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A recent ultraviolet luminosity function (UVLF) analysis in the HubbleFrontier Fields, behind foreground lensing clusters, has helped solidifyestimates of the faint-end of the $z \sim 5-9$ UVLF at up to five magnitudesfainter than in the field. These measurements provide valuable informationregarding the role of low luminosity galaxies in reionizing the universe andcan help in calibrating expectations for JWST observations. We fit asemi-empirical model to the lensed and previous UVLF data from Hubble. This fitconstrains the average star formation efficiency (SFE) during reionization,with the lensed UVLF measurements probing halo mass scales as small as $M \sim2 \times 10^9 {\rm M}_\odot$. The implied trend of SFE with halo mass isbroadly consistent with an extrapolation from previous inferences at $M \gtrsim10^{10} {\rm M}_\odot$, although the joint data prefer a shallower SFE. Thispreference, however, is partly subject to systematic uncertainties in thelensed measurements. Near $z \sim 6$ we find that the SFE peaks at $\sim 20 \%$between $\sim 10^{11}-10^{12} {\rm M}_\odot$. Our best fit model is consistentwith Planck 2018 determinations of the electron scattering optical depth, andmost current reionization history measurements, provided the escape fraction ofionizing photons is $f_{\rm esc} \sim 10-20\%$. The joint UVLF accounts fornearly $80\%$ of the ionizing photon budget at $z \sim 8$. Finally, we showthat recent JWST UVLF estimates at $z \gtrsim 11$ require strong departuresfrom the redshift evolution suggested by the Hubble data.

The Star Formation Efficiency During Reionization as Inferred from the Hubble Frontier Fields