We report a new analysis of the Hubble Frontier Fields clusters Abell 2744 and MACS 0416 using wavelet decomposition to remove the cluster light , enabling the detection of highly magnified ( > 50 \times ) galaxies a factor of 10 \times fainter in luminosity than previous studies .
We find 167 galaxies at z \gtrsim 6 , and with this sample we are able to characterize the UV luminosity function to M _ { UV } = -12.5 at z \sim 6 , -14 at z \sim 7 and -15 at z \sim 8 .
We find a steep faint-end slope ( \alpha < -2 ) , and with our improved statistics at the faint end we reduce the fractional uncertainty on \alpha to < 2 \% at z \sim 6 - 7 and 4 \% at z \sim 8 .
We also investigate the systematic uncertainty due to the lens modelling by using every available lens model individually and comparing the results ; this systematic fractional uncertainty on \alpha is < 4 \% at all redshifts .
We now directly observe galaxies in the luminosity regime where simulations predict a change in the faint-end slope of the luminosity function \citep 2013ApJ…766…94J,2015ApJ…807L..12O,2015MNRAS.453.1503B,2015arXiv151200563L yet our results provide statistically very strong evidence against any turnover in the luminosity range probed .
Thus we find strong support for the extension of the steep luminosity function to M _ { UV } = -13 at z > 6 , consistent with the number of faint galaxies needed to reionize the Universe .