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We present a self consistent method to perfom a joint analysis ofSunyaev-Zel'dovich and weak gravitational lensing observation of galaxyclusters. The spatial distribution of the cluster main constituents isdescribed by a perturbative approach. Assuming the hydrostatic equilibrium andthe equation of state, we are able to deduce, from observations, maps ofprojected gas density and gas temperature. The method then naturally entails aX-ray emissivity prediction which can be compared to observed X-ray emissivitymaps. When tested on simulated clusters (noise free), this prediction turns outto be in very good agreement with the simulated surface brightness. Thesimulated and predicted surface brightness images have a correlationcoefficient higher than 0.9 and the total flux differ by 0.9 % or 9 % in thetwo simulated clusters we studied. The method should be easily used on realdata in order to provide a physical description of the cluster physics and ofits constituents. The tests performed show that we can recover the amount andthe spatial distributions of both the baryonic and non-baryonic material withan accuracy better than 10 %. So, in principle, in it might indeed help toalleviate some well known bias affecting, eg baryon fraction measurements.Comment: 11 pages. 15 figures. Submitted to A&

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