El Gordo needs El Anzuelo: Probing the structure of cluster members with multi-band extended arcs in JWST data

Gravitational lensing by galaxy clusters involves hundreds of galaxies over a large redshift range and increases the likelihood of rare phenomena (supernovae, dark substructures, etc.). We present the detailed analysis of \elanz, a prominent quintuply imaged dusty star-forming galaxy (\(\zs=2.29\)), mainly lensed by three members of the massive galaxy cluster ACT-CL\,J0102\(-\)4915, also known as \elgor (\(z_{\rm d}=0.87\)). We leverage JWST/NIRCam images, which contain lensing features that were unseen in previous HST images, using a Bayesian, multi-wavelength, differentiable and GPU-accelerated modeling framework that combines \herculens (lens modeling) and \nifty (field model and inference) software packages. For one of the deflectors, we complement lensing constraints with stellar kinematics measured from VLT/MUSE data. In our lens model, we explicitly include the mass distribution of the cluster, locally corrected by a constant shear field. We find that the two main deflectors (L1 and L2) have logarithmic mass density slopes steeper than isothermal, with \(\gamma_{\rm L1} = 2.23\pm0.05\) and \(\gamma_{\rm L2} = 2.21\pm0.04\). We argue that such steep density profiles can arise due to tidally truncated mass distributions, which we probe thanks to the cluster lensing boost and the strong asymmetry of the lensing configuration. Moreover, our three-dimensional source model captures most of the surface brightness of the lensed galaxy, revealing a clump with a maximum diameter of \(400\) parsecs at the source redshift, visible at wavelengths \(\lambda_{\rm rest}\gtrsim0.6\) \(\mu\)m. Finally, we caution on using point-like features within extended arcs to constrain galaxy-scale lens models before securing them with extended arc modeling.