Strong-Lensing Analysis of MACS,J0717.5+3745 from Hubble Frontier Fields
  observations: How well can the mass distribution be constrained?
  [abridged] We present a strong-lensing analysis of MACSJ0717.5+3745, based on
the full depth of the Hubble Frontier Field (HFF) observations, which brings
the number of multiply imaged systems to 61, ten of which are spectroscopically
confirmed. The total number of images comprised in these systems rises to 165.
Our analysis uses a parametric mass reconstruction technique, as implemented in
the Lenstool software, to constrain a mass distribution composed of four
large-scale mass components + galaxy-scale perturbers. We find a superposition
of cored isothermal mass components to provide a good fit to the observational
constraints, resulting in a very shallow mass distribution for the smooth
(large-scale) component. Given the implications of such a flat mass profile, we
investigate whether a model composed of "peaky" non-cored mass components can
also reproduce the observational constraints. We find that such a non-cored
mass model reproduces the observational constraints equally well. Although the
total mass distributions of both models are consistent, as well as the
integrated two dimensional mass profiles, we find that the smooth and the
galaxy-scale components are very different. We conclude that, even in the HFF
era, the generic degeneracy between smooth and galaxy-scale components is not
broken, in particular in such a complex galaxy cluster. Consequently, insights
into the mass distribution of MACS J0717 remain limited, underlining the need
for additional probes beyond strong lensing. Our findings also have
implications for estimates of the lensing magnification: we show that the
amplification difference between the two models is larger than the error
associated with either model. This uncertainty decreases the area of the image
plane where we can reliably study the high-redshift Universe by 50 to 70%.
