Calibrating the standard candles with strong lensing

Abstract: We propose a new model-independent strategy to calibrate the distance relation in Type Ia supernova (SN) observations and to probe the intrinsic properties of SNe Ia, especially the absolute magnitude $M_B$, basing on strong lensing observations in the upcoming Large Synoptic Survey Telescope (LSST) era. The strongly lensed quasars can provide the Time Delay Distances (TDD) and the Angular Diameter Distances (ADD) to the lens galaxies. These absolute distance measurements can model-independently anchor the SNe Ia at cosmological distances. We simulated 55 high-quality lensing systems with $5\%$ uncertainties for both TDD and ADD measurements basing on future observation conditions. For the time delay distances and the angular diameter distances as the calibration standards, the calibrated $1\sigma$ uncertainties of $M_{B}$ are approximately 0.24 mag and 0.03 mag, respectively. Besides, we also consider an evolving distance relation, for example, caused by the cosmic opacity. In this case, the $1\sigma$ uncertainties of $M_B$ calibrated with TDD and ADD are approximately 0.31 mag and 0.06 mag, respectively. The results show that the ADD method will be a promising tool for calibrating supernovae.