Joint deprojection of Sunyaev-Zeldovich and X-ray images of galaxy clusters

We present two non-parametric deprojection methods aimed at recovering the threedimensional density and temperature profiles of galaxy clusters from spatially resolved thermal Sunyaev-Zeldovich (tSZ) and X-ray surface brightness maps, thus avoiding the use of X-ray spectroscopic data. In both methods, the cluster is assumed spherically symmetric and modelled with an onion-skin structure. The first method follows a direct geometrical approach, in which the deprojection is performed independently for the tSZ and X-ray images, and the resulting profiles are then combined in order to extract density and temperature. The second method is based on the maximization of a single joint (tSZ and X-ray) likelihood function. This allows us to simultaneously fit the two signals by following a Monte Carlo Markov Chain (MCMC) approach. These techniques are tested against both an idealized spherical beta-model cluster and a set of clusters extracted from cosmological hydrodynamical simulations with and without instrumental noise. In the first case, the quality of reconstruction is excellent and demonstrates that such methods do not suffer from any intrinsic bias. As for the application to simulations, we projected each cluster along the three orthogonal directions defined by the principal axes of the momentum of inertia tensor. This enables us to check any bias in the deprojection associated to the cluster elongation along the line of sight. After averaging over all the three projection directions, we find an overall good reconstruction, with a small (less than or similar to 10 per cent) overestimate of the gas density profile. This turns into a comparable overestimate of the gas mass within the virial radius, which we ascribe to the presence of residual gas clumping. Apart from this small bias, the reconstruction has an intrinsic scatter of about 5 per cent, which is dominated by gas clumpiness. Cluster elongation along the line of sight biases the deprojected temperature profile upwards at r less than or similar to 0.2r(vir) and downwards at larger radii. A comparable bias is also found in the deprojected temperature profile. Overall, this turns into a systematic underestimate of the gas mass, up to 10 per cent. We point out that our recovered temperature profiles are much closer to the mass-weighted profiles than those obtained from the X-ray spectroscopic-like temperature. These results confirm the potentiality of combining tSZ and X-ray imaging observations to the study of the thermal structure of the intra-cluster medium out to large cluster-centric distances.