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Baryonic processes, such as feedback or clump infall, may resolve the discrepancy between the cuspy density profiles of cold dark matter (cold DM or CDM) and the constant-density cores inferred from galaxy kinematics. Mass modelling high redshift galaxies can be valuable to capture this transition, but is challenging owing to their small apparent size and low surface brightness. In this talk, I will present recent work to constrain the DM profile of distant (0.5 < z < 1.5) star-forming galaxies (SFGs) by combining the enhanced spatial resolution of cluster lensing with the sensitivity of a 3D morpho-kinematic modelling of MUSE datacubes. We study a sample of ~40 strongly lensed, intermediate-mass SFGs (log Mstar/Msun ~ 9.5 - 10.5), selected for their high [OII] S/N and spatial extent within the MUSE Lensing Cluster survey. We extend the morpho-kinematic modelling code GalPaK3D to recover their intrinsic DM distribution from [OII] kinematics and test the influence of star formation using ancillary data from the HFF-DeepSpace survey. Our results suggest a correlation between SFR and cored DM profiles, consistent with results from Bouche et al. 2021 and the feedback-induced core formation scenario. Futhermore, we find that stellar masses inferred from [OII] kinematics are consistent with SED-derived masses.
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