A Geometrically Supported $z\sim10$ Candidate Multiply-Imaged by the
  Hubble Frontier Fields Cluster Abell 2744
  The deflection angles of lensed sources increase with their distance behind a
given lens. We utilize this geometric effect to corroborate the
$z_{phot}\simeq9.8$ photometric redshift estimate of a faint near-IR dropout,
triply-imaged by the massive galaxy cluster Abell 2744 in deep Hubble Frontier
Fields images. The multiple images of this source follow the same symmetry as
other nearby sets of multiple images which bracket the critical curves and have
well defined redshifts (up to $z_{spec}\simeq3.6$), but with larger deflection
angles, indicating that this source must lie at a higher redshift. Similarly,
our different parametric and non-parametric lens models all require this object
be at $z\gtrsim4$, with at least 95\% confidence, thoroughly excluding the
possibility of lower-redshift interlopers. To study the properties of this
source we correct the two brighter images for their magnifications, leading to
a SFR of $\sim0.3 M_{\odot}$/yr, a stellar mass of $\sim4\times10^{7}
M_{\odot}$, and an age of $\lesssim220$ Myr (95\% confidence). The intrinsic
apparent magnitude is 29.9 AB (F160W), and the rest-frame UV ($\sim1500 \AA$)
absolute magnitude is $M_{UV,AB}=-17.6$. This corresponds to $\sim0.1
L^{*}_{z=8}$ ($\sim0.2 L^{*}_{z=10}$, adopting $dM^{*}/dz\sim0.45$), making
this candidate one of the least luminous galaxies discovered at $z\sim10$.
