Keck spectroscopy of faint 3 < z < 7 Lyman break galaxies – I. New constraints on cosmic reionization from the luminosity and redshift-dependent fraction of Lyman α emission

We present the first results of a new Keck spectroscopic survey of UV faint Lyman break galaxies in the redshift range 3 1.9 with respect to the predicted z ≃ 7 value, a result which, if confirmed with future surveys, would suggest an increase in the neutral fraction by this epoch. Given the abundant supply of z and Y drops now available from deep Hubble WFC3/IR surveys, we show it will soon be possible to significantly improve estimates of the Lyα fraction using optical and near-infrared multi-object spectrographs, thereby extending the study conducted in this paper to 7 ≲ z ≲ 8