XIV. Time-delay and differential dust extinction determination with lensed type II supernova color curves

The Hubble tension is one of the most relevant unsolved problems in cosmology today. Strongly gravitationally lensed transient objects, such as strongly lensed supernovae, are an independent and competitive probe that can be used to determine the Hubble constant. In this context, the time delay between different images of lensed supernovae is a key ingredient. We present a method to retrieve time delays and the amount of differential dust extinction between multiple images of lensed type IIP supernovae (SNe IIP) through their color curves, which display a kink in the time evolution. With several realistic mock color curves based on an observed SN (not strongly lensed) from the Carnegie Supernova Project (CSP), our results show that we can determine the time delay with an uncertainty of approximately ± 1.0 days. This is achievable with light curves with a 2-day time interval and up to 35% missing data due to weather-related losses. Accounting for additional factors such as microlensing, seeing, shot noise from the host and lens galaxies, and blending of the SN images would likely increase the estimated uncertainties. Differentiated dust extinction is more susceptible to uncertainties because it depends on imposing the correct extinction law. Further, we also investigate the kink structure in the color curves for different rest-frame wavelength bands, particularly rest-frame ultraviolet (UV) light curves from the Neil Gehrels Swift Observatory (SWIFT), finding sufficiently strong kinks for our method to work for typical lensed SN redshifts that would redshift the kink feature to optical wavelengths. With the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST), hundreds of strongly lensed supernovae will be detected, and our new method for lensed SN IIP is readily applicable to provide delays.