Follow-up of SN 2025wny IV: Photometric Time-delay Measurements of a Strongly Lensed Superluminous Supernova

We present photometric time-delay measurements of SN 2025wny, the first strongly lensed Type I superluminous supernova (SLSN-I), discovered at $z = 2.015$. Time-delay measurements from strongly lensed supernovae provide an independent probe of cosmology and the Hubble constant, $H_0$, without reliance on the local distance ladder. Using multi-facility imaging data, we performed scene-modelling photometry to deblend four of the lensed images (A-D) and construct $grizJ$-band light curves. We modelled the resolved light curves with Gaussian process regression using GausSN (Hayes et al. 2024) to infer relative time delays and magnifications between the lensed images. We found that a constant magnification model provides a suboptimal description of the data, motivating a time-dependent sigmoid magnification model to account for evolving relative magnification of image A. We measured time delays of $Δt_{AB} = -10.6^{+2.2}_{-2.5}$ days and $Δt_{AC} = 1.2^{+2.7}_{-2.6}$ days (68% credible intervals), consistent with independent spectroscopic measurements from Johansson et al. (2026). Combining the photometric time delays with the lens model of Mörtsell et al. (2026) gives $H_{0,\:\rm photo} = 80.5^{+26.4}_{-16.7}\;\rm km\,s^{-1}\,Mpc^{-1}$, while including the spectroscopic time delays as well yields $H_{0,\:\rm comb} = 70.8^{+8.2}_{-6.1}\;{\rm km\,s^{-1}\,Mpc^{-1}}$. Our results further demonstrate the potential of strongly lensed supernovae as independent probes of $H_0$.