Measuring the hydrostatic mass bias in galaxy clusters by combining Sunyaev-Zel'dovich and CMB lensing data

The cosmological parameters prefered by the cosmic microwave background (CMB) primary anisotropies predict many more galaxy clusters than those that have been detected via the thermal Sunyaev-Zeldovich (tSZ) effect. This tension has attracted considerable attention since it could be evidence of physics beyond the simplest $\Lambda$CDM model. However, an accurate and robust calibration of the mass-observable relation for clusters is necessary for the comparison, which has been proven difficult to obtain so far. Here, we present new contraints on the mass-pressure relation by combining tSZ and CMB lensing measurements about optically-selected clusters. Consequently, our galaxy cluster sample is independent from the data employed to derive cosmological constrains. We estimate an average hydrostatic mass bias of $b = 0.26 \pm 0.07$, with no significant mass nor redshift evolution. This value greatly reduces the tension between the predictions of $\Lambda$CDM and the observed abundance of tSZ clusters while being in agreement with recent estimations from tSZ clustering. On the other hand, our value for $b$ is higher than the predictions from hydro-dynamical simulations. This suggests the existence of mechanisms driving large departures from hydrostatic equilibrium and that are not included in state-of-the-art simulations, and/or unaccounted systematic errors such as biases in the cluster catalogue due to the optical selection.Comment: 4 pages, 3 figure

Reconstruction of the two-dimensional gravitational potential of galaxy clusters from X-ray and Sunyaev-Zel'dovich measurements

The mass of galaxy clusters is not a direct observable, nonetheless it is commonly used to probe cosmological models. Based on the combination of all main cluster observables, that is, the X-ray emission, the thermal Sunyaev-Zel'dovich (SZ) signal, the velocity dispersion of the cluster galaxies, and gravitational lensing, the gravitational potential of galaxy clusters can be jointly reconstructed. We derive the two main ingredients required for this joint reconstruction: the potentials individually reconstructed from the observables and their covariance matrices, which act as a weight in the joint reconstruction. We show here the method to derive these quantities. The result of the joint reconstruction applied to a real cluster will be discussed in a forthcoming paper. We apply the Richardson-Lucy deprojection algorithm to data on a two-dimensional (2D) grid. We first test the 2D deprojection algorithm on a $\beta$-profile. Assuming hydrostatic equilibrium, we further reconstruct the gravitational potential of a simulated galaxy cluster based on synthetic SZ and X-ray data. We then reconstruct the projected gravitational potential of the massive and dynamically active cluster Abell 2142, based on the X-ray observations collected with XMM-Newton and the SZ observations from the Planck satellite. Finally, we compute the covariance matrix of the projected reconstructed potential of the cluster Abell 2142 based on the X-ray measurements collected with XMM-Newton. The gravitational potentials of the simulated cluster recovered from synthetic X-ray and SZ data are consistent, even though the potential reconstructed from X-rays shows larger deviations from the true potential. Regarding Abell 2142, the projected gravitational cluster potentials recovered from SZ and X-ray data reproduce well the projected potential inferred from gravitational-lensing observations. (abridged)Comment: accepted for publication in the journal A&

The XMM Cluster Outskirts Project (X-COP): Physical conditions to the virial radius of Abell 2142

Context. Galaxy clusters are continuously growing through the accretion of matter in their outskirts. This process induces inhomogeneities in the gas density distribution (clumping) which need to be taken into account to recover the physical properties of the intracluster medium (ICM) at large radii. Aims. We studied the thermodynamic properties in the outskirts (R > R500) of the massive galaxy cluster Abell 2142 by combining the Sunyaev Zel'dovich (SZ) effect with the X-ray signal. Methods. We combined the SZ pressure profile measured by Planck with the XMM-Newton gas density profile to recover radial profiles of temperature, entropy and hydrostatic mass out to 2R500. We used a method that is insensitive to clumping to recover the gas density, and we compared the results with traditional X-ray measurement techniques. Results. When taking clumping into account, our joint SZ/X-ray entropy profile is consistent with the predictions from pure gravitational collapse, whereas a significant entropy flattening is found when the effect of clumping is neglected. The hydrostatic mass profile recovered using joint X-ray/SZ data agrees with that obtained from spectroscopic X-ray measurements and with mass reconstructions obtained through weak lensing and galaxy kinematics. Conclusions. We found that clumping can explain the entropy flattening observed by Suzaku in the outskirts of several clusters. When using a method insensitive to clumping for the reconstruction of the gas density, the thermodynamic properties of Abell 2142 are compatible with the assumption that the thermal gas pressure sustains gravity and that the entropy is injected at accretion shocks, with no need to evoke more exotic physics. Our results highlight the need for X-ray observations with sufficient spatial resolution, and large collecting area, to understand the processes at work in cluster outer regions.Comment: 22 pages, 32 figures, accepted in the journal A&

The XMM Cluster Outskirts Project (X-COP): thermodynamic properties of the intracluster medium out to R 200 in Abell 2319

Aims. We present the joint analysis of the X-ray and Sunyaev Zel’dovich(SZ) signals in Abell 2319, the galaxy cluster with the highest signal-to-noise ratio in SZ Planck maps and that has been surveyed within our XMM-Newton Cluster Outskirts Project (X-COP), a very large program which aims to grasp the physical condition in 12 local (z < 0.1) and massive (M200 > 3 × 1014 M⊙) galaxy clusters out to R200 and beyond. Methods. We recover the profiles of the thermodynamic properties by the geometrical deprojection of the X-ray surface brightness, of the SZ Comptonization parameter, and accurate and robust spectroscopic measurements of the gas temperature out to 3.2 Mpc (1.6 R200 ), 4 Mpc (2 R200 ), and 1.6 Mpc (0.8 R200 ), respectively. We resolve the clumpiness of the gas density to be below 20% over the entire observed volume. We also demonstrate that most of this clumpiness originates from the ongoing merger and can be associated with large-scale inhomogeneities (the “residual” clumpiness). We estimate the total mass through the hydrostatic equilibrium equation. This analysis is done both in azimuthally averaged radial bins and in eight independent angular sectors, enabling us to study in detail the azimuthal variance of the recovered properties. Results. Given the exquisite quality of the X-ray and SZ datasets, their radial extension, and their complementarity, we constrain at R200 the total hydrostatic mass, modelled with a Navarro–Frenk–White profile at very high precision (M200 = 10.7 ± 0.5stat. ± 0.9syst. × 1014 M⊙). We identify the ongoing merger and how it is affecting differently the gas properties in the resolved azimuthal sectors. We have several indications that the merger has injected a high level of non-thermal pressure in this system: the clumping free density profile is above the average profile obtained by stacking Rosat/PSPC observations; the gas mass fraction recovered using our hydrostatic mass profile exceeds the expected cosmic gas fraction beyond R500; the pressure profile is flatter than the fit obtained by the Planck Collaboration; the entropy profile is flatter than the mean profile predicted from non-radiative simulations; the analysis in azimuthal sectors has revealed that these deviations occur in a preferred region of the cluster. All these tensions are resolved by requiring a relative support of about 40% from non-thermal to the total pressure at R200