Multiply-imaged time-varying sources behind galaxy clusters - Comparing
  FRBs to QSOs, SNe, and GRBs
  With upcoming (continuum) surveys of high-resolution radio telescopes,
detection rates of fast radio bursts (FRBs) might approach $10^5$ per sky per
day by future extremely large observatories, such as the possible extension of
the Square Kilometer Array (SKA) to a phase 2 array. Depending on the redshift
distribution of FRBs and using the repeating FRB121102 as a model, we calculate
a detection rate of multiply-imaged FRBs with their multiply-imaged hosts
caused by the distribution of galaxy-cluster scale gravitational lenses of the
order of $10^{-4}$ per square degree per year for a minimum total flux of the
host of 10 $\mu$Jy at 1.4 GHz for SKA phase 2. Our comparison of estimated
detection rates for quasars, supernovae, gamma ray bursts, and FRBs shows that
multiple images of FRBs could be more numerous than those of gamma ray bursts
and supernovae and as numerous as multiple images of quasars. Time delays
between the multiple images of an FRB break degeneracies in model-based and
model-independent lens reconstructions as other time-varying sources do, yet
without a microlensing bias as FRBs are more point-like and have shorter
duration times. We estimate the relative imprecision of FRB time-delay
measurements to be $10^{-10}$ for time delays on the order of 100 days for
galaxy-cluster scale lenses, yielding more precise (local) lens properties than
time delays from the other time-varying sources. Using the lens modelling
software Grale, we show the increase in accuracy and precision of the
reconstructed scaled surface mass density map of a simulated cluster-scale lens
when adding time delays for one set of multiple images to the set of
observational constraints.
