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 < z < 7. Combined with earlier Keck and published European Southern Observatory (ESO) VLT data, our spectroscopic sample contains more than 600 dropouts offering new insight into the nature of sub-L* sources typical of those likely to dominate the cosmic reionization process. In this first paper, in a series discussing these observations, we characterize the fraction of strong Lyα emitters within the continuum-selected dropout population. By quantifying how the `Lyα fraction', x_Lyα, varies with redshift, we seek to constrain changes in Lyα transmission associated with reionization. In order to distinguish the effects of reionization from other factors which affect the Lyα fraction [e.g. dust, interstellar medium (ISM) kinematics], we study the luminosity and redshift-dependence of the Lyα fraction over 3 <~ z <~ 6, when the intergalactic medium (IGM) is known to be ionized. These results reveal that low-luminosity galaxies show strong Lyα emission much more frequently (x_Lyα = 0.47 +/- 0.16 at M_UV = -19) than luminous systems (x_Lyα = 0.08 +/- 0.02 at M_UV = -21), and that at fixed luminosity, the prevalence of strong Lyman α emission increases moderately with redshift over 3 < z < 6 (d x_Lyα/d z = 0.05 +/- 0.03). Based on the bluer mean UV slopes of the strong Lyα emitting galaxies in our data set (<β>_Lyα - <β>_noLyα = -0.33 +/- 0.09 at M_UV = -20.5) we argue that the Lyα fraction trends are governed by redshift and luminosity-dependent variations in the dust obscuration, with likely additional contributions from trends in the kinematics and covering fraction of neutral hydrogen. Using the limited infrared spectroscopy of candidate z ~= 7 galaxies, we find a tentative decrease in the Lyα fraction by a factor of >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.