CHEX-MATE: towards a consistent universal pressure profile and cluster mass reconstruction

In a self-similar paradigm of structure formation, the thermal pressure of the hot intra-cluster gas follows a universal distribution once the profile of each cluster is normalised based on the proper mass and redshift dependencies. The reconstruction of such a universal pressure profile requires an individual estimate of the mass of each cluster. In this context, we present a method to jointly fit, for the first time, the universal pressure profile and individual cluster $M_{500}$ masses over a sample of galaxy clusters, properly accounting for correlations between the profile shape and amplitude, and masses scaling the individual profiles. We demonstrate the power of the method and show that a consistent exploitation of the universal pressure profile and cluster mass estimates when modelling the thermal pressure in clusters is necessary to avoid biases. In particular, the method, informed by a cluster mass scale, outputs individual cluster masses with same accuracy and better precision than input masses. Using data from the {\guillemotleft}Cluster HEritage project with XMM-Newton: Mass Assembly and Thermodynamics at the Endpoint of structure formation{\guillemotright}, we investigate a sample of $\sim 25$ galaxy clusters spanning mass and redshift ranges of $2 \lesssim M_{500}/10^{14} \; \mathrm{M}_{\odot} \lesssim 14$ and $0.07 < z < 0.6$.