Reconstruction of the two-dimensional gravitational potential of galaxy clusters from X-ray and Sunyaev-Zel'dovich measurements

Abstract

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. <BR /> 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. <BR /> 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 β-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. <BR /> 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. <BR /> 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.