We present the results of a numerical study based on the analysis of the MUSIC-2 simulations, aimed at estimating the expected concentration-mass relation for the CLASH cluster sample. We study nearly 1400 halos simulated at high spatial and mass res
olution, which were projected along many lines-of-sight each. We study the shape of both their density and surface-density profiles and fit them with a variety of radial functions, including the Navarro-Frenk-White, the generalised Navarro-Frenk-White, and the Einasto density profiles. We derive concentrations and masses from these fits and investigate their distributions as a function of redshift and halo relaxation. We use the X-ray image simulator X-MAS to produce simulated Chandra observations of the halos and we use them to identify objects resembling the X-ray morphologies and masses of the clusters in the CLASH X-ray selected sample. We also derive a concentration-mass relation for strong-lensing clusters. We find that the sample of simulated halos which resemble the X-ray morphology of the CLASH clusters is composed mainly by relaxed halos, but it also contains a significant fraction of un-relaxed systems. For such a sample we measure an average 2D concentration which is ~11% higher than found for the full sample of simulated halos. After accounting for projection and selection effects, the average NFW concentrations of CLASH clusters are expected to be intermediate between those predicted in 3D for relaxed and super-relaxed halos. Matching the simulations to the individual CLASH clusters on the basis of the X-ray morphology, we expect that the NFW concentrations recovered from the lensing analysis of the CLASH clusters are in the range [3-6], with an average value of 3.87 and a standard deviation of 0.61. Simulated halos with X-ray morphologies similar to those of the CLASH clusters are affected by a modest orientation bias.
We aim at investigating potential biases in lensing and X-ray methods to measure the cluster mass profiles. We do so by performing realistic simulations of lensing and X-ray observations that are subsequently analyzed using observational techniques.
The resulting mass estimates are compared among them and with the input models. Three clusters obtained from state-of-the-art hydrodynamical simulations, each of which has been projected along three independent lines-of-sight, are used for this analysis. We find that strong lensing models can be trusted over a limited region around the cluster core. Extrapolating the strong lensing mass models to outside the Einstein ring can lead to significant biases in the mass estimates, if the BCG is not modeled properly for example. Weak lensing mass measurements can be largely affected by substructures, depending on the method implemented to convert the shear into a mass estimate. Using non-parametric methods which combine weak and strong lensing data, the projected masses within R200 can be constrained with a precision of ~10%. De-projection of lensing masses increases the scatter around the true masses by more than a factor of two due to cluster triaxiality. X-ray mass measurements have much smaller scatter (about a factor of two smaller than the lensing masses) but they are generally biased low by 5-20%. This bias is ascribable to bulk motions in the gas of our simulated clusters. Using the lensing and the X-ray masses as proxies for the true and the hydrostatic equilibrium masses of the simulated clusters and averaging over the cluster sample we are able to measure the lack of hydrostatic equilibrium in the systems we have investigated.
