Prospects for the Determination of H₀ through Observation of Multiply Imaged Supernovae in Galaxy Cluster Fields

We assess the possibility of determining the Hubble constant H_0 by measuring time delays between multiple images of supernovae gravitationally lensed by rich clusters of galaxies and combining these delay measurements with detailed cluster-potential models based on other lensing constraints. Such a lensing determination of H_0 would be complementary to those obtained from galaxy-QSO lensing studies, and could potentially be better calibrated. We show that relatively low-redshift (z approximately 0.2), significantly elliptical clusters have appreciable lensing cross sections for observable image pairings with tractable time delays on the order of a few years despite large lensing mass scales. We find that a targeted search for such image pairs would be a significant undertaking for current observatories, but that it would be appropriate for a facility such as the proposed Large-aperture Synoptic Survey Telescope.