Hydrodynamical Simulations Of Galaxy Clusters Research Articles

Putting plasma in the cosmological picture

Dr Klaus Dolag and his colleagues in the COMPLEX group aim to include plasma-physical effects in hydrodynamical simulations of galaxy clusters, which could lead to new insights into how they form and evolve.

The Concentration–Mass relation of massive, dynamically relaxed galaxy clusters: agreement between observations and ΛCDM simulations

ABSTRACT The relationship linking a galaxy cluster’s total mass with the concentration of its mass profile and its redshift is a fundamental prediction of the Cold Dark Matter (CDM) paradigm of cosmic structure formation. However, confronting those predictions with observations is complicated by the fact that simulated clusters are not representative of observed samples where detailed mass profile constraints are possible. In this work, we calculate the symmetry-peakiness-alignment (SPA) morphology metrics for maps of X-ray emissivity from the three hundred project hydrodynamical simulations of galaxy clusters at four redshifts, and thereby select a sample of morphologically relaxed, simulated clusters, using observational criteria. These clusters have on average earlier formation times than the full sample, confirming that they are both morphologically and dynamically more relaxed than typical. We constrain the concentration–mass–redshift relation of both the relaxed and complete sample of simulated clusters, assuming power-law dependences on mass (κm) and 1 + z (κζ), finding κm = −0.12 ± 0.07 and κζ = −0.27 ± 0.19 for the relaxed subsample. From an equivalently selected sample of massive, relaxed clusters observed with Chandra, we find κm = −0.12 ± 0.08 and κζ = −0.48 ± 0.19, in good agreement with the simulation predictions. The simulated and observed samples also agree well on the average concentration at a pivot mass and redshift providing further validation of the ΛCDM paradigm in the properties of the largest gravitationally collapsed structures observed. This also represents the first clear detection of decreasing concentration with redshift, a longstanding prediction of simulations in data.

The probability of galaxy–galaxy strong lensing events in hydrodynamical simulations of galaxy clusters

Context. An excess of galaxy–galaxy strong lensing (GGSL) in galaxy clusters compared to expectations from the Λ cold-dark-matter (CDM) cosmological model has recently been reported. Theoretical estimates of the GGSL probability are based on the analysis of numerical hydrodynamical simulations in ΛCDM cosmology. Aims. We quantify the impact of the numerical resolution and active galactic nucleus (AGN) feedback scheme adopted in cosmological simulations on the predicted GGSL probability, and determine if varying these simulation properties can alleviate the gap with observations. Methods. We analyze cluster-size halos (M200 > 5 × 1014 M⊙) simulated with different mass and force resolutions and implementing several independent AGN feedback schemes. Our analysis focuses on galaxies with Einstein radii in the range 0.″5 ≤ θE ≤ 3″. Results. We find that improving the mass resolution by factors of 10 and 25, while using the same galaxy formation model that includes AGN feedback, does not affect the GGSL probability. We find similar results regarding the choice of gravitational softening. On the contrary, adopting an AGN feedback scheme that is less efficient at suppressing gas cooling and star formation leads to an increase in the GGSL probability by a factor of between 3 and 6. However, we notice that such simulations form overly massive galaxies whose contribution to the lensing cross section would be significant but that their Einstein radii are too large to be consistent with the observations. The primary contributors to the observed GGSL cross sections are galaxies with smaller masses that are compact enough to become critical for lensing. The population with these required characteristics appears to be absent from simulations. Conclusion. Based on these results, we reaffirm the tension between observations of GGSL and theoretical expectations in the framework of the ΛCDM cosmological model. The GGSL probability is sensitive to the galaxy formation model implemented in the simulations. Still, all the tested models have difficulty simultaneously reproducing the stellar mass function and the internal structure of galaxies.

A deep learning approach to infer galaxy cluster masses from Planck Compton-y parameter maps

Galaxy clusters are useful laboratories to investigate the evolution of the Universe, and accurately measuring their total masses allows us to constrain important cosmological parameters. However, estimating mass from observations that use different methods and spectral bands introduces various systematic errors. This paper evaluates the use of a Convolutional Neural Network (CNN) to reliably and accurately infer the masses of galaxy clusters from the Compton-y parameter maps provided by the Planck satellite. The CNN is trained with mock images generated from hydrodynamic simulations of galaxy clusters, with Planck's observational limitations taken into account. We observe that the CNN approach is not subject to the usual observational assumptions, and so is not affected by the same biases. By applying the trained CNNs to the real Planck maps, we find cluster masses compatible with Planck measurements within a 15% bias. Finally, we show that this mass bias can be explained by the well known hydrostatic equilibrium assumption in Planck masses, and the different parameters in the Y500-M500 scaling laws. This work highlights that CNNs, supported by hydrodynamic simulations, are a promising and independent tool for estimating cluster masses with high accuracy, which can be extended to other surveys as well as to observations in other bands.

Cosmological hydrodynamical simulations of galaxy clusters: X-ray scaling relations and their evolution

We analyse cosmological hydrodynamical simulations of galaxy clusters to study the X-ray scaling relations between total masses and observable quantities such as X-ray luminosity, gas mass, X-ray temperature, and $Y_{X}$. Three sets of simulations are performed with an improved version of the smoothed particle hydrodynamics GADGET-3 code. These consider the following: non-radiative gas, star formation and stellar feedback, and the addition of feedback by active galactic nuclei (AGN). We select clusters with $M_{500} > 10^{14} M_{\odot} E(z)^{-1}$, mimicking the typical selection of Sunyaev-Zeldovich samples. This permits to have a mass range large enough to enable robust fitting of the relations even at $z \sim 2$. The results of the analysis show a general agreement with observations. The values of the slope of the mass-gas mass and mass-temperature relations at $z=2$ are 10 per cent lower with respect to $z=0$ due to the applied mass selection, in the former case, and to the effect of early merger in the latter. We investigate the impact of the slope variation on the study of the evolution of the normalization. We conclude that cosmological studies through scaling relations should be limited to the redshift range $z=0-1$, where we find that the slope, the scatter, and the covariance matrix of the relations are stable. The scaling between mass and $Y_X$ is confirmed to be the most robust relation, being almost independent of the gas physics. At higher redshifts, the scaling relations are sensitive to the inclusion of AGNs which influences low-mass systems. The detailed study of these objects will be crucial to evaluate the AGN effect on the ICM.

COOL CORE CLUSTERS FROM COSMOLOGICAL SIMULATIONS

We present results obtained from a set of cosmological hydrodynamic simulations of galaxy clusters, aimed at comparing predictions with observational data on the diversity between cool-core (CC) and non-cool-core (NCC) clusters. Our simulations include the effects of stellar and AGN feedback and are based on an improved version of the smoothed particle hydrodynamics code GADGET-3, which ameliorates gas mixing and better captures gas-dynamical instabilities by including a suitable artificial thermal diffusion. In this Letter, we focus our analysis on the entropy profiles, the primary diagnostic we used to classify the degree of cool-coreness of clusters, and on the iron profiles. In keeping with observations, our simulated clusters display a variety of behaviors in entropy profiles: they range from steadily decreasing profiles at small radii, characteristic of cool-core systems, to nearly flat core isentropic profiles, characteristic of non-cool-core systems. Using observational criteria to distinguish between the two classes of objects, we find that they occur in similar proportions in both simulations and in observations. Furthermore, we also find that simulated cool-core clusters have profiles of iron abundance that are steeper than those of NCC clusters, which is also in agreement with observational results. We show that the capability of our simulations to generate a realistic cool-core structure in the cluster population is due to AGN feedback and artificial thermal diffusion: their combined action allows us to naturally distribute the energy extracted from super-massive black holes and to compensate for the radiative losses of low-entropy gas with short cooling time residing in the cluster core.

TEMPERATURE STRUCTURE OF THE INTRACLUSTER MEDIUM FROM SMOOTHED-PARTICLE HYDRODYNAMICS AND ADAPTIVE-MESH REFINEMENT SIMULATIONS

Analyses of cosmological hydrodynamic simulations of galaxy clusters suggest that X-ray masses can be underestimated by 10% to 30%. The largest bias originates by both violation of hydrostatic equilibrium and an additional temperature bias caused by inhomogeneities in the X-ray emitting intra-cluster medium (ICM). To elucidate on this large dispersion among theoretical predictions, we evaluate the degree of temperature structures in cluster sets simulated either with smoothed-particle-hydrodynamics (SPH) and adaptive-mesh-refinement (AMR) codes. We find that the SPH simulations produce larger temperature variations connected to the persistence of both substructures and their stripped cold gas. This difference is more evident in no-radiative simulations, while it is reduced in the presence of radiative cooling. We also find that the temperature variation in radiative cluster simulations is generally in agreement with the observed one in the central regions of clusters. Around R_500 the temperature inhomogeneities of the SPH simulations can generate twice the typical hydrostatic-equilibrium mass bias of the AMR sample. We emphasize that a detailed understanding of the physical processes responsible for the complex thermal structure in ICM requires improved resolution and high sensitivity observations in order to extend the analysis to higher temperature systems and larger cluster-centric radii.

On the role of AGN feedback on the thermal and chemodynamical properties of the hot intracluster medium

We present an analysis of the properties of the ICM in an extended set of cosmological hydrodynamical simulations of galaxy clusters and groups performed with the TreePM+SPH GADGET-3 code. Besides a set of non-radiative simulations, we carried out two sets of simulations including radiative cooling, star formation, metal enrichment and feedback from supernovae, one of which also accounts for the effect of feedback from AGN resulting from gas accretion onto super-massive black holes. These simulations are analysed with the aim of studying the relative role played by SN and AGN feedback on the general properties of the diffuse hot baryons in galaxy clusters and groups: scaling relations, temperature, entropy and pressure radial profiles, and ICM chemical enrichment. We find that simulations including AGN feedback produce scaling relations that are in good agreement with X-ray observations at all mass scales. However, our simulations are not able to account for the observed diversity between CC and NCC clusters: unlike for observations, we find that temperature and entropy profiles of relaxed and unrelaxed clusters are quite similar and resemble more the observed behaviour of NCC clusters. As for the pattern of metal enrichment, we find that an enhanced level of iron abundance is produced by AGN feedback with respect to the case of purely SN feedback. As a result, while simulations including AGN produce values of iron abundance in groups in agreement with observations, they over-enrich the ICM in massive clusters. The efficiency of AGN feedback in displacing enriched gas from halos into the inter-galactic medium at high redshift also creates a widespread enrichment in the outskirts of clusters and produces profiles of iron abundance whose slope is in better agreement with observations.

A phenomenological model for the intracluster medium that matches X-ray and Sunyaev–Zel'dovich observations

Cosmological hydrodynamical simulations of galaxy clusters are still challenged to produce a model for the intracluster medium that matches all aspects of current X-ray and Sunyaev-Zel'dovich observations. To facilitate such comparisons with future simulations and to enable realistic cluster population studies for modeling e.g., non-thermal emission processes, we construct a phenomenological model for the intracluster medium that is based on a representative sample of observed X-ray clusters. We create a mock galaxy cluster catalog based on the large collisionless N-body simulation MultiDark, by assigning our gas density model to each dark matter cluster halo. Our clusters are classified as cool-core and non cool-core according to a dynamical disturbance parameter. We demonstrate that our gas model matches the various observed Sunyaev-Zel'dovich and X-ray scaling relations as well as the X-ray luminosity function, thus enabling to build a reliable mock catalog for present surveys and forecasts for future experiments. In a companion paper, we apply our catalogs to calculate non-thermal radio and gamma-ray emission of galaxy clusters. We make our cosmologically complete multi-frequency mock catalogs for the (non-)thermal cluster emission at different redshifts publicly and freely available online through the MultiDark database (www.multidark.org).

Characterizing diffused stellar light in simulated galaxy clusters

[Abridged] In this paper, we carry out a detailed analysis of the performance of two different methods to identify the diffuse stellar light in cosmological hydrodynamical simulations of galaxy clusters. One method is based on a dynamical analysis of the stellar component. The second method is closer to techniques commonly employed in observational studies. Both the dynamical method and the method based on the surface brightness limit criterion are applied to the same set of hydrodynamical simulations for a large sample about 80 galaxy clusters. We find significant differences between the ICL and DSC fractions computed with the two corresponding methods, which amounts to about a factor of two for the AGN simulations, and a factor of four for the CSF set. We also find that the inclusion of AGN feedback boosts the DSC and ICL fractions by a factor of 1.5-2, respectively, while leaving the BCG+ICL and BCG+DSC mass fraction almost unchanged. The sum of the BCG and DSC mass stellar mass fraction is found to decrease from ~80 per cent in galaxy groups to ~60 per cent in rich clusters, thus in excess of what found from observational analysis. We identify the average surface brightness limits that yields the ICL fraction from the SBL method close to the DSC fraction from the dynamical method. These surface brightness limits turn out to be brighter in the CSF than in the AGN simulations. This is consistent with the finding that AGN feedback makes BCGs to be less massive and with shallower density profiles than in the CSF simulations. The BCG stellar component, as identified by both methods, are slightly older and more metal-rich than the stars in the diffuse component.

Reconstructing three-dimensional parameters of galaxy clusters via multifrequency Sunyaev–Zeldovich observations

The Sunyaev-Zeldovich (SZ) effect is a promising tool to study physical properties of the hot X-ray emitting intracluster medium (ICM) in galaxy clusters. To date, most SZ observations have been interpreted in combination with X-ray follow-up measurements in order to determine the ICM temperature and estimate the cluster mass. Future high-resolution, multifrequency SZ observations promise to enable detailed studies of the ICM structures, by measuring the ICM temperature through the temperature-dependent relativistic corrections. In this work we develop a non-parametric method to derive three-dimensional physical quantities, including temperature, pressure, total mass, and peculiar velocities, of galaxy clusters from SZ observations alone. We test the performance of this method using hydrodynamical simulations of galaxy clusters, in order to assess systematic uncertainties in the reconstructed physical parameters. In particular, we analyze mock Cerro Chajnantor Atacama Telescope (CCAT) SZ observations, taking into account various sources of systematic uncertainties associated with instrumental effects and astrophysical foregrounds. We show that our method enables accurate reconstruction of the three-dimensional ICM profiles, while retaining full information about the gas distribution. We discuss the application of this technique for ongoing and future multifrequency SZ observations.

Baryon census in hydrodynamical simulations of galaxy clusters

We carry out an analysis of a set of cosmological SPH hydrodynamical simulations of galaxy clusters and groups aimed at studying the total baryon budget in clusters, and how this budget is shared between the hot diffuse component and the stellar component. Using the TreePM+SPH GADGET-3 code, we carried out one set of non-radiative simulations, and two sets of simulations including radiative cooling, star formation and feedback from supernovae (SN), one of which also accounting for the effect of feedback from active galactic nuclei (AGN). The analysis is carried out with the twofold aim of studying the implication of stellar and hot gas content on the relative role played by SN and AGN feedback, and to calibrate the cluster baryon fraction and its evolution as a cosmological tool. We find that both radiative simulation sets predict a trend of stellar mass fraction with cluster mass that tends to be weaker than the observed one. However this tension depends on the particular set of observational data considered. Including the effect of AGN feedback alleviates this tension on the stellar mass and predicts values of the hot gas mass fraction and total baryon fraction to be in closer agreement with observational results. We further compute the ratio between the cluster baryon content and the cosmic baryon fraction, Y_b, as a function of cluster-centric radius and redshift. At R_500 we find for massive clusters with M_500>2\times10^{14} h^{-1} M_sun that Y_b is nearly independent of the physical processes included and characterized by a negligible redshift evolution: Y_{b,500}=0.85+/-0.03 with the error accounting for the intrinsic r.m.s. scatter within the set of simulated clusters. At smaller radii, R_2500, the typical value of Y_b slightly decreases, by an amount that depends on the physics included in the simulations, while its scatter increases by about a factor of two.

Hydrodynamical simulations of galaxy clusters in dark energy cosmologies – II. c–M relation

We use hydrodynamical simulations of different dark energy cosmologies to investigate the concentration-mass (c-M) relation in galaxy clusters. In particular, we consider a reference \Lambda CDM model, two quintessence models with inverse power-law potentials (RP and SUGRA), and two extended quintessence models, one with positive and one with negative coupling with gravity (EQp and EQn respectively). All the models are normalized in order to match CMB data from WMAP3. We fit both the dark matter only and the total mass profile with a NFW profile, and recover the concentration of each halo from the fit using different definition. We consider both the complete catalog of clusters and groups and subsamples of objects at different level of relaxation. We find that the definition itself of the concentration can lead to differences up to 20% in its value and that these differences are smaller when more relaxed objects are considered. The c-M relation of our reference \Lambda CDM model is in good agreement with the results in literature, and relaxed objects have a higher normalization and a shallower slope with respect to the complete sample. The inclusion of baryon physics is found to influence more high-mass systems than low-mass ones, due to a higher concentration of baryons in the inner regions of massive halos. For the different dark energy models, we find that for \Lambda CDM, RP and SUGRA the normalization of the c-M relation is linked to the growth factor, with models having a higher value of \sigma 8 D+ having also a higher normalization. This simple scheme is no longer valid for EQp and EQn because in these models a time dependent effective gravitational interaction, whose redshift evolution depends on the sign of the coupling, is present. This leads to a decrease (increase) of the expected normalization in the EQp (EQn) model. [Abridged]

X-ray mass proxies from hydrodynamic simulations of galaxy clusters - I

We present a detailed study of scaling relations between total cluster mass and three mass proxies based on X-ray observables: temperature of the intra-cluster medium, gas mass and the product of the two, Y_X. Our analysis is based on two sets of high-resolution hydrodynamical simulations performed with the TreePM-SPH GADGET code. The first set includes about 140 clusters with masses above 5x10^13 M_sun/h (30 having mass above 10^15 M_sun/h), that have been simulated with (i) non-radiative physics and including (ii) cooling, star formation, chemical enrichment and the effect of supernova feedback triggering galactic ejecta. This large statistics is used to quantify the robustness of the scaling relations, to determine their redshift evolution and to calibrate their intrinsic scatter and its distribution. We use a smaller set of clusters including 18 halos with masses above 5x10^13 M_sun/h to test the robustness of mass proxies against changing the physical processes included in simulations (thermal conduction, artificial viscosity, cooling and star formation, galactic winds and AGN feedback). We find the M-Y_X scaling relation to be the least sensitive one to variations of the ICM physics, with its slope and redshift evolution close to the self-similar model predictions. The distribution of the scatter around the best-fitting relations is close to a log-normal one. M_gas has the smallest scatter in mass, with values of sigma_lnM = 0.04-0.06, depending on the physics included in the simulation, and with a mild dependence on redshift. The M-T relation is the one with the largest scatter, with sigma_lnM > 0.1 at z=0, increasing to > 0.15 at z=1. The intrinsic scatter in the M-Y_X relation is slightly larger than in the M-M_gas relation. These results confirm that both Y_X and M_gas mass proxies are well suited for cosmological applications of future large X-ray surveys. [abridged]

GAS CLUMPING IN THE OUTSKIRTS OF ΛCDM CLUSTERS

Recent Suzaku X-ray observations revealed that the observed entropy profile of the intracluster medium (ICM) deviates significantly from the prediction of hydrodynamical simulations of galaxy clusters. In this work, we show that gas clumping introduces significant biases in X-ray measurements of the ICM profiles in the outskirts of galaxy clusters. Using hydrodynamical simulations of galaxy cluster formation in a concordance Lambda-CDM model, we demonstrate that gas clumping leads to an overestimate of the observed gas density and causes flattening of the entropy profile. Our results suggest that gas clumping must be taken into account when interpreting X-ray measurements of cluster outskirts.

Ram pressure stripping in a galaxy formation model - I. A novel numerical approach

We develop a new numerical approach to describe the action of ram pressure stripping (RPS) within a semi-analytic model of galaxy formation and evolution which works in combination with non-radiative hydrodynamical simulations of galaxy clusters. The new feature in our method is the use of the gas particles to obtain the kinematical and thermodynamical properties of the intragroup and intracluster medium (ICM). This allows a self-consistent estimation of the RPS experienced by satellite galaxies. We find that the ram pressure (RP) in the central regions of clusters increases approximately one order of magnitude between z = 1 and 0, consistent with the increase in the density of the ICM. The mean RP experienced by galaxies within the virial radius increases with decreasing redshift. In clusters with virial masses M_vir ~10^15 h^-1 M_Sun, over 50 per cent of satellite galaxies have experienced RP ~10^(-11) h^2 dyn cm^-2 or higher for z <= 0.5. In smaller clusters (M_vir ~10^14 h^-1 M_Sun) the mean RP are approximately one order of magnitude lower at all redshifts. RPS has a strong effect on the cold gas content of galaxies for all cluster masses. At z = 0, over 70 per cent of satellite galaxies within the virial radius are completely depleted of cold gas. For the more massive clusters the fraction of depleted galaxies is already established at z ~ 1, whereas for the smaller clusters this fraction increases appreciably between z = 1 and 0. This indicates that the rate at which the cold gas is stripped depends on the virial mass of the host cluster. Compared to our new approach, the use of an analytic profile to describe the ICM results in an overestimation of the RP larger than 50 per cent for z >= 0.5.

Substructures in hydrodynamical cluster simulations

The abundance and structure of dark matter subhalos has been analyzed extensively in recent studies of dark matter-only simulations, but comparatively little is known about the impact of baryonic physics on halo substructures. We here extend the SUBFIND algorithm for substructure identification such that it can be reliably applied to dissipative hydrodynamical simulations that include star formation. This allows, in particular, the identification of galaxies as substructures in simulations of clusters of galaxies, and a determination of their content of gravitationally bound stars, dark matter, and hot and cold gas. Using a large set of cosmological cluster simulations, we present a detailed analysis of halo substructures in hydrodynamical simulations of galaxy clusters, focusing in particular on the influence both of radiative and non-radiative gas physics, and of non-standard physics such as thermal conduction and feedback by galactic outflows. We also examine the impact of numerical nuisance parameters such as artificial viscosity parameterizations. We find that diffuse hot gas is efficiently stripped from subhalos when they enter the highly pressurized cluster atmosphere. This has the effect of decreasing the subhalo mass function relative to a corresponding dark matter-only simulation. These effects are mitigated in radiative runs, where baryons condense in the central subhalo regions and form compact stellar cores. However, in all cases, only a very small fraction, of the order of one percent, of subhalos within the cluster virial radii preserve a gravitationally bound hot gaseous atmosphere. (abridged)

ROTATION AND TURBULENCE OF THE HOT INTRACLUSTER MEDIUM IN GALAXY CLUSTERS

Cosmological simulations of galaxy clusters typically find that the weight of a cluster at a given radius is not balanced entirely by the thermal gas pressure of the hot intracluster medium (ICM), with theoretical studies emphasizing the role of random turbulent motions to provide the necessary additional pressure support. Using a set of high-resolution, hydrodynamical simulations of galaxy clusters that include radiative cooling and star formation and are formed in a cold dark matter (CDM) universe, we find instead that in the most relaxed clusters rotational support exceeds that from random turbulent motions for radii 0.1–0.5 r500, while at larger radii, out to 0.8 r500, they remain comparable. We also find that the X-ray images of the ICM flatten prominently over a wide radial range, 0.1–0.4 r500. When compared with the average ellipticity profile of the observed X-ray images computed for nine relaxed nearby clusters, we find that the observed clusters are much rounder than the relaxed CDM clusters within ≈0.4 r500. Moreover, while the observed clusters display an average ellipticity profile that does not vary significantly with radius, the ellipticity of the relaxed CDM clusters declines markedly with increasing radius, suggesting that the ICM of the observed clusters rotates less rapidly than that of the relaxed CDM clusters out to ≈0.6 r500. When these results are compared with those obtained from a simulation without radiative cooling, we find a cluster ellipticity profile in much better agreement with the observations, implying that overcooling has a substantial impact on the gasdynamics and morphology out to larger radii than previously recognized. It also suggests that the 10–20% systematic errors from nonthermal gas pressure support reported for simulated cluster masses, obtained from fitting simulated X-ray data over large radial ranges within r500, may need to be revised downward. These results demonstrate the utility of X-ray ellipticity profiles as a probe of ICM rotation and overcooling which should be used to constrain future cosmological cluster simulations.

Reconstructing mass profiles of simulated galaxy clusters by combining Sunyaev-Zeldovich and X-ray images

We present a method to recover mass profiles of galaxy cluster s by combining data on thermal Sunyaev‐Zeldovich (tSZ) and X‐ray imaging, thereby avoiding to use any information on X‐ ray spectroscopy. This method, which represents a development of the geometrical deprojection technique presented in Ameglio et al. (2007), implements the solution of the hydrostatic equilibrium equation. In order to quantify the efficiency of our mass reconstructions, we apply our technique to a set of hydrodynamical simulations of galaxy clusters. We propose two versions of our method of mass reconstruction. Method 1 is completely model‐independent and assumes as fitting parameters the values of gas density an d total mass within different radial bins. Method 2 assumes instead the analytic mass profi le proposed by Navarro et al. (1997) (NFW). We find that the main source of bias in recoverin g the mass profiles is due to deviations from hydrostatic equilibrium, which cause an underestimate of the mass of about 10 per cent at r500 and up to 20 per cent at the virial radius. Method 1 provides a reconstructed mass which is biased low by about 10 per cent, with a 20 per cent scatter, with respect to the true mass profiles. Method 2 proves to be more stable, reducin g the scatter to 10 per cent, but with a larger bias of 20 per cent, mainly induced by the deviations from equilibrium in the outskirts. To better understand the results of Method 2, we check how well it allows to recover the relation between mass and concentration parameter. When analyzing the 3D mass profiles we find that including in the fit the inner 5 per cent of the viria l radius biases high the halo concentration, thus suggesting that the NFW profile is not a p erfect fit in the central regions of our simulations including cooling and star formation. Also, at a fixed mass, hotter clusters tend to have larger concentration. Our procedure recovers the concentration parameter essentially unbiased but with a scatter of about 50 per cent. In gen eral, our analysis demonstrates that combining X‐ray imaging with spatially resolved tSZ data is a valid alternative to using X‐ray spectroscopy to recover the mass of galaxy clusters.

Chemical enrichment of galaxy clusters from hydrodynamical simulations

We present cosmological hydrodynamical simulations of galaxy clusters aimed at studying the process of metal enrichment of the intra--cluster medium (ICM). These simulations have been performed by implementing a detailed model of chemical evolution in the Tree-SPH \gd code. This model allows us to follow the metal release from SNII, SNIa and AGB stars, by properly accounting for the lifetimes of stars of different mass, as well as to change the stellar initial mass function (IMF), the lifetime function and the stellar yields. As such, our implementation of chemical evolution represents a powerful instrument to follow the cosmic history of metal production. The simulations presented here have been performed with the twofold aim of checking numerical effects, as well as the impact of changing the model of chemical evolution and the efficiency of stellar feedback.