MUSE-DARK

II. 3D morpho-kinematic modelling of lensed galaxies: Tully-Fisher relation of z  ∼  1 star-forming galaxies

¹ Universite Claude Bernard Lyon 1, CRAL UMR5574, ENS de Lyon, CNRS, Villeurbanne F-69622, France
² Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
³ Observatoire Astronomique de Strasbourg, Université de Strasbourg, CNRS, UMR 7550, 67000 Strasbourg, France
⁴ French-Chilean Laboratory for Astronomy, IRL 3386, CNRS and Universidad de Concepción, Departamento de Astronomía, Barrio Universitario s/n, Concepción, Chile
⁵ Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France
⁶ IRAP, Université de Toulouse, CNRS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 19 March 2026
Accepted: 27 March 2026

Abstract

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 GalPaK^3D 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_★ = 10^8.1 − 10^10.3 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 < 6). Restricting the analysis to 95 rotationally supported SFGs with well-constrained velocities, we find a significant evolution of the sTFR zero point (Δ b^sTFR = −0.42^+0.05_−0.05 dex in stellar mass) but no detectable evolution of the bTFR zero point (Δ b^bTFR = 0.00^+0.06_−0.06 dex in baryonic mass) relative to z ≈ 0. Our results are consistent with a mild evolution of the stellar-to-halo mass ratio and support the view that the sTFR has evolved only weakly over the past ∼8 Gyr, aside from shifts driven by the redshift dependence of halo-defining quantities such as the critical density and overdensity. The absence of detectable evolution in the bTFR zero point suggests that the increasing contribution of cold gas mass at higher redshift fully compensates for the evolution observed in the stellar component alone.