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.