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Keck Spectroscopy of Lyman-break Galaxies and its Implications for the UV-continuum and Ly_alpha Luminosity Functions at z>6

We present Keck spectroscopic observations of z>6 Lyman-break galaxy (LBG) candidates in the Subaru Deep Field (SDF). The candidates were selected as i'-dropout objects down to z'=27 AB magnitudes from an ultra-deep SDF z'-band image. With the Keck spectroscopy we identified 19 LBGs with prominent Ly_alpha emission lines at 6< z < 6.4. The median value of the Ly_alpha rest-frame equivalent widths (EWs) is ~50 A, with four EWs >100 A. This well-defined spectroscopic sample spans a UV-continuum luminosity range of -21.8< M_{UV}<-19.5 (0.6~5 L*_{UV}) and a Ly_alpha luminosity range of (0.3~3) x 10^{43} erg s^{-1} (0.3~3 L*_ {Ly_alpha}). We derive the UV and Ly_alpha luminosity functions (LFs) from our sample at <z>~6.2 after we correct for sample incompleteness. We find that our measurement of the UV LF is consistent with the results of previous studies based on photometric LBG samples at 5<z<7. Our Ly_alpha LF is also generally in agreement with the results of Ly_alpha-emitter surveys at z~5.7 and 6.6. This study shows that deep spectroscopic observations of LBGs can provide unique constraints on both the UV and Ly_alpha LFs at z>6.