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 $z\sim10$.