MUSE-DARK

Extending local kinematic studies to earlier cosmic times is valuable to understand how galaxies evolve in relation to their dark matter haloes. In a series of papers on lensed kinematics, we seek to combine the sensitivity of 3D forward modelling to low signal-to-noise ratio outskirts with the enhanced spatial resolution provided by cluster lensing. In this first paper, we (i) present and validate our methodology, which directly constrains the source parameters by incorporating lensing deflections into the GalPaK3D forward-modelling algorithm, and (ii) investigate the evolution of the stellar-mass and baryonic-mass Tully–Fisher relations (sTFR and bTFR) since z ∼ 1 as a demonstration. We define a robust sample of strongly lensed star-forming galaxies (SFGs) from the MUSE Lensing Cluster survey, spanning magnifications μ = 1.4 − 12.4 and stellar masses M★ = 108.1 − 1010.3 M⊙. Using a series of mock galaxies representative of our sample, we find that our method is significantly more reliable at recovering morpho-kinematic properties than approaches that ignore differential magnification, even for relatively modest magnifications (μ