Comparing Masses in Literature (CoMaLit)-I. Bias and scatter in weak lensing and X-ray mass estimates of clusters

The first building block to use galaxy clusters in astrophysics and cosmology is the accurate determination of their mass. Two of the most well regarded direct mass estimators are based on weak lensing (WL) determinations or X-ray analyses assuming hydrostatic equilibrium (HE). By comparing these two mass measurements in samples of rich clusters, we determined the intrinsic scatters, $\sigma_\mathrm{WL}\sim$15 per cent for WL masses and $\sigma_\mathrm{HE}\sim$25 per cent for HE masses. The certain assessment of the bias is hampered by differences as large as $\sim$40 per cent in either WL or HE mass estimates reported by different groups. If the intrinsic scatter in the mass estimate is not considered, the slope of any scaling relation `observable--mass' is biased towards shallower values, whereas the intrinsic scatter of the scaling is over-estimated.Comment: 14 pages, 7 figures; v2: 16 pages, 8 figures, MNRAS in press; results unchanged; extended presentation of the statistical method and of the correlations; products from the CoMaLit series are hosted and updated at http://pico.bo.astro.it/~sereno/CoMaLi

Note on a polytropic beta-model to fit the X-ray surface brightness of clusters of galaxies

In this note, I suggest that the beta-model used to fit the X-ray surface brightness profiles of extended sources, like groups and clusters of galaxies, has to be corrected when the counts are collected in a wide energy band comparable to the mean temperature of the source and a significant gradient in the gas temperature is observed. I present a revised version of the beta-model for the X-ray brightness that applies to a intracluster gas with temperature and density related by a polytropic equation and extends the standard version that is strictly valid for an isothermal gas. Given a temperature gradient observed through an energy window of 1--10 keV typical for the new generation of X-ray observatories, the beta parameter can change systematically up to 20 per cent from the value obtained under isothermal assumption, i.e. by an amount larger that any statistical uncertainty obtained from the present data. Within the virial regions of typical clusters of galaxies, these systematic corrections affect the total gravitating mass estimate by 5--10 per cent, the gas mass by 10--30 per cent and the gas fraction value up to 50 per cent, when compared to the measurements obtained under the isothermal assumption.Comment: 5 pages, references added, version printed on MNRAS. Also available at http://www-xray.ast.cam.ac.uk/~settori/paper.htm

CoMaLit - II. The scaling relation between mass and Sunyaev-Zel'dovich signal for Planck selected galaxy clusters

We discuss the scaling relation between mass and integrated Compton parameter of a sample of galaxy clusters from the all-sky {\it Planck} Sunyaev-Zel'dovich catalogue. Masses were measured with either weak lensing, caustics techniques, or assuming hydrostatic equilibrium. The retrieved $Y_{500}$-$M_{500}$ relation does not strongly depend on the calibration sample. We found a slope of 1.4-1.9, in agreement with self-similar predictions, with an intrinsic scatter of $20\pm10$ per cent. The absolute calibration of the relation can not be ascertained due to systematic differences of $\sim$20-40 per cent in mass estimates reported by distinct groups. Due to the scatter, the slope of the conditional scaling relation, to be used in cosmological studies of number counts, is shallower, $\sim$1.1-1.6. The regression methods employed account for intrinsic scatter in the mass measurements too. We found that Planck mass estimates suffer from a mass dependent bias.Comment: 14 pages, 7 figures; v2: 17 pages, 11 figures; MNRAS in press, results unchanged; extended discussion of the Planck calibration sample; added discussion of conditional vs symmetric scaling relations and of mixture of Gaussian functions as distribution of the independent variable; products from the CoMaLit series at http://pico.bo.astro.it/~sereno/CoMaLi

On the Discrepancy between Theoretical and X-Ray Concentration-Mass Relations for Galaxy Clusters

[Abridged] In the past 15 years, the concentration-mass relation has been investigated diffusely in theoretical studies. On the other hand, only recently has this relation been derived from X-ray observations. When that happened, the results caused a certain level of concern: the X-ray normalizations and slopes were found significantly dissimilar from those predicted by theory. We analyzed 52 objects, simulated each time with different physical recipes for the baryonic component, as well as 60 synthetic X-ray images, to determine if these discrepancies are real or artificial. In particular, we investigate how the simulated concentration-mass relation depends (1) on the radial range used to derive the concentration, (2) on the presence of baryons in the simulations, and on the prescription used to reproduce the gas. Finally, we evaluate (3) how the results differ when adopting an X-ray approach for the analysis and (4) how the selection functions based on X-ray luminosity can impact the results. All effects studied go in the direction of alleviating the discrepancy between observations and simulations, although with different significance: while the fitting radial range and the baryonic component play only a minor role, the X-ray approach and selection function have profound repercussion on the resulting concentration-mass relation.Comment: 15 pages, 11 figures, 3 tables, ApJ in press. Significant extension of the study of the selection-function influence and more attentive treatment of errors (results unchanged

Mass, shape and thermal properties of A1689 by a multi-wavelength X-ray, lensing and Sunyaev-Zel'dovich analysis

Knowledge of mass and concentration of galaxy clusters is crucial to understand their formation and evolution. Unbiased estimates require the understanding of the shape and orientation of the halo as well as its equilibrium status. We propose a novel method to determine the intrinsic properties of galaxy clusters from a multi-wavelength data set spanning from X-ray spectroscopic and photometric data to gravitational lensing to the Sunyaev-Zel'dovich effect (SZe). The method relies on two quite non informative geometrical assumptions: the distributions of total matter or gas are approximately ellipsoidal and co-aligned; they have different, constant axial ratios but share the same degree of triaxiality. Weak and strong lensing probe the features of the total mass distribution in the plane of the sky. X-ray data measure size and orientation of the gas in the plane of the sky. Comparison with the SZ amplitude fixes the elongation of the gas along the line of sight. These constraints are deprojected thanks to Bayesian inference. The mass distribution is described as a Navarro-Frenk-White halo with arbitrary orientation, gas density and temperature are modelled with parametric profiles. We applied the method to Abell 1689. Independently of the priors, the cluster is massive, M_{200}=(1.3+-0.2)*10^{15}M_sun, and over-concentrated, c_{200}=8+-1, but still consistent with theoretical predictions. The total matter is triaxial (minor to major axis ratio ~0.5+-0.1 exploiting priors from N-body simulations) with the major axis nearly orientated along the line of sight. The gas is rounder (minor to major axis ratio ~0.6+-0.1) and deviates from hydrostatic equilibrium. The contribution of non-thermal pressure is ~20-50 per cent in inner regions, <~ 300 kpc, and ~25+-5 per cent at ~1.5 Mpc.Comment: 14 pages; MNRAS, in pres

Self-similarity of temperature profiles in distant galaxy clusters: the quest for a Universal law

We present the XMM-Newton temperature profiles of 12 bright clusters of galaxies at 0.4<z<0.9, with 5<kT<11 keV. The normalized temperature profiles (normalized by the mean temperature T500) are found to be generally self-similar. The sample was subdivided in 5 cool-core (CC) and 7 non cool-core (NCC) clusters, by introducing a pseudo-entropy ratio sigma=(T_IN/T_OUT)X(EM_IN/EM_OUT)^-1/3 and defining the objects with sigma<0.6 as CC clusters and those with sigma>=0.6 as NCC clusters. The profiles of CC and NCC clusters differ mainly in the central regions, with the latters exhibiting a marginally flatter central profile. A significant dependence of the temperature profiles on the pseudo-entropy ratio sigma is detected by fitting a function of both r and sigma, showing an indication that the outer part of the profiles becomes steeper for higher values of sigma (i.e. transitioning towards the NCC clusters). No significant evidence of redshift evolution could be found within the redshift range sampled by our clusters (0.4<z<0.9). A comparison of our high-z sample with intermediate clusters at 0.1<z<0.3, showed how both the CC and NCC clusters temperature profiles have experienced some sort of evolution. This can be due by the fact that higher z clusters are at less advanced stage of their formation and did not have enough time to create a relaxed structure, characterized by a central temperature dip in CC clusters and by flatter profiles in NCC clusters. This is the first time that a systematic study of the temperature profiles of galaxy clusters at z>0.4 has been attempted, as we were able to define the closest possible relation to a Universal law for the temperature profiles of galaxy clusters at 0.1<z<0.9, showing a dependence on both the state of relaxation of the clusters and the redshift.Comment: 14 pages, 8 figures, A&A in press, minor changes (language editing

The mass-concentration relation in lensing clusters: the role of statistical biases and selection effects

The relation between mass and concentration of galaxy clusters traces their formation and evolution. Massive lensing clusters were observed to be over-concentrated and following a steep scaling in tension with predictions from the concordance $\Lambda$CDM paradigm. We critically revise the relation in the CLASH, the SGAS, the LOCUSS, and the high-redshift samples of weak lensing clusters. Measurements of mass and concentration are anti-correlated, which can bias the observed relation towards steeper values. We corrected for this bias and compared the measured relation to theoretical predictions accounting for halo triaxiality, adiabatic contraction of the halo, presence of a dominant BCG and, mostly, selection effects in the observed sample. The normalisation, the slope and the scatter of the expected relation are strongly sample-dependent. For the considered samples, the predicted slope is much steeper than that of the underlying relation characterising dark-matter only clusters. We found that the correction for statistical and selection biases in observed relations mostly solve the tension with the $\Lambda$CDM model.Comment: 13 pages, 3 figures; v2: 14 pages, minor changes, in press on MNRA