We present Gemini/GNIRS spectroscopic observations of 4 z-band (z~7) dropout galaxies and VLT/XSHOOTER observations of one z-band dropout and 3 Y-band (z~8-9) dropout galaxies in the Hubble Ultra Deep Field, which were selected with Wide Field Camera 3 imaging on the Hubble Space Telescope. We find no evidence of Lyman-alpha emission with a typical 5-sigma sensitivity of 5X10^-18erg/cm^2/s, and we use the upper limits on Lyman-alpha flux and the broad-band magnitudes to constrain the rest-frame equivalent widths for this line emission. Accounting for incomplete spectral coverage, we survey 3.0 z-band dropouts and 2.9 Y-band dropouts to a Lyman-alpha rest-frame equivalent width limit > 120Ang (for an unresolved emission line); for an equivalent width limit of 50Ang the effective numbers of drop-outs surveyed fall to 1.2 z-band drop-outs and 1.5 Y-band drop-outs. A simple model where the fraction of high rest-frame equivalent width emitters follows the trend seen at z=3-6.5 is inconsistent with our non-detections at z=7-9 at the ~ 1-sigma level for spectrally unresolved lines, which may indicate that a significant neutral HI fraction in the intergalactic medium suppresses the Lyman-alpha line in z-drop and Y-drop galaxies at z > 7.
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