectral distortion contributes to the systematics of cluster temperature measurements. It essentially depends on the neutral (atomic+molecular) Galactic hydrogen density column, N H , which remains challenging to map across the sky in the lack of a straightforward tracer of the molecular gas phase in the ISM. Combining data from the HI4PI and Planck HFI sky surveys, we investigate the mass fraction of molecular gas across the line of sight of CHEX-MATE galaxy clusters by searching for thermal dust emission excess with respects to the neutral atomic hydrogen density column, N HI . Consistent with earlier studies of the ISM based on IRAS and Planck data, we detect dust emission excess along the line of sight of some members of the CHEX-MATE cluster catalogue that are mostly localised behind dense ISM regions. We find that the CHEX-MATE cluster catalogue can be divided into three categories: 40% of members are located behind low N HI regions where the molecular mass fraction is negligible, 40% of members are located behind intermediate N HI regions where the molecular gas fraction would reach 5% on average, and the remaining 20% of members are located behind high N HI regions that locally exhibit even higher molecular gas fractions. The apparent cluster temperature shifts associated with the molecular content of the ISM are about 1% or less for most CHEX-MATE clusters, but can exceed 5% in the highest N HI regions.

Temperature profiles of the hot galaxy cluster intracluster medium (ICM) have a complex non-linear structure that traditional parametric modelling may fail to fully approximate. For this study, we made use of neural networks, for the first time, to construct a data-driven non-parametric model of ICM temperature profiles. A new deconvolution algorithm was then introduced to uncover the true (3D) temperature profiles from the observed projected (2D) temperature profiles. An auto-encoder-inspired neural network was first trained by learning a non-linear interpolatory scheme to build the underlying model of 3D temperature profiles in the radial range of [0.02-2] R$_{500}$, using a sparse set of hydrodynamical simulations from the THREE HUNDRED PROJECT. A deconvolution algorithm using a learning-based regularisation scheme was then developed. The model was tested using high and low resolution input temperature profiles, such as those expected from simulations and observations, respectively. We find that the proposed deconvolution and deprojection algorithm is robust with respect to the quality of the data, the morphology of the cluster, and the deprojection scheme used. The algorithm can recover unbiased 3D radial temperature profiles with a precision of around 5\% over most of the fitting range. We apply the method to the first sample of temperature profiles obtained with XMM{\it -Newton} for the CHEX-MATE project and compared it to parametric deprojection and deconvolution techniques. Our work sets the stage for future studies that focus on the deconvolution of the thermal profiles (temperature, density, pressure) of the ICM and the dark matter profiles in galaxy clusters, using deep learning techniques in conjunction with X-ray, Sunyaev Zel'Dovich (SZ) and optical datasets.

The Shapley Supercluster ($\langle z \rangle\approx0.048$) contains several tens of gravitationally bound clusters and groups, making it it is an ideal subject for radio studies of cluster mergers. We used new high sensitivity radio observations to investigate the less energetic events of mass assembly in the Shapley Supercluster from supercluster down to galactic scales. We created total intensity images of the full region between A 3558 and A 3562, from $\sim 230$ to $\sim 1650$ MHz, using ASKAP, MeerKAT and the GMRT, with sensitivities ranging from $\sim 6$ to $\sim 100$ $\mu$Jy beam$^{-1}$. We performed a detailed morphological and spectral study of the extended emission features, complemented with ESO-VST optical imaging and X-ray data from XMM-Newton. We report the first GHz frequency detection of extremely low brightness intercluster diffuse emission on a $\sim 1$ Mpc scale connecting a cluster and a group, namely: A 3562 and the group SC 1329--313. It is morphologically similar to the X-ray emission in the region. We also found (1) a radio tail generated by ram pressure stripping in the galaxy SOS 61086 in SC 1329-313; (2) a head-tail radio galaxy, whose tail is broken and culminates in a misaligned bar; (3) ultrasteep diffuse emission at the centre of A 3558. Finally (4), we confirm the ultra-steep spectrum nature of the radio halo in A 3562. Our study strongly supports the scenario of a flyby of SC 1329-313 north of A 3562 into the supercluster core. [abridged...]

Using a MeerKAT observation of the galaxy cluster A3562 (a member of the Shapley supercluster), we have discovered a narrow, long and straight, very faint radio filament, which branches out at a straight angle from the tail of a radio galaxy located in projection near the core of the cluster. The radio filament spans 200 kpc and aligns with a sloshing cold front seen in the X-rays, staying inside the front in projection. The radio spectral index along the filament appears uniform (within large uncertainties) at alpha similar or equal to -1.5. We propose that the radio galaxy is located outside the cold front but dips its tail under the front. The tangential wind that blows there may stretch the radio plasma from the radio galaxy into a filamentary structure. Some reacceleration is needed in this scenario to keep the radio spectrum uniform. Alternatively, the cosmic-ray electrons from that spot in the tail can spread along the cluster magnetic field lines, straightened by that same tangential flow, via anomalously fast diffusion. Our radio filament can provide constraints on this process. We also uncover a compact radio source at the brightest cluster galaxy that is 2-3 orders of magnitude less luminous than those in typical cluster central galaxies-probably an example of a brightest cluster galaxy starved of accretion fuel by gas sloshing.

We present LOw Frequency ARray observations of the Coma Cluster field at 144 MHz. The cluster hosts one of the most famous radio halos, a relic, and a low surface brightness bridge. We detect new features that allow us to make a step forward in the understanding of particle acceleration in clusters. The radio halo extends for more than 2 Mpc, which is the largest extent ever reported. To the northeast of the cluster, beyond the Coma virial radius, we discover an arc-like radio source that could trace particles accelerated by an accretion shock. To the west of the halo, coincident with a shock detected in the X-rays, we confirm the presence of a radio front, with different spectral properties with respect to the rest of the halo. We detect a radial steepening of the radio halo spectral index between 144 and 342 MHz, at similar to 30 ' from the cluster center, that may indicate a non-constant re-acceleration time throughout the volume. We also detect a mild steepening of the spectral index toward the cluster center. For the first time, a radial change in the slope of the radio-X-ray correlation is found, and we show that such a change could indicate an increasing fraction of cosmic-ray versus thermal energy density in the cluster outskirts. Finally, we investigate the origin of the emission between the relic and the source NGC 4789, and we argue that NGC 4789 could have crossed the shock originating the radio emission visible between its tail and the relic.

The Cluster HEritage project with XMM-Newton – Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE) is a three-mega-second Multi-Year Heritage Programme to obtain X-ray observations of a minimally-biased, signal-to-noise-limited sample of 118 galaxy clusters detected by Planck through the Sunyaev–Zeldovich effect. The programme, described in detail in this paper, aims to study the ultimate products of structure formation in time and mass. It is composed of a census of the most recent objects to have formed (Tier-1: 0.05 < z < 0.2; 2 × 10 14 M ⊙ < M 500 < 9 × 10 14 M ⊙ ), together with a sample of the highest mass objects in the Universe (Tier-2: z < 0.6; M 500 > 7.25 × 10 14 M ⊙ ). The programme will yield an accurate vision of the statistical properties of the underlying population, measure how the gas properties are shaped by collapse into the dark matter halo, uncover the provenance of non-gravitational heating, and resolve the major uncertainties in mass determination that limit the use of clusters for cosmological parameter estimation. We will acquire X-ray exposures of uniform depth, designed to obtain individual mass measurements accurate to 15 − 20% under the hydrostatic assumption. We present the project motivations, describe the programme definition, and detail the ongoing multi-wavelength observational (lensing, SZ, radio) and theoretical effort that is being deployed in support of the project.

Complementarily to X-ray observations, the thermal SZ effect is a powerful tool to probe the baryonic content of galaxy clusters from their core to their peripheries. While contaminations by astrophysical and instrumental backgrounds require us to scan the thermal SZ signal across various frequencies, the multi-scale nature of cluster morphologies require us to observe such objects at various angular resolutions. We developed component separation algorithms that take advantage of sparse representations to combine these heterogeneous pieces of information, separate the thermal SZ signal from its contaminants, detect and map the thermal SZ signal of galaxy clusters from nearby to more distant clusters of the Planck catalogue. Spatially weighted likelihoods allow us in particular to connect parametric fittings of the component Spectral Energy Distribution with wavelet and curvelet imaging, but also to combine signals registered with beams of various width. Such techniques already allow us to detect sub-structures in the peripheries of nearby clusters with Planck, and could be extended to observations performed at higher angular resolutions.

The Sunyaev–Zel’dovich effect is the ideal probe for investigating the outskirts of galaxy clusters. To map this signal, we apply a spectral imaging technique which combines parametric component separation and sparse representations. Our procedure is an improved version of an existing algorithm, which now features a better treatment of astrophysical contaminants, and the implementation of a new beam deconvolution. We use the most recent frequency maps delivered by Planck , and we consider the clusters analysed in the XMM Cluster Outskirts Project (X-COP). In particular, we focus on the images of two clusters which may be possibly interacting with neighbouring objects, namely A2029 and RXCJ1825. We also highlight the advantages of the new beam deconvolution method, through a comparison with the original version of the imaging algorithm.

Galaxy clusters are the endpoints of structure formation and are continuously growing through the merging and accretion of smaller structures. Numerical simulations predict that a fraction of their energy content is not yet thermalized, mainly in the form of kinetic motions (turbulence, bulk motions). Measuring the level of non-thermal pressure support is necessary to understand the processes leading to the virialization of the gas within the potential well of the main halo and to calibrate the biases in hydrostatic mass estimates. We present high-quality measurements of hydrostatic masses and intracluster gas fraction out to the virial radius for a sample of 13 nearby clusters with availableXMM-NewtonandPlanckdata. We compare our hydrostatic gas fractions with the expected universal gas fraction to constrain the level of non-thermal pressure support. We find that hydrostatic masses require little correction and infer a median non-thermal pressure fraction of ∼6% and ∼10% atR500andR200, respectively. Our values are lower than the expectations of hydrodynamical simulations, possibly implying a faster thermalization of the gas. If instead we use the mass calibration adopted by thePlanckteam, we find that the gas fraction of massive local systems implies a mass bias 1 − b = 0.85 ± 0.05 for Sunyaev–Zeldovich-derived masses, with some evidence for a mass-dependent bias. Conversely, the high bias required to matchPlanckcosmic microwave background and cluster count cosmology is excluded by the data at high significance, unless the most massive halos are missing a substantial fraction of their baryons.

Context. The hot plasma in a galaxy cluster is expected to be heated to high temperatures through shocks and adiabatic compression. The thermodynamical properties of the gas encode information on the processes leading to the thermalization of the gas in the cluster’s potential well and on non-gravitational processes such as gas cooling, AGN feedback, shocks, turbulence, bulk motions, cosmic rays and magnetic field. Aims. In this work we present the radial profiles of the thermodynamic properties of the intracluster medium (ICM) out to the virial radius for a sample of 12 galaxy clusters selected from the Planck all-sky survey. We determine the universal profiles of gas density, temperature, pressure, and entropy over more than two decades in radius, from 0.01 R 500 to 2 R 500 . Methods. We exploited X-ray information from XMM-Newton and Sunyaev-Zel’dovich constraints from Planck to recover thermodynamic properties out to 2 R 500 . We provide average functional forms for the radial dependence of the main quantities and quantify the slope and intrinsic scatter of the population as a function of radius. Results. We find that gas density and pressure profiles steepen steadily with radius, in excellent agreement with previous observational results. Entropy profiles beyond R 500 closely follow the predictions for the gravitational collapse of structures. The scatter in all thermodynamical quantities reaches a minimum in the range [0.2 − 0.8] R 500 and increases outward. Somewhat surprisingly, we find that pressure is substantially more scattered than temperature and density. Conclusions. Our results indicate that once accreting substructures are properly excised, the properties of the ICM beyond the cooling region ( R > 0.3 R 500 ) follow remarkably well the predictions of simple gravitational collapse and require few non-gravitational corrections.