We present the results of a new search for galaxies at redshift z ~ 9 in the first two Hubble Frontier Fields with completed HST WFC3/IR and ACS imaging. To ensure robust photometric redshift solutions, and to minimize incompleteness, we confine our search to objects with H_{160} < 28.6 (AB mag), consider only image regions with an rms noise sigma_{160} > 30 mag (within a 0.5-arcsec diameter aperture), and insist on detections in both H_{160} and J_{140}. The result is a survey covering an effective area (after accounting for magnification) of 10.9 sq. arcmin, which yields 12 galaxies at 8.4 < z < 9.5. Within the Abell-2744 cluster and parallel fields we confirm the three brightest objects reported by Ishigaki et al. (2014), but recover only one of the four z > 8.4 sources reported by Zheng et al. (2014). In the MACSJ0416.1-240 cluster field we report five objects, and explain why each of these eluded detection or classification as z ~ 9 galaxies in the published searches of the shallower CLASH data. Finally, we uncover four z ~ 9 galaxies from the previously unsearched MACSJ0416.1-240 parallel field. Based on the published magnification maps we find that only one of these 12 galaxies is likely boosted by more than a factor of two by gravitational lensing. Consequently we are able to perform a fairly straightforward reanalysis of the normalization of the z ~ 9 UV galaxy luminosity function as explored previously in the HUDF12 programme. We conclude that the new data strengthen the evidence for a continued smooth decline in UV luminosity density (and hence star-formation rate density) from z ~ 8 to z ~ 9, contrary to recent reports of a marked drop-off at these redshifts. This provides further support for the scenario in which early galaxy evolution is sufficiently extended to explain cosmic reionization.
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