Lensed Type Ia Supernovae as Probes of Cluster Mass Models
  Using three magnified Type Ia supernovae (SNe Ia) detected behind CLASH
clusters, we perform a first pilot study to see whether standardizable candles
can be used to calibrate cluster mass maps created from strong lensing
observations. Such calibrations will be crucial when next generation HST
cluster surveys (e.g. FRONTIER) provide magnification maps that will, in turn,
form the basis for the exploration of the high redshift Universe. We classify
SNe using combined photometric and spectroscopic observations, finding two of
the three to be clearly of type SN Ia and the third probable. The SNe exhibit
significant amplification, up to a factor of 1.7 at $\sim5\sigma$ significance
(SN-L2). We conducted this as a blind study to avoid fine tuning of parameters,
finding a mean amplification difference between SNe and the cluster lensing
models of $0.09 \pm 0.09^{stat} \pm 0.05^{sys}$ mag. This impressive agreement
suggests no tension between cluster mass models and high redshift standardized
SNe Ia. However, the measured statistical dispersion of $\sigma_{\mu}=0.21$ mag
appeared large compared to the dispersion expected based on statistical
uncertainties ($0.14$). Further work with the supernova and cluster lensing
models, post unblinding, reduced the measured dispersion to
$\sigma_{\mu}=0.12$. An explicit choice should thus be made as to whether SNe
are used unblinded to improve the model, or blinded to test the model. As the
lensed SN samples grow larger, this technique will allow improved constraints
on assumptions regarding e.g. the structure of the dark matter halo.
