The Hubble constant from strongly lensed supernovae with standardizable magnifications

The dominant uncertainty in the current measurement of the Hubble constant ($H_0$) with strong gravitational lensing time delays is attributed to uncertainties in the mass profiles of the main deflector galaxies. Strongly lensed supernovae (glSNe) can provide, in addition to measurable time delays, lensing magnification constraints when knowledge about the unlensed apparent brightness of the explosion is imposed. We present a hierarchical Bayesian framework to combine a dataset of SNe that are not strongly lensed and a dataset of strongly lensed SNe with measured time delays. We jointly constrain (i) $H_0$ using the time delays as an absolute distance indicator, (ii) the lens model profiles using the magnification ratio of lensed and unlensed fluxes on the population level and (iii) the unlensed apparent magnitude distribution of the SNe population and the redshift-luminosity relation of the relative expansion history of the Universe. We apply our joint inference framework on a future expected data set of glSNe, and forecast that a sample of 144 glSNe of Type~Ia with well measured time series and imaging data will measure $H_0$ to 1.5\%. We discuss strategies to mitigate systematics associated with using absolute flux measurements of glSNe to constrain the mass density profiles. Using the magnification of SNe images is a promising and complementary alternative to using stellar kinematics. Future surveys, such as the Rubin and \textit{Roman} observatories, will be able to discover the necessary number of glSNe, and with additional follow-up observations this methodology will provide precise constraints on mass profiles and $H_0$.