The rates and time-delay distribution of multiply imaged supernovae behind lensing clusters

Time delays of gravitationally lensed sources can be used to constrain the mass model of a deflector and determine cosmological parameters. We here present an analysis of the time-delay distribution of multiply imaged sources behind 17 strong lensing galaxy clusters with well-calibrated mass models. We find that for time delays less than 1000 days, at z = 3.0, their logarithmic probability distribution functions are well represented by P (log Δ t ) = 5.3 × 10 −4 Δ t / M 250 2 , with = 0.77, where M 250 is the projected cluster mass inside 250 kpc (in 10 14 M ☉ ), and is the power-law slope of the distribution. The resultant probability distribution function enables us to estimate the time-delay distribution in a lensing cluster of known mass. For a cluster with M 250 = 2 × 10 14 M ☉ , the fraction of time delays less than 1000 days is approximately 3%. Taking Abell 1689 as an example, its dark halo and brightest galaxies, with central velocity dispersions σ⩾500kms −1 , mainly produce large time delays, while galaxy-scale mass clumps are responsible for generating smaller time delays. We estimate the probability of observing multiple images of a supernova in the known images of Abell 1689. A two-component model of estimating the supernova rate is applied in this work. For a magnitude threshold of m AB = 26.5, the yearly rate of Type Ia (core-collapse) supernovae with time delays less than 1000 days is 0.004±0.002 (0.029±0.001). If the magnitude threshold is lowered to m AB ∼ 27.0, the rate of core-collapse supernovae suitable for time delay observation is 0.044±0.015 per year.