YOUNG GALAXY CANDIDATES IN THE HUBBLE FRONTIER FIELDS. II. MACS J0416-2403

We searched for z greater than or similar to 7 Lyman-break galaxies in the optical-to-mid-infrared Hubble Frontier Field and associated parallel field observations of the strong-lensing cluster MACS J0416-2403. We discovered 22 candidates, of which 6 lie at z greater than or similar to 9 and 1 lies at z greater than or similar to 10. Based on the Hubble and Spitzer photometry, all have secure photometric redshifts and a negligible probability of being at lower redshifts according to their peak-probability ratios, R. This substantial increase in the number of known high-redshift galaxies allows a solid determination of the luminosity function (LF) at z greater than or similar to 8. The number of high-z candidates in the parallel field is considerably higher than that in the Abell 2744 parallel field. Our candidates have median stellar masses of (M-*) similar to log 8.44(-0.31)(+0.55)M(circle dot), star formation rates (SFRs) of similar to 1.8(-0.4)(+0.5) M-circle dot yr(-1), and SFR-weighted ages of less than or similar to 300(-140)(+70) Myr. Finally, we are able to put strong constraints on the z = 7, 8, 9, and 10 LFs. One of the objects in the cluster field is a z similar or equal to 10 candidate, with a magnification of mu similar to 20 +/- 13. This object is likely the faintest z similar to 10 object known to date, allowing a first look into the extreme faint end (L similar to 0.04 L*) of the z similar to 10 LF (It is named Tayna in the Aymara language).