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

A recent ultraviolet luminosity function (UVLF) analysis in the Hubble Frontier Fields, behind foreground lensing clusters, has helped solidify estimates of the faint-end of the $z \sim 5-9$ UVLF at up to five magnitudes fainter than in the field. These measurements provide valuable information regarding the role of low luminosity galaxies in reionizing the universe and can help in calibrating expectations for JWST observations. We fit a semi-empirical model to the lensed and previous UVLF data from Hubble. This fit constrains the average star formation efficiency (SFE) during reionization, with the lensed UVLF measurements probing halo mass scales as small as $M \sim 2 \times 10^9 {\rm M}_\odot$. The implied trend of SFE with halo mass is broadly consistent with an extrapolation from previous inferences at $M \gtrsim 10^{10} {\rm M}_\odot$, although the joint data prefer a shallower SFE. This preference, however, is partly subject to systematic uncertainties in the lensed 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 consistent with Planck 2018 determinations of the electron scattering optical depth, and most current reionization history measurements, provided the escape fraction of ionizing photons is $f_{\rm esc} \sim 10-20\%$. The joint UVLF accounts for nearly $80\%$ of the ionizing photon budget at $z \sim 8$. Finally, we show that recent JWST UVLF estimates at $z \gtrsim 11$ require strong departures from the redshift evolution suggested by the Hubble data.