Follow-up of SN 2025wny V: Lens Modelling and Cosmography of a Strongly Lensed Superluminous Supernova at $z = 2.015$ using Space Data

Abstract: We present a lensing and cosmographic analysis of the strongly lensed Type I superluminous supernova SN 2025wny at redshift $z=2.015$, multiply imaged by two foreground galaxies at $z=0.376$. Using imaging obtained with the Hubble Space Telescope and the James Webb Space Telescope, we model the lens system with two elliptical power-law mass distributions and an external shear component. In addition to the supernova image positions, the modelling incorporates the surface-brightness distribution of the lensed host galaxy. The inferred Einstein radii are $θ<em>{\rm E,1}\simeq 1.6$" and $θ</em>{\rm E,2}\simeq 0.7$ - $0.8$", with broadly consistent results across all filters. After accounting for microlensing by stars in the lens galaxies, the posterior distribution spans total magnifications of approximately $μ<em>{\rm tot}\sim 5$--$50$, with flux ratios of the multiple images consistent with observations. Combining the lens models with spectroscopically and photomerically measured time delays yields a filter-marginalized constraint of [ H_0 = 66.7^{+7.6}{-6.3}\; {\rm km\,s^{-1}\,Mpc^{-1}}, ] for a fiducial model with isothermal mass profiles. Allowing the density slopes of the lens galaxies to vary over a broad range results in [ H_0 = 70.8^{+8.2}_{-6.1}\; {\rm km\,s^{-1}\,Mpc^{-1}}. ] These values are conditional on the adopted parameterization of the lens mass distribution, the assumed priors on the density slopes, and possible additional lensing contributions from the surrounding large-scale environment. We find that incorporating the currently available stellar kinematic measurements has only a modest effect on the inferred value of $H_0$. Future measurements of the lens-galaxy kinematics and a detailed characterization of the lens environment will further strengthen the utility of SN 2025wny as a cosmological probe.