A comprehensive separation of dark matter and baryonic mass components in galaxy clusters I: Mass constraints from Abell S1063

In this two-part series, we present a multi-probe mass modelling method for massive galaxy clusters, designed to disentangle the contributions of individual mass components (Dark matter, intra-cluster gas, stellar masses). In this first paper, we focus on recovering the mass constraint datasets required for the modelling approach introduced in the second paper. Specifically, we measure the light distribution, stellar mass, and kinematics of the cluster members, the brightest cluster galaxy (BCG), and the intra-cluster light (ICL) in Abell S1063. To that end, we developed a new method to extract the light profiles of the cluster members, BCG, and ICL, while accounting for contamination from nearby foreground and background galaxies in \textsc{Hubble Space Telescope} (HST) imaging. We obtained light profiles for $289$ cluster members using a dual Pseudo-Isothermal Elliptical (dPIE) model based on the HST F160W filter, while the BCG \& ICL is modelled as a single component using a multi-Gaussian expansion. To estimate stellar masses and velocity dispersions, we rely on multi-band HST photometry and \textsc{VLT/MUSE} integral field spectroscopy, respectively. Stellar masses are derived using three different spectral energy distribution (SED) models. We measure the line-of-sight velocity dispersions of the cluster members at their half-light radii, as determined from their light profiles, while for the BCG \& ICL components, we use elliptical annular apertures. Thanks to these measurements, we will be able to constrain the cluster stellar mass content, which is detailed in the second paper of the series. We publicly release these measurements with intermediary data products.