Exploring the dependence of the Hubble constant from the cluster-lensed supernova SN Refsdal on mass model assumptions

The Hubble constant, $H_0$, which is a crucial parameter in astrophysics and cosmology, is under significant tension. We explore an independent technique to measure $H_0$ based on the time-delay cosmography with strong gravitational lensing of a supernova lensed by a galaxy cluster, focusing on SN Refsdal in MACS J1149.5+2223, the first gravitationally lensed supernova with resolved multiple images. We carefully examine the dependence of constraints on the Hubble constant on the choice of lens mass models, employing 23 lens mass models with different assumptions on dark matter halos and external perturbations. Remarkably, we observe that the dependence on the choice of lens mass models is not significantly large, suggesting the robustness of the constraint on the Hubble constant from SN Refsdal. We combine measurements for the 23 lens mass models to obtain $H_0=70.0^{+4.7}_{-4.9}km/s/Mpc$ assuming equal weighting. We find that best-fitting Hubble constant values correlate with radial density profiles of the lensing cluster, implying a room for improving the constraint on the Hubble constant with future observations of more multiple images. We also find a clear correlation between best-fitting Hubble constant values and magnification factors of supernova multiple images. This correlation highlights the importance of gravitationally lensed Type Ia supernovae for accurate and robust Hubble constant measurements.