A Rigorous Free-form Lens Model of Abell 2744 to Meet the Hubble
  Frontier Fields Challenge
  Hubble Frontier Fields (HFF) imaging of the most powerful lensing clusters
provides access to the most magnified distant galaxies. The challenge is to
construct lens models capable of describing these complex massive, merging
clusters so that individual lensed systems can be reliably identified and their
intrinsic properties accurately derived. We apply the free-form lensing method
(WSLAP+) to A2744, providing a model independent map of the cluster mass,
magnification, and geometric distance estimates to multiply-lensed sources. We
solve simultaneously for a smooth cluster component on a pixel grid, together
with local deflections by the cluster member galaxies. Combining model
prediction with photometric redshift measurements, we correct and complete
several systems recently claimed, and identify 4 new systems - totalling 65
images of 21 systems spanning a redshift range of 1.4<z<9.8. The reconstructed
mass shows small enhancements in the directions where significant amounts of
hot plasma can be seen in X-ray. We compare photometric redshifts with
"geometric redshifts", finding a high level of self-consistency. We find
excellent agreement between predicted and observed fluxes - with a best-fit
slope of 0.999+-0.013 and an RMS of ~0.25 mag, demonstrating that our
magnification correction of the lensed background galaxies is very reliable.
Intriguingly, few multiply-lensed galaxies are detected beyond z~7.0, despite
the high magnification and the limiting redshift of z~11.5 permitted by the HFF
filters. With the additional HFF clusters we can better examine the
plausibility of any pronounced high-z deficit, with potentially important
implications for the reionization epoch and the nature of dark matter.
