Precise Strong Lensing Mass Modeling of Four Hubble Frontier Fields
  Clusters and a Sample of Magnified High-Redshift Galaxies
  We conduct precise strong lensing mass modeling of four ${\it Hubble}$
Frontier Fields (HFF) clusters, Abell$~$2744, MACS$~$J0416.1$-$2403,
MACS$~$J0717.5$+$3745, and MACS$~$J1149.6$+$2223, for which HFF imaging
observations are completed. We construct a refined sample of more than 100
multiple images for each cluster by taking advantage of the full depth HFF
images, and conduct mass modeling using the ${\small \rm GLAFIC}$ software,
which assumes simply parametrized mass distributions. Our mass modeling also
exploits a magnification constraint from the lensed Type Ia supernova HFF14Tom
for Abell$~$2744 and positional constraints from the multiple images S1$-$S4 of
the lensed supernova SN Refsdal for MACS$~$J1149.6$+$2223. We find that our
best-fitting mass models reproduce the observed image positions with RMS errors
of $\sim 0.4$ arcsec, which are smaller than RMS errors in previous mass
modeling that adopted similar numbers of multiple images. Our model predicts a
new image of SN Refsdal with a relative time delay and magnification that are
fully consistent with a recent detection of reappearance. We then construct
catalogs of $z\sim 6-9$ dropout galaxies behind the four clusters and estimate
magnification factors for these dropout galaxies with our best-fitting mass
models. The dropout sample from the four cluster fields contains $\sim 120$
galaxies at $z\gtrsim 6$, about 20 of which are predicted to be magnified by a
factor of more than 10. Some of the high-redshift galaxies detected in the HFF
have lensing-corrected magnitudes of $M_{\rm UV}\sim -15$ to $-14$. Our
analysis demonstrates that the HFF data indeed offer an ideal opportunity to
study faint high-redshift galaxies. All lensing maps produced from our mass
modeling will be made available on the STScI website.
