Cluster physics from joint weak gravitational lensing and Sunyaev-Zel'dovich data

We present a self consistent method to perform a joint analysis of Sunyaev-Zel'dovich and weak gravitational lensing observation of galaxy clusters. The spatial distribution of the cluster main components is described by a perturbative approach. Assuming hydrostatic equilibrium and the equation of state, we are able to deduce, from observations, maps of projected gas density and gas temperature. The method then naturally entails a X-ray emissivity prediction which can be compared to observed X-ray emissivity maps. By comparing with 2 simulated clusters we find that this prediction turns out to be in very good agreement with the simulations. The simulated and predicted surface brightness images have a correlation coefficient higher than 0.9 and their total flux differs by 0.9% or 9%. The method should be able to deal with real data in order to provide a physical description of the state of the cluster and of its constituents. The tests performed show that we can recover the amount and the spatial distributions of both the baryonic and non-baryonic material with an accuracy better than 10%. So, in principle, it might indeed help to alleviate some well known biases affecting, e.g. baryon fraction measurements.