Riccardo Valdarnini

Total mass biases in X-ray galaxy clusters

Context. The exploitation of clusters of galaxies as cosmological probes relies on accurate measurements of their total gravitating mass. X-ray observations provide a powerful means of probing the total mass distribution in galaxy clusters, but might be affected by observational biases and rely on simplistic assumptions originating from our limited understanding of the intracluster medium physics. Aims. This paper is aimed at elucidating the reliability of X-ray total mass estimates in clusters of galaxies by properly disentangling various biases of both observational and physical origin. Methods. We use N-body/SPH simulation of a large sample of ∼100 galaxy clusters and investigate total mass biases by comparing the mass reconstructed adopting an observational-like approach with the true mass in the simulations. X-ray surface brightness and temperature profiles extracted from the simulations are fitted with different models and adopting different radial fitting ranges in order to investigate modeling and extrapolation biases. Different theoretical definitions of gas temperature are used to investigate the effect of spectroscopic temperatures and a power ratio analysis of the surface brightness maps allows us to assess the dependence of the mass bias on cluster dynamical state. Moreover, we perform a study on the reliability of hydrostatic and hydrodynamical equilibrium mass estimates using the full three-dimensional information in the simulation. Results. A model with a low degree of sophistication such as the polytropic β-model can introduce, in comparison with a more adequate model, an additional mass underestimate of the order of ∼10% at r500 and ∼15% at r200. Underestimates due to extrapolation alone are at most of the order of ∼10% on average, but can be as large as ∼50% for individual objects. Masses are on average biased lower for disturbed clusters than for relaxed ones and the scatter of the bias rapidly increases with increasingly disturbed dynamical state. The bias originating from spectroscopic temperatures alone is of the order of 10% at all radii for the whole numerical sample, but strongly depends on both dynamical state and cluster mass. From the full three dimensional information in the simulations we find that the hydrostatic equilibrium assumption yields masses underestimated by ∼10–15% and that masses computed by means of the hydrodynamical estimator are unbiased. Finally, we show that there is excellent agreement between our findings, results from similar analyses based on both Eulerian and Lagrangian simulations, and recent observational work based on the comparison between X-ray and gravitational lensing mass estimates.

LoCuSS: a comparison of cluster mass measurements from XMM-Newton and Subaru-testing deviation from hydrostatic equilibrium and non-thermal pressure support

We acknowledge support from KICP in Chicago for hospitality, and thank our LoCuSS collaborators, especially Masahiro Takada and Keiichi Umetsu, for helpful comments on the manuscript. Y.Y.Z. thanks Massimo Meneghetti and Gabriel Pratt for useful discussion. Y.Y.Z. acknowledges support by the DFG through Emmy Noether Research Grant RE 1462/ 2, through Schwerpunkt Program 1177, and through project B6 “Gravitational Lensing and X-ray Emission by Non-Linear Structures” of Transregional Collaborative Research Centre TRR 33 The Dark Universe, and support by the German BMBF through the Verbundforschung under grant 50 OR 0601. This work is supported by a Grant-in-Aid for the COE Program “Exploring New Science by Bridging Particle-Matter Hierarchy” and G-COE Program “Weaving Science Web beyond Particle-Matter Hierarchy” in Tohoku University, funded by theMinistry of Education, Science, Sports and Culture of Japan. This work is, in part, supported by a Grant-in-Aid for Science Research in a Priority Area “Probing the Dark Energy through an Extremely Wide and Deep Survey with Subaru Telescope” (18072001) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan. N.O. is, in part, supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (20740099). A.F. acknowledges support from BMBF/DLR under grant 50 OR 0207 and MPG, and was partially supported by a NASA grant NNX08AX46G to UMBC. G.P.S. acknowledges support from the Royal Society and STFC. D.P.M. acknowledges support provided by NASA through Hubble Fellowship grant HF-51259.01 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555.

Iron abundances and heating of the intracluster medium in hydrodynamical simulations of galaxy clusters

Results from a large set of hydrodynamical smoothed particle hydrodynamics (SPH) simulations of galaxy clusters in a flat ΛCDM cosmology are used to investigate the metal enrichment and heating of the intracluster medium (ICM). The physical modelling of the gas includes radiative cooling, star formation, energy feedback and metal enrichment which follow from the explosions of supernovae of type II and Ia. The metallicity dependence of the cooling function is also taken into account. The gas is metal-enriched from star particles according to the SPH prescriptions. The simulations have been performed to study the dependence of final metal abundances and heating of the ICM on the numerical resolution and the model parameters. For a fiducial set of model prescriptions the results indicate radial iron profiles in broad agreement with observations; global iron abundances are also consistent with data. It is found that the iron distribution in the intracluster medium is critically dependent on the shape of the metal deposition profile. At large radii the radial iron abundance profiles in the simulations are steeper than those in the data, suggesting a dynamical evolution of simulated clusters different from those observed. For low-temperature clusters simulations yield iron abundances below the allowed observational range, unless a minimum diffusion length of metals in the ICM is introduced. The simulated emission-weighted radial temperature profiles are in good agreement with data for cooling flow clusters, but at very small distances from the cluster centres (∼2 per cent of the virial radii) the temperatures are a factor of ∼2 higher than the measured spectral values. The luminosity–temperature relation is in excellent agreement with the data; cool clusters (TX∼ 1 keV) have a core excess entropy of ∼200 keV cm2 and their X-ray properties are unaffected by the amount of feedback energy that has heated the ICM. The findings support the model proposed recently by Bryan, where the cluster X-ray properties are determined by radiative cooling. The fraction of hot gas fg at the virial radius increases with TX, and the distribution obtained from the simulated cluster sample is consistent with the observational ranges.

The impact of numerical viscosity in SPH simulations of galaxy clusters

The goal of this paper is to investigate in N-body/SPH hydrodynamical cluster simulations the impact of artificial viscosity on the ICM thermal and velocity field statistical properties. To properly reduce the effects of artificial viscosity, a time-dependent artificial viscosity scheme is implemented in an SPH code in which each particle has its own viscosity parameter, whose time evolution is governed by the local shock conditions. The new SPH code is verified in a number of test problems with known analytical or numerical reference solutions and is then used to construct a large set of N-body/SPH hydrodynamical cluster simulations. These simulations are designed to study in SPH simulations the impact of artificial viscosity on the thermodynamics of the ICM and its velocity field statistical properties by comparing results extracted at the present epoch from runs with different artificial viscosity parameters, cluster dynamical states, numerical resolution, and physical modeling of the gas. Spectral properties of the gas velocity field are investigated by measuring the velocity power spectrum E(k) for the simulated clusters. Over a limited range, the longitudinal component Ec(k) exhibits a Kolgomorov-like scaling ∝k −5/3 , whilst the solenoidal power spectrum component Es(k) is strongly influenced by numerical resolution effects. The dependence of the spectra E(k) on dissipative effects is found to be significant at length scales 256 3 gas particles are necessary to provide a correct description of turbulent spectral properties over a decade in wavenumbers, whilst radial profiles of thermodynamic variables can be reliably obtained using N > 64 3 particles. Finally, simulations in which the gas can cool radiatively are characterized by the presence in the cluster inner regions of high levels of turbulence, generated by the interaction of the compact cool gas core with the ambient medium. These findings strongly support the viability of a turbulent heating model in which radiative losses in the core are compensated by heat diffusion and viscous dissipation of turbulent motion.

Measurement of the Dark Matter Velocity Anisotropy in Galaxy Clusters

The internal dynamics of a dark matter structure may have the remarkable property that the local temperature in the structure depends on direction. This is parameterized by the velocity anisotropy ? which must be zero for relaxed collisional structures, but has been shown to be nonzero in numerical simulations of dark matter structures. Here, we present a method for inferring the radial profile of the velocity anisotropy of the dark matter halo in a galaxy cluster from X-ray observables of the intracluster gas. This nonparametric method is based on a universal relation between the dark matter temperature and the gas temperature which is confirmed through numerical simulations. We apply this method to observational data and we find that ? is significantly different from zero at intermediate radii. Thus, we find a strong indication that dark matter is effectively collisionless on the dynamical timescale of clusters, which implies an upper limit on the self-interaction cross-section per unit mass ?/m 1 cm2 g?1. Our results may provide an independent way to determine the stellar mass density in the central regions of a relaxed cluster, as well as a test of whether a cluster is in fact relaxed.

The MUSIC of Galaxy Clusters II: X-ray global properties and scaling relations

We present the X-ray properties and scaling relations of a large sample of clusters extracted from the Marenostrum MUltidark SImulations of galaxy Clusters (MUSIC) dataset. We focus on a sub-sample of 179 clusters at redshift z � 0.11, with 3.2 × 10 14 h −1 M⊙ < Mvir < 2 × 10 15 h −1 M⊙, complete in mass. We employed the X-ray photon simulator PHOX to obtain synthetic Chandra observations and derive observable-like global properties of the intracluster medium (ICM), as X-ray temperature (TX) and luminosity (LX). TX is found to slightly under-estimate the true mass-weighted temperature, although tracing fairly well the cluster total mass. We also study the effects of TX on scaling relations with cluster intrinsic properties: total (M500 and gas Mg,500 mass; integrated Compton parameter (YSZ) of the Sunyaev-Zel’dovich (SZ) thermal effect; YX = Mg,500 TX. We confirm that YX is a very good mass proxy, with a scatter on M500 YX and YSZ YX lower than 5%. The study of scaling relations among X-ray, intrinsic and SZ properties indicates that simulated MUSIC clusters reasonably resemble the self-similar prediction, especially for correlations involving TX. The observational approach also allows for a more direct comparison with real clusters, from which we find deviations mainly due to the physical description of the ICM, affecting TX and, particularly, LX.

Clustering of galaxy clusters. II: Rare events in the cluster distribution

Subsamples of the Abell and ACO cluster catalogs, which are nearly complete, are analyzed in order to study the large-scale structure traced by rich clusters. A variety of statistical techniques, minimal spanning trees, percolation, void probability functions, and cluster alignments, are used and the findings are compared with that expected from an ensemble of simulated cluster catalogs having the same selection functions and low-order clustering as the real data

A Global Descriptor of Spatial Pattern Interaction in the Galaxy Distribution

We present the function J as a morphological descriptor for point patterns formed by the distribution of galaxies in the universe. This function was recently introduced in the field of spatial statistics, and is based on the nearest-neighbor distribution and the void probability function. The J descriptor allows us to distinguish clustered (i.e., correlated) from regular (i.e., anticorrelated) point distributions. We outline the theoretical foundations of the method, perform tests with a Matern cluster process as an idealized model of galaxy clustering, and apply the descriptor to galaxies and loose groups in the Perseus-Pisces Survey. A comparison with mock samples extracted from a mixed dark matter simulation shows that the J descriptor can be profitably used to constrain (or in this case reject) viable models of cosmic structure formation.

Global cluster morphology and its evolution: X-ray data versus CDM, ΛCDM and CHDM models

Abstract The global structure of galaxy clusters and its evolution are tested within a large set of TREESPH simulations aimed to allow a systematic statistical comparison with available X–ray data. Structure tests are based on the so–called power ratios introduced by Buote & Tsai (1995)[ApJ, 452, 522]. The cosmological models considered are flat CDM, ΛCDM ( Ω Λ =0.7 ) and CHDM ( Ω h =0.2 , 1 massive ν). All models are normalized so to provide a fair number density of clusters. For each model we perform a P3M cosmological simulation in a large box, where we select the volumes where the most massive 40 clusters form. Then we go back to the initial redshift and run a hydrodynamical TREESPH simulation for each of them. In this way we can perform a statistical comparison of the global morphology of clusters, expected in each cosmological model, with ROSAT data, using the Student t-test, the F-test and the Kolmogorov–Smirnov test. The last test and its generalization to 2-dimensional distributions are also used to compare the joint distributions of 2 or 3 power ratios. We find that using DM distribution, instead of gas, as was done in some of previous analyses, leads to systematically biased results, as the baryon distribution is substantially less structured than DM distribution. We also find that the cosmological models considered have different behaviours in respect to these tests: ΛCDM has the worst performance. CDM and the CHDM mixture considered here have similar scores. Although the general trend of power ratio distributions is already fit by these models, a further improvement is expected either from a different DM mix or a non-flat CDM model.

Hydrodynamic capabilities of an SPH code incorporating an artificial conductivity term with a gravity-based signal velocity

This paper investigates the hydrodynamic performances of an smoothed particle hydrodynamics (SPH) code incorporating an artificial heat conductivity term in which the adopted signal velocity is applicable when gravity is present. To this end, we analyze results from simulations produced using a suite of standard hydrodynamical test problems. In accordance with previous findings, we show that the performances of SPH in describing the development of Kelvin-Helmholtz instabilities depend strongly on both the consistency of the initial condition set-up and the leading error in the momentum equation due to incomplete kernel sampling. In contrast, the presence of artificialconductivity does not significantly affect theresults.An errorand stabilityanalysis shows that thequartic B-splinekernel (M5) possesses very good stability properties and so we propose its use with a large neighbor number, between ∼50 (2D) to ∼100 (3D), to improve convergence in simulation results without being affected by the so-called clumping instability. Moreover, the results of the Sod shock tube demonstrate that to obtain simulation profiles in accord with the analytic solution, for simulations employing kernels with a non-zero first derivative at the origin, it is necessary to use a much larger number of neighbors than in the case of the M5 runs. Our SPH simulations of the blob test show that in order to achieve blob disruption it is necessary to include an artificial conductivity term. However, we find that in the regime of strong supersonic flows an appropriate limiting condition, which depends on the Prandtl number, must be imposed on the artificial conductivity SPH coefficients in order to avoid an unphysical amount of heat diffusion. Our results from hydrodynamic simulations that include self-gravity show profiles of hydrodynamic variables that are in much better agreement with those produced using mesh-based codes. In particular, the final levels of core entropies in cosmological simulations of galaxy clusters are consistent with those found using AMR codes. This demonstrates that the proposed diffusion scheme is capable of mimicking the process of entropy mixing that is produced during structure formation because of the diffusion caused by turbulence. Finally, the results of our Rayleigh-Taylor instability test demonstrate that in the regime of very subsonic flows the code still has several difficulties in the treatment of hydrodynamic instabilities. These problems are intrinsic to the way in which standard SPH gradients are calculated and not to the implementation of the artificial conductivity term. To overcome these difficulties, several numerical schemes have been proposed that, if coupled with the SPH implementation presented in this paper, could solve the issues that have recently been addressed in investigating SPH performances to model subsonic turbulence.