Gravitational lensing of type Ia supernovae by galaxy clusters

Abstract

We propose a method to remove the mass sheet degeneracy that arises when the mass of galaxy clusters is inferred from gravitational shear. The method utilizes high-redshift standard candles that undergo weak lensing. Natural candidates for such standard candles are type Ia supernovae (SN Ia). When corrected with the light-curve shape (LCS), the peak magnitude of SN Ia provides a standard candle with an uncertainty in apparent magnitude of $Δm\simeq 0.1-0.2$. Gravitational magnification of a background SN Ia by an intervening cluster would cause a mismatch between the observed SN Ia peak magnitude compared to that expected from its LCS and redshift. The average detection rate for SN Ia with a significant mismatch of $\ge2Δm$ behind a cluster at $z\simeq0.05-0.15$ is about $1-2$ supernovae per cluster per year at $J,I,R\lesssim25-26$. Since SNe are point-like sources for a limited period, they can experience significant microlensing by MACHOs in the intracluster medium. Microlensing events caused by MACHOs of $\sim10^{-4} M_\odot$ are expected to have time scales similar to that of the SN light curve. Both the magnification curve by a MACHO and the light curve of a SN Ia have characteristic shapes that allow to separate them. Microlensing events due to MACHOs of smaller mass can unambiguously be identified in the SN light curve if the latter is continuously monitored. The average number of identifiable microlensing events per nearby cluster ($z\lesssim0.05$) per year is $\sim 0.02 (f/0.01)$, where $f$ is the fraction of the cluster mass in MACHOs of masses $10^{-7} < M_{macho}/M_\odot < 10^{-4}$.