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Tchernin, C.; Bartelmann, M.; Huber, K.; Dekel, A.; Hurier, G.; Majer, C. L.; Meyer, S.; Zinger, E.; Eckert, D.; Meneghetti, M.; Merten, J. (2018): Reconstruction of the two-dimensional gravitational potential of galaxy clusters from X-ray and Sunyaev-Zel'dovich measurements. In: Astronomy & Astrophysics, Vol. 614, A38
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Context. The mass of galaxy clusters is not a direct observable, nonetheless it is commonly used to probe cosmological models. Based on the combination of all main cluster observables, that is, the X-ray emission, the thermal Sunyaev-Zel'dovich (SZ) signal, the velocity dispersion of the cluster galaxies, and gravitational lensing, the gravitational potential of galaxy clusters can be jointly reconstructed. Aims. We derive the two main ingredients required for this joint reconstruction: the potentials individually reconstructed from the observables and their covariance matrices, which act as a weight in the joint reconstruction. We show here the method to derive these quantities. The result of the joint reconstruction applied to a real cluster will be discussed in a forthcoming paper. Methods. We apply the Richardson-Lucy deprojection algorithm to data on a two-dimensional (2D) grid. We first test the 2D deprojection algorithm on a beta-profile. Assuming hydrostatic equilibrium, we further reconstruct the gravitational potential of a simulated galaxy cluster based on synthetic SZ and X-ray data. We then reconstruct the projected gravitational potential of the massive and dynamically active cluster Abell 2142, based on the X-ray observations collected with XMM-Newton and the SZ observations from the Planck satellite. Finally, we compute the covariance matrix of the projected reconstructed potential of the cluster Abell 2142 based on the X-ray measurements collected with XMM-Newton. Results. The gravitational potentials of the simulated cluster recovered from synthetic X-ray and SZ data are consistent, even though the potential reconstructed from X-rays shows larger deviations from the true potential. Regarding Abell 2142, the projected gravitational cluster potentials recovered from SZ and X-ray data reproduce well the projected potential inferred from gravitational-lensing observations. We also observe that the covariance matrix of the potential for Abell 2142 reconstructed from XMM-Newton data sensitively depends on the resolution of the deprojected grid and on the smoothing scale used in the deprojection. Conclusions. We show that the Richardson-Lucy deprojection method can be effectively applied on a grid and that the projected potential is well recovered from real and simulated data based on X-ray and SZ signal. The comparison between the reconstructed potentials from the different observables provides additional information on the validity of the assumptions as function of the projected radius.