Cosmology with supernova Encore in the strong lensing cluster MACS J0138−2155

The strongly lensed supernova (SN) Encore, at a redshift of z = 1.949 and discovered behind the galaxy cluster MACS J0138-2155 at z = 0.336, provides a rare opportunity for time-delay cosmography and studies of the SN host galaxy, where previously another SN, called SN Requiem, had appeared. To enable these studies, we combined new James Webb Space Telescope (JWST) imaging, archival Hubble Space Telescope (HST) imaging, and new Very Large Telescope (VLT) spectroscopic data to construct state-of-the-art lens mass models that are composed of cluster dark-matter (DM) haloes and galaxies. We fitted the surface brightness distributions of the galaxies in the field of view using S & eacute;rsic profiles to determine their photometric and structural parameters across six JWST and five HST filters. We used the colour-magnitude and colour-colour relations of spectroscopically confirmed cluster members to select additional cluster members, and identified a total of 84 galaxies belonging to the galaxy cluster. We constructed seven different mass models using a variety of DM halo mass profiles and explored both multi-plane and approximate single-plane lens models. As constraints, we used the observed positions of 23 multiple images from eight multiple image systems that originate from four galaxies with distinct spectroscopic redshifts in the range of 0.767-3.420. In addition, we used stellar velocity dispersion measurements to obtain priors on the galaxy mass distributions. We find that six of the seven models fit well to the observed image positions, with a root-mean-square (rms) scatter of <= 0.032 '' between the model-predicted and observed positions for systems identified with JWST and HST images, including SN Encore and SN Requiem (the rms scatter is 0.24 '' for all positions, including those identified with MUSE images). Mass models with cored-isothermal DM profiles fit well to the observations, whereas the mass model with a Navarro-Frenk-White cluster DM profile has an image-position chi 2 value that is four times higher. We built our ultimate model by combining four multi-lens-plane mass models in order to incorporate uncertainties due to model parameterizations. Our two approximate mass models with a single-lens plane allow us to perform direct comparisons with single-plane models built independently by other teams. Using our ultimate model, we predict the image positions and magnifications of SN Encore and SN Requiem. We also provide the effective convergence and shear of SN Encore for micro-lensing studies. Our work lays the foundation for building state-of-the-art mass models of the cluster for future cosmological analysis and SN host galaxy studies.