arXiv subjects

Massimo Meneghetti

Publications and source records attributed to Massimo Meneghetti.

At least 73 records · Page 4Linked to original sources

arXiv2017

Simulation-based marginal likelihood for cluster strong lensing cosmology

Comparisons between observed and predicted strong lensing properties of galaxy clusters have been routinely used to claim either tension or consistency with $Λ$CDM cosmology. However, standard approaches to such cosmological tests are unable to quantify the preference for one cosmology over another. We advocate approximating the relevant Bayes factor using a marginal likelihood that is based on the following summary statistic: the posterior probability distribution function for the parameters of the scaling relation between Einstein radii and cluster mass, $α$ and $β$. We demonstrate, for the first time, a method of estimating the marginal likelihood using the X-ray selected $z>0.5$ MACS clusters as a case in point and employing both N-body and hydrodynamic simulations of clusters. We investigate the uncertainty in this estimate and consequential ability to compare competing cosmologies, that arises from incomplete descriptions of baryonic processes, discrepancies in cluster selection criteria, redshift distribution, and dynamical state. The relation between triaxial cluster masses at various overdensities provide a promising alternative to the strong lensing test.

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arXiv2017

Fast Weak Lensing Simulations with Halo Model

Full ray-tracing maps of gravitational lensing, constructed from N-Body simulations, represent a fundamental tool to interpret present and future weak lensing data. However the limitation of computational resources and storage capabilities severely restrict the number of realizations that can be performed in order to accurately sample both the cosmic shear models and covariance matrices. In this paper we present a halo model formalism for weak gravitational lensing that alleviates these issues by producing weak-lensing mocks at a reduced computational cost. Our model takes as input the halo population within a desired light-cone and the linear power spectrum of the underlined cosmological model. We examine the contribution given by the presence of substructures within haloes to the cosmic shear power spectrum and quantify it to the percent level. Our method allows us to reconstruct high-resolution convergence maps, for any desired source redshifts, of light-cones that realistically trace the matter density distribution in the universe, account for masked area and sample selections. We compare our analysis on the same large scale structures constructed using ray-tracing techniques and find very good agreements both in the linear and non-linear regimes up to few percent levels. The accuracy and speed of our method demonstrate the potential of our halo model for weak lensing statistics and the possibility to generate a large sample of convergence maps for different cosmological models as needed for the analysis of large galaxy redshift surveys.

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arXiv2017

Mapping substructure in the HST Frontier Fields cluster lenses and in cosmological simulations

We map the lensing-inferred substructure in the first three clusters observed by the Hubble Space Telescope Frontier Fields Initiative (HSTFF): Abell 2744 (z = 0.308), MACSJ0416, (z = 0.396) and MACSJ1149 (z = 0.543). Statistically resolving dark-matter subhaloes down to ~10^{9.5} solar masses, we compare the derived subhalo mass functions (SHMFs) to theoretical predictions from analytical models and with numerical simulations in a Lambda Cold Dark Matter (LCDM) cosmology. Mimicking our observational cluster member selection criteria in the HSTFF, we report excellent agreement in both amplitude and shape of the SHMF over four decades in subhalo mass (10^{9-13} solar masses). Projection effects do not appear to introduce significant errors in the determination of SHMFs from simulations. We do not find evidence for a substructure crisis, analogous to the missing satellite problem in the Local Group, on cluster scales, but rather excellent agreement of the count-matched HSTFF SHMF down to M_{sub halo}/M_{halo} ~ 10^{-5}. However, we do find discrepancies in the radial distribution of sub haloes inferred from HSTFF cluster lenses compared to determinations from simulated clusters. This suggests that although the selected simulated clusters match the HSTFF sample in mass, they do not adequately capture the dynamical properties and complex merging morphologies of these observed cluster lenses. Therefore, HSTFF clusters are likely observed in a transient evolutionary stage that is presently insufficiently sampled in cosmological simulations. The abundance and mass function of dark matter substructure in cluster lenses continues to offer an important test of the LCDM paradigm, and at present we find no tension between model predictions and observations.

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arXiv2017

CLUMP-3D. Three dimensional lensing and multi-probe analysis of MACS J1206.2-0847, a remarkably regular cluster

Multi-wavelength techniques can probe the distribution and the physical properties of baryons and dark matter in galaxy clusters from the inner regions out to the peripheries. We present a full three-dimensional analysis combining strong and weak lensing, X-ray surface brightness and temperature, and the Sunyaev-Zel'dovich effect. The method is applied to MACS J1206.2-0847, a remarkably regular, face-on, massive, M_{200}=(1.1+-0.2)*10^{15}M_Sun/h, cluster at z=0.44. The measured concentration, c_{200}=6.3+-1.2, and the triaxial shape are common to halos formed in a LCDM scenario. The gas has settled in and follows the shape of the gravitational potential, which is evidence of pressure equilibrium via the shape theorem. There is no evidence for significant non-thermal pressure and the equilibrium is hydrostatic.

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arXiv2016

Constraints on the Mass, Concentration, and Nonthermal Pressure Support of Six CLASH Clusters from a Joint Analysis of X-ray, SZ, and Lensing Data

We present a joint analysis of Chandra X-ray observations, Bolocam thermal Sunyaev-Zel'dovich (SZ) effect observations, Hubble Space Telescope (HST) strong lensing data, and HST and Subaru Suprime-Cam weak lensing data. The multiwavelength dataset is used to constrain parametric models for the distribution of dark and baryonic matter in a sample of six massive galaxy clusters selected from the Cluster Lensing And Supernova survey with Hubble (CLASH). For five of the six clusters, the multiwavelength dataset is well described by a relatively simple model that assumes spherical symmetry, hydrostatic equilibrium, and entirely thermal pressure support. The joint analysis yields considerably better constraints on the total mass and concentration of the cluster compared to analysis of any one dataset individually. The subsample of five galaxy clusters is used to place an upper limit on the fraction of pressure support in the intracluster medium (ICM) due to nonthermal processes, such as turbulence and bulk flow of the gas. We constrain the nonthermal pressure fraction at r500c to be less than 0.11 at 95 percent confidence. This is in tension with state-of-the-art hydrodynamical simulations, which predict a nonthermal pressure fraction of approximately 0.25 at r500c for clusters of similar mass and redshift. This tension may be explained by the sample selection and/or our assumption of spherical symmetry.

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arXiv2016

Characterising Strong Lensing Galaxy Clusters using the Millennium-XXL and MOKA simulations

In this paper we investigate the strong lensing statistics in galaxy clusters. We extract dark matter haloes from the Millennium-XXL simulation, compute their Einstein radius distribution, and find a very good agreement with Monte Carlo predictions produced with the MOKA code. The distribution of the Einstein radii is well described by a log-normal distribution, with a considerable fraction of the largest systems boosted by different projection effects. We discuss the importance of substructures and triaxiality in shaping the size of the critical lines for cluster size haloes. We then model and interpret the different deviations, accounting for the presence of a Bright Central Galaxy (BCG) and two different stellar mass density profiles. We present scaling relations between weak lensing quantities and the size of the Einstein radii. Finally we discuss how sensible is the distribution of the Einstein radii on the cosmological parameters Ω_M-σ_8 finding that cosmologies with higher Ω_M and σ_8 possess a large sample of strong lensing clusters. The Einstein radius distribution may help distinguish Planck13 and WMAP7 cosmology at 3σ.

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arXiv2016

The Morphologies and Alignments of Gas, Mass, and the Central Galaxies of CLASH Clusters of Galaxies

Morphology is often used to infer the state of relaxation of galaxy clusters. The regularity, symmetry, and degree to which a cluster is centrally concentrated inform quantitative measures of cluster morphology. The Cluster Lensing and Supernova survey with Hubble Space Telescope (CLASH) used weak and strong lensing to measure the distribution of matter within a sample of 25 clusters, 20 of which were deemed to be relaxed based on their X-ray morphology and alignment of the X-ray emission with the BCG. Towards a quantitative characterization of this important sample of clusters, we present uniformly estimated X-ray morphological statistics for all 25 CLASH clusters. We compare X-ray morphologies of CLASH clusters with those identically measured for a large sample of simulated clusters from the MUSIC-2 simulations, selected by mass. We confirm a threshold in X-ray surface brightness concentration of C>0.4 for cool-core clusters, where C is the ratio of X-ray emission inside 100 kpc/h70 compared to inside 500 kpc/h70. We report and compare morphologies of these clusters inferred from Sunyaev-Zeldovich Effect (SZE) maps of the hot gas and in from projected mass maps based on strong and weak lensing. We find a strong agreement in alignments of the orientation of major axes for the lensing, X-ray, and SZE maps of nearly all of the CLASH clusters at radii of 500 kpc (approximately 0.5R500 for these clusters). We also find a striking alignment of clusters shapes at the 500 kpc scale, as measured with X-ray, SZE, and lensing, with that of the near-infrared stellar light at 10 kpc scales for the 20 "relaxed" clusters. This strong alignment indicates a powerful coupling between the cluster- and galaxy-scale galaxy formation processes.

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arXiv2016

Cosmology through arc statistics I: sensitivity to $Ω_m$ and $σ_8$

The next generation of large sky photometric surveys will finally be able to use arc statistics as a cosmological probe. Here we present the first of a series of papers on this topic. In particular, we study how arc counts are sensitive to the variation of two cosmological parameters: the (total) matter density parameter, $Ω_m$, and the normalisation of the primordial power spectrum, expressed in terms of $σ_8$. Both these parameters influence the abundances of collapsed structures and their internal structure. We compute the expected number of gravitational arcs with various length-to-width ratios in mock light cones, by varying these cosmological parameters in the ranges $0.1\leqΩ_m\leq0.5$ and $0.6\leqσ_8\leq 1$. We find that the arc counts dependence on $Ω_m$ and $σ_8$ is similar, but not identical, to that of the halo counts. We investigate how the precision of the constraints on the cosmological parameters based on arc counts depends on the survey area. We find that the constraining power of arc statistics degrades critically only for surveys covering an area smaller than $10\%$ of the whole sky. Finally, we consider the case in which the search for arcs is done only in frames where galaxy clusters have been previously identified. Adopting the selection function for galaxy clusters expected to be detected from photometric data in future wide surveys, we find that less than $10\%$ of the arcs will be missed, with only a small degradation of the corresponding cosmological constraints.

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arXiv2015

The Detection and Statistics of Giant Arcs Behind CLASH Clusters

We developed an algorithm to find and characterize gravitationally lensed galaxies (arcs) to perform a comparison of the observed and simulated arc abundance. Observations are from the Cluster Lensing And Supernova survey with Hubble (CLASH). Simulated CLASH images are created using the MOKA package and also clusters selected from the high resolution, hydrodynamical simulations, MUSIC, over the same mass and redshift range as the CLASH sample. The algorithm' s arc elongation accuracy, completeness and false positive rate are determined and used to compute an estimate of the true arc abundance. We derive a lensing efficiency of $4 \pm 1$ arcs (with length $\ge 6"$ and length-to-width ratio $\ge 7$) per cluster for the X-ray selected CLASH sample, $4 \pm 1$ arcs per cluster for the MOKA simulated sample and $3 \pm 1$ arcs per cluster for the MUSIC simulated sample. The observed and simulated arc statistics are in full agreement. We measure the photometric redshifts of all detected arcs and find a median redshift $z_s = 1.9$ with 33% of the detected arcs having $z_s > 3$. We find that the arc abundance does not depend strongly on the source redshift distribution but is sensitive to the mass distribution of the dark matter halos (e.g. the $c-M$ relation). Our results show that consistency between the observed and simulated distributions of lensed arc sizes and axial ratios can be achieved by using cluster-lensing simulations that are carefully matched to the selection criteria used in the observations.

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arXiv2015

Illuminating a Dark Lens : A Type Ia Supernova Magnified by the Frontier Fields Galaxy Cluster Abell 2744

SN HFF14Tom is a Type Ia Supernova (SN) discovered at z = 1.3457 +- 0.0001 behind the galaxy cluster Abell 2744 (z = 0.308). In a cosmology-independent analysis, we find that HFF14Tom is 0.77 +- 0.15 magnitudes brighter than unlensed Type Ia SNe at similar redshift, implying a lensing magnification of mu_obs = 2.03 +- 0.29. This observed magnification provides a rare opportunity for a direct empirical test of galaxy cluster lens models. Here we test 17 lens models, 13 of which were generated before the SN magnification was known, qualifying as pure "blind tests". The models are collectively fairly accurate: 8 of the models deliver median magnifications that are consistent with the measured mu to within 1-sigma. However, there is a subtle systematic bias: the significant disagreements all involve models overpredicting the magnification. We evaluate possible causes for this mild bias, and find no single physical or methodological explanation to account for it. We do find that model accuracy can be improved to some extent with stringent quality cuts on multiply-imaged systems, such as requiring that a large fraction have spectroscopic redshifts. In addition to testing model accuracies as we have done here, Type Ia SN magnifications could also be used as inputs for future lens models of Abell 2744 and other clusters, providing valuable constraints in regions where traditional strong- and weak-lensing information is unavailable.

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arXiv2015

Disentangling dark sector models using weak lensing statistics

We perform multi-plane ray-tracing using the GLAMER gravitational lensing code within high-resolution light-cones extracted from the CoDECS simulations: a suite of cosmological runs featuring a coupling between Dark Energy and Cold Dark Matter. We show that the presence of the coupling is evident not only in the redshift evolution of the normalisation of the convergence power spectrum, but also in differences in non-linear structure formation with respect to ΛCDM. Using a tomographic approach under the assumption of a ΛCDM cosmology, we demonstrate that weak lensing measurements would result in a σ8 value that changes with the source redshift if the true underlying cosmology is a coupled Dark Energy one. This provides a generic null test for these types of models. We also find that different models of coupled Dark Energy can show either an enhanced or a suppressed correlation between convergence maps with differing source redshifts as compared to ΛCDM. This would provide a direct way to discriminate between different possible realisations of the coupled Dark Energy scenario. Finally, we discuss the impact of the coupling on several lensing observables for different source redshifts and angular scales with realistic source redshift distributions for current ground-based and future space-based lensing surveys.

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arXiv2015

CLASH-X: A Comparison of Lensing and X-ray Techniques for Measuring the Mass Profiles of Galaxy Clusters

We present profiles of temperature (Tx), gas mass, and hydrostatic mass estimated from new and archival X-ray observations of CLASH clusters. We compare measurements derived from XMM and Chandra observations with one another and compare both to gravitational lensing mass profiles derived with CLASH HST and ground-based lensing data. Radial profiles of Chandra and XMM electron density and enclosed gas mass are nearly identical, indicating that differences in hydrostatic masses inferred from X-ray observations arise from differences in Tx measurements. Encouragingly, cluster Txs are consistent with one another at ~100-200 kpc radii but XMM Tx systematically decline relative to Chandra Tx at larger radii. The angular dependence of the discrepancy suggests additional investigation on systematics such as the XMM point spread function correction, vignetting and off-axis responses. We present the CLASH-X mass-profile comparisons in the form of cosmology-independent and redshift-independent circular-velocity profiles. Ratios of Chandra HSE mass profiles to CLASH lensing profiles show no obvious radial dependence in the 0.3-0.8 Mpc range. However, the mean mass biases inferred from the WL and SaWLens data are different. e.g., the weighted-mean value at 0.5 Mpc is = 0.12 for the WL comparison and = -0.11 for the SaWLens comparison. The ratios of XMM HSE mass profiles to CLASH lensing profiles show a pronounced radial dependence in the 0.3-1.0 Mpc range, with a weighted mean mass bias of value rising to ~0.3 at ~1 Mpc for the WL comparison and of 0.25 for SaWLens comparison. The enclosed gas mass profiles from both Chandra and XMM rise to a value 1/8 times the total-mass profiles inferred from lensing at 0.5 Mpc and remain constant outside of that radius, suggesting that [8xMgas] profiles may be an excellent proxy for total-mass profiles at >0.5 Mpc in massive galaxy clusters.

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arXiv2015

Hubble Space Telescope Combined Strong and Weak Lensing Analysis of the CLASH Sample: Mass and Magnification Models and Systematic Uncertainties

We present results from a comprehensive lensing analysis in HST data, of the complete CLASH cluster sample. We identify new multiple-images previously undiscovered allowing improved or first constraints on the cluster inner mass distributions and profiles. We combine these strong-lensing constraints with weak-lensing shape measurements within the HST FOV to jointly constrain the mass distributions. The analysis is performed in two different common parameterizations (one adopts light-traces-mass for both galaxies and dark matter while the other adopts an analytical, elliptical NFW form for the dark matter), to provide a better assessment of the underlying systematics - which is most important for deep, cluster-lensing surveys, especially when studying magnified high-redshift objects. We find that the typical (median), relative systematic differences throughout the central FOV are $\sim40\%$ in the (dimensionless) mass density, $κ$, and $\sim20\%$ in the magnification, $μ$. We show maps of these differences for each cluster, as well as the mass distributions, critical curves, and 2D integrated mass profiles. For the Einstein radii ($z_{s}=2$) we find that all typically agree within $10\%$ between the two models, and Einstein masses agree, typically, within $\sim15\%$. At larger radii, the total projected, 2D integrated mass profiles of the two models, within $r\sim2\arcmin$, differ by $\sim30\%$. Stacking the surface-density profiles of the sample from the two methods together, we obtain an average slope of $d\log (Σ)/d\log(r)\sim-0.64\pm0.1$, in the radial range [5,350] kpc. Lastly, we also characterize the behavior of the average magnification, surface density, and shear differences between the two models, as a function of both the radius from the center, and the best-fit values of these quantities.

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arXiv2014

CLASH: Weak-Lensing Shear-and-Magnification Analysis of 20 Galaxy Clusters

We present a joint shear-and-magnification weak-lensing analysis of a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters at 0.19<z<0.69 selected from the Cluster Lensing And Supernova survey with Hubble (CLASH). Our analysis uses wide-field multi-color imaging, taken primarily with Suprime-Cam on the Subaru Telescope. From a stacked shear-only analysis of the X-ray-selected subsample, we detect the ensemble-averaged lensing signal with a total signal-to-noise ratio of ~25 in the radial range of 200 to 3500kpc/h. The stacked tangential-shear signal is well described by a family of standard density profiles predicted for dark-matter-dominated halos in gravitational equilibrium, namely the Navarro-Frenk-White (NFW), truncated variants of NFW, and Einasto models. For the NFW model, we measure a mean concentration of $c_{200c}=4.01^{+0.35}_{-0.32}$ at $M_{200c}=1.34^{+0.10}_{-0.09} 10^{15}M_{\odot}$. We show this is in excellent agreement with Lambda cold-dark-matter (LCDM) predictions when the CLASH X-ray selection function and projection effects are taken into account. The best-fit Einasto shape parameter is $α_E=0.191^{+0.071}_{-0.068}$, which is consistent with the NFW-equivalent Einasto parameter of $\sim 0.18$. We reconstruct projected mass density profiles of all CLASH clusters from a joint likelihood analysis of shear-and-magnification data, and measure cluster masses at several characteristic radii. We also derive an ensemble-averaged total projected mass profile of the X-ray-selected subsample by stacking their individual mass profiles. The stacked total mass profile, constrained by the shear+magnification data, is shown to be consistent with our shear-based halo-model predictions including the effects of surrounding large-scale structure as a two-halo term, establishing further consistency in the context of the LCDM model.

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arXiv2014

The strongest gravitational lenses: III. The order statistics of the largest Einstein radii

The Einstein radius (ER) of a gravitational lens encodes information about decisive quantities such as halo mass, concentration, triaxiality, and orientation with respect to the observer. Thus, the largest Einstein radii can potentially be utilised to test the predictions of the LCDM model. Hitherto, studies have focussed on the single largest observed ER. We extend those studies by employing order statistics to formulate exclusion criteria based on the n largest Einstein radii and apply these criteria to the strong lensing analysis of 12 MACS clusters at z>0.5. We obtain the order statistics of Einstein radii by a MC approach, based on the semi-analytic modelling of the halo population on the past lightcone. After sampling the order statistics, we fit a GEV distribution to the first-order distribution, which allows us to derive analytic relations for the order statistics of the Einstein radii. We find that the Einstein radii of the 12 MACS clusters are not in conflict with the LCDM expectations. Our exclusion criteria indicate that, in order to exhibit tension with the concordance model, one would need to observe approximately twenty Einstein radii >30", ten >35" or five >42" in the range of 0.5<z<1.0 on the full sky. Furthermore, we find that, with increasing order, the haloes with the largest Einstein radii are on average less aligned along the line-of-sight and less triaxial. In general, the cumulative distribution functions steepen for higher orders, giving them better constraining power. (abridged)

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arXiv2014

Three Gravitationally Lensed Supernovae Behind CLASH Galaxy Clusters

We report observations of three gravitationally lensed supernovae (SNe) in the Cluster Lensing And Supernova survey with Hubble (CLASH) Multi-Cycle Treasury program. These objects, SN CLO12Car (z = 1.28), SN CLN12Did (z = 0.85), and SN CLA11Tib (z = 1.14), are located behind three different clusters, MACSJ1720.2+3536 (z = 0.391), RXJ1532.9+3021 (z = 0.345), and Abell 383 (z = 0.187), respectively. Each SN was detected in Hubble Space Telescope (HST) optical and infrared images. Based on photometric classification, we find that SNe CLO12Car and CLN12Did are likely to be Type Ia supernovae (SNe Ia), while the classification of SN CLA11Tib is inconclusive. Using multi-color light-curve fits to determine a standardized SN Ia luminosity distance, we infer that SN CLO12Car was approximately 1.0 +/- 0.2 mag brighter than field SNe Ia at a similar redshift and ascribe this to gravitational lens magnification. Similarly, SN CLN12Did is approximately 0.2 +/- 0.2 mag brighter than field SNe Ia. We derive independent estimates of the predicted magnification from CLASH strong+weak lensing maps of the clusters: 0.83 +/- 0.16 mag for SN CLO12Car, 0.28 +/- 0.08 mag for SN CLN12Did, and 0.43 +/- 0.11 mag for SN CLA11Tib. The two SNe Ia provide a new test of the cluster lens model predictions: we find that the magnifications based on the SN Ia brightness and those predicted by the lens maps are consistent. Our results herald the promise of future observations of samples of cluster-lensed SNe Ia (from the ground or space) to help illuminate the dark-matter distribution in clusters of galaxies, through the direct determination of absolute magnifications.

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arXiv2014

Mass and Concentration estimates from Weak and Strong Gravitational Lensing: a Systematic Study

We study how well halo properties of galaxy clusters, like mass and concentration, are recovered using lensing data. In order to generate a large sample of systems at different redshifts we use the code MOKA. We measure halo mass and concentration using weak lensing data alone (WL), fitting to an NFW profile the reduced tangential shear profile, or by combining weak and strong lensing data, by adding information about the size of the Einstein radius (WL+SL). For different redshifts, we measure the mass and the concentration biases and find that these are mainly caused by the random orientation of the halo ellipsoid with respect to the line-of-sight. Since our simulations account for the presence of a bright central galaxy, we perform mass and concentration measurements using a generalized NFW profile which allows for a free inner slope. This reduces both the mass and the concentration biases. We discuss how the mass function and the concentration mass relation change when using WL and WL+SL estimates. We investigate how selection effects impact the measured concentration-mass relation showing that strong lens clusters may have a concentration 20-30% higher than the average, at fixed mass, considering also the particular case of strong lensing selected samples of relaxed clusters. Finally, we notice that selecting a sample of relaxed galaxy clusters, as is done in some cluster surveys, explain the concentration-mass relation biases.

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arXiv2014

CLASH-VLT: Constraints on the Dark Matter Equation of State from Accurate Measurements of Galaxy Cluster Mass Profiles

A pressureless scenario for the Dark Matter (DM) fluid is a widely adopted hypothesis, despite the absence of a direct observational evidence. According to general relativity, the total mass-energy content of a system shapes the gravitational potential well, but different test particles perceive this potential in different ways depending on their properties. Cluster galaxy velocities, being $\ll$c, depend solely on the gravitational potential, whereas photon trajectories reflect the contributions from the gravitational potential plus a relativistic-pressure term that depends on the cluster mass. We exploit this phenomenon to constrain the Equation of State (EoS) parameter of the fluid, primarily DM, contained in galaxy clusters. We use the complementary information provided by the kinematic and lensing mass profiles of the galaxy cluster MACS 1206.2-0847 at $z=0.44$, as obtained in an extensive imaging and spectroscopic campaign within the CLASH survey. The unprecedented high quality of our data-set and the properties of this cluster are well suited to determine the EoS parameter of the cluster fluid. Since baryons contribute at most $15\%$ to the total mass in clusters and their pressure is negligible, the EoS parameter we derive describes the behavior of the DM fluid. We obtain the most stringent constraint on the DM EoS parameter to date, $w=(p_r+2\,p_t)/(3\,c^2ρ)=0.00\pm0.15\mathrm{(stat)}\pm0.08\mathrm{(syst)}$, averaged over the radial range $0.5\,\mathrm{Mpc}\leq$$r$$\leq$$r_{200}$, where $p_r$ and $p_t$ are the radial and tangential pressure, and $ρ$ is the density. We plan to further improve our constraint by applying the same procedure to all clusters from the ongoing CLASH-VLT program.

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