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 $H_0$.
