As Lyman-alpha photons are scattered by neutral hydrogen, a change with redshift in the Lyman-alpha equivalent width distribution of distant galaxies offers a promising probe of the degree of ionization in the intergalactic medium and hence when cosmic reionization ended. This simple test is complicated by the fact that Lyman-alpha emission can also be affected by the evolving astrophysical details of the host galaxies. In the first paper in this series, we demonstrated both a luminosity and redshift dependent trend in the fraction of Lyman-alpha emitters seen within color-selected Lyman-break galaxies (LBGs) over the range 3<z<6; lower luminosity galaxies and those at higher redshift show an increased likelihood of strong emission. Here we present the results from much deeper 12.5 hour exposures with the Keck DEIMOS spectrograph focused primarily on LBGs at z~6 which enable us to confirm the redshift dependence of line emission more robustly and to higher redshift than was hitherto possible. We find 54+/-11% of faint z~6 LBGs show strong (W_0>25 A) emission, an increase of 1.6x from a similar sample observed at z~4. With a total sample of 74 z~6 LBGs, we determine the luminosity-dependent Lyman-alpha equivalent width distribution. Assuming continuity in these trends to the new population of z~7 sources located with the Hubble WFC3/IR camera, we predict that unless the neutral fraction rises in the intervening 200 Myr, the success rate for spectroscopic confirmation using Lyman-alpha emission should be high.
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