We report the first direct and robust measurement of the faint-end slope of the Lyα emitter (LAE) luminosity function (LF) at z = 5.7. Candidate LAEs from a low-spectral-resolution blind search with IMACS on Magellan-Baade were targeted at higher resolution to distinguish high-redshift LAEs from foreground galaxies. All but 2 of our 42 single-emission-line systems have flux ergs s-1 cm-2, making these the faintest emission-lines observed for a z = 5.7 sample with known completeness, an essential property for determining the faint end slope of the LAE LF. We find 13 LAEs as compared to 29 foreground galaxies, in very good agreement with the modeled foreground counts predicted in Dressler et al. that had been used to estimate a faint-end slope of α = -2.0 for the LAE LF. A 32% LAE fraction, LAE/(LAE+foreground) within the flux interval ergs s-1 cm-2 constrains the faint end slope of the LF to (1σ). We show how this steep LF should provide, to the limit of our observations, -16, more than 20% of the flux necessary to maintain ionization at z = 5.7, with a factor of 10 extrapolation in flux reaching more than 50%. This is in addition to the comparable contribution by brighter Lyman Break Galaxies -18. We suggest that this bodes well for a sufficient supply of Lyman continuum photons by similar, low-mass star-forming galaxies within the reionization epoch at , only 250 Myr earlier.

Abstract: Lyman break galaxies (LBGs) are promising probes for clustering measurements at high redshift, z > 2, a region only covered so far by Lyman-α forest measurements. In this paper, we investigate the feasibility of selecting LBGs by exploiting the existence of a strong deficit of flux shortward of the Lyman limit, due to various absorption processes along the line of sight. The target selection relies on deep imaging data from the HSC and CLAUDS surveys in the g, r, z and u bands, respectively, with median depths reaching 27 AB in all bands. The selections were validated by several dedicated spectroscopic observation campaigns with DESI. Visual inspection of spectra has enabled us to develop an automated spectroscopic typing and redshift estimation algorithm specific to LBGs. Based on these data and tools, we assess the efficiency and purity of target selections optimised for different purposes. Selections providing a wide redshift coverage retain 57% of the observed targets after spectroscopic confirmation with DESI, and provide an efficiency for LBGs of 83±3%, for a purity of the selected LBG sample of 90±2%. This would deliver a confirmed LBG density of ~ 620 deg-2 in the range 2.3 < z < 3.5 for a r-band limiting magnitude r < 24.2. Selections optimised for high redshift efficiency retain 73% of the observed targets after spectroscopic confirmation, with 89±4% efficiency for 97±2% purity. This would provide a confirmed LBG density of ~ 470 deg-2 in the range 2.8 < z < 3.5 for a r-band limiting magnitude r < 24.5. A preliminary study of the LBG sample 3d-clustering properties is also presented and used to estimate the LBG linear bias. A value of b LBG = 3.3 ± 0.2  (stat.) is obtained for a mean redshift of 2.9 and a limiting magnitude in r of 24.2, in agreement with results reported in the literature.