Gravitational lens time delays for distant supernovae: break the degeneracy between radial mass profiles and the Hubble constant

An attempt to measure the Hubble constant with gravitational lens time delays is often limited by the strong degeneracy between radial mass profiles of lens galaxies and the Hubble constant. We show that strong gravitational lensing of type Ia supernovae breaks this degeneracy; the standard candle nature of type Ia supernova luminosity function allows one to measure the magnification factor directly, and this information is essential to constrain radial mass profiles and the Hubble constant separately. Our numerical simulation demonstrates that the Hubble constant can be determined with ∼ 5% accuracy from only several lens events if magnification factors are used as constraints. Therefore, distant supernova survey is a promising way to measure the global Hubble constant independently with the local estimates.