Resolving the line-of-sight structure of galaxy clusters by combining X-ray and lensing data

The projected gravitational potential of galaxy clusters is reflected in both their X-ray emission and their imprint on the images of background sources due to their gravitational lensing effects. Since these projections of the potential are weighted differently along the line-of-sight, we propose a method to combine them and remove the degeneracy between two cases: (i) a cluster consisting of a single potential well, or (ii) an apparent cluster composed of several potential wells projected onto each other. We demonstrate with simulated data of potential models that this method indeed allows to significantly distinguish multiple from single clusters. The confidence limit for this distinction depends on the mass ratio between the clusters. It ranges from ~ 15 sigma for mass ratio 1:1 to ~ 4 sigma for mass ratio 1:6. Furthermore, the method reconstructs the correct cluster mass, the correct mass ratio of the two clusters, and the correct scale radii with typical fractional accuracies of a few percent at 3 sigma confidence. As an aside, our method allows to accurately determine gas fractions in clusters, also with 3 sigma fractional accuracies of order a few percent. We argue that our method provides an alternative to the commonly used beta-fit technique, and yields more reliable results in a broader range of cases.