CHEX-MATE: Joint fit of the universal pressure profile and galaxy cluster masses

Within the self-similar framework of structure formation, the thermal pressure of the hot intra-cluster medium follows a universal distribution that is independent of the cluster mass scale. Once normalised to the proper mass and redshift dependencies, this pressure distribution becomes common to all clusters. Reconstructing such a universal pressure profile requires individual estimates of each cluster's mass. In this work, we present a methodology to simultaneously fit the universal pressure profile alongside the masses of individual clusters in a sample, while properly accounting for correlations between the profile's shape, its amplitude, and cluster masses. We apply this method to a sub-sample of clusters from the CHEX-MATE project and demonstrate the strong impact that the assumed pressure profile has on the measured signal. This effect propagates into the thermal Sunyaev-Zel'dovich (tSZ) power spectrum and, in turn, influences the determination of cosmological parameters.