Massive galaxy clusters at intermediate redshifts act as gravitational lenses
that can magnify supernovae (SNe) occurring in background galaxies. We assess
the possibility to use lensed SNe to put constraints on the mass models of
galaxy clusters and the Hubble parameter at high redshift. Due to the standard
candle nature of Type Ia supernovae (SNe Ia), observational information on the
lensing magnification from an intervening galaxy cluster can be used to
constrain the model for the cluster mass distribution. A statistical analysis
using parametric cluster models was performed to investigate the possible
improvements from lensed SNe Ia for the accurately modeled galaxy cluster A1689
and the less well constrained cluster A2204. Time delay measurements obtained
from SNe lensed by accurately modeled galaxy clusters can be used to measure
the Hubble parameter. For a survey of A1689 we estimate the expected rate of
detectable SNe Ia and of multiply imaged SNe. The velocity dispersion and core
radius of the main cluster potential show strong correlations with the
predicted magnifications and can therefore be constrained by observations of
SNe Ia in background galaxies. This technique proves especially powerful for
galaxy clusters with only few known multiple image systems. The main
uncertainty for measurements of the Hubble parameter from the time delay of
strongly lensed SNe is due to cluster model uncertainties. For the extremely
well modeled cluster A1689, a single time delay measurement could be used to
determine the Hubble parameter with a precision of ~ 10%. We conclude that
observations of SNe Ia behind galaxy clusters can be used to improve the mass
modeling of the large scale component of galaxy clusters and thus the
distribution of dark matter. Time delays from SNe strongly lensed by accurately
modeled galaxy clusters can be used to measure the Hubble constant at high
redshifts.Comment: 10 pages, 8 figures, 3 tables. Accepted for publication in A&