Francisco Javier Castander
Institute for Space Studies of Catalonia 
 

We discuss the combination of optical, radio and X-rays observations of clusters of galaxies to constrain their gravitational potentials. Each observational set provides different information about the cluster: the distortions of background galaxies depend on the cluster projected potential; the Sunyaev-Zel'dovich (SZ) decrement, on the integrated pressure along the line of sight and the X-ray emission, on the square of the projected gas density.

We summarise some approaches in the literature to combine these datasets.  We use a maximum likelihood analysis to combine weak lensing, X-ray and SZ data to derive the cluster potential. We discuss different approaches to construct the likelihood functions and the different assumptions required.