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Following our previous spectroscopic observations of $z>7$ galaxies withGemini/GNIRS and VLT/XSHOOTER, which targeted a total of 8 objects, we presenthere our results from a deeper and larger VLT/FORS2 spectroscopic sample ofWide Field Camera 3 selected $z>7$ candidate galaxies. With our FORS2 setup wecover the 737-1070nm wavelength range, enabling a search for Lyman-$\alpha$ inthe redshift range spanning 5.06 - 7.80. We target 22 $z$-band dropouts andfind no evidence of Lyman-$\alpha$ emission, with the exception of a tentativedetection ($<5\sigma$, which is our adopted criterion for a secure detection)for one object. The upper limits on Lyman-$\alpha$ flux and the broad-bandmagnitudes are used to constrain the rest-frame Equivalent Widths for this lineemission. We analyse our FORS2 observations in combination with our previousGNIRS and XSHOOTER observations, and suggest that a simple model where thefraction of high rest-frame Equivalent Width emitters follows the trend seen at$z=3-6.5$ is inconsistent with our non-detections at $z\sim7.8$ at the 96\%confidence level. This may indicate that a significant neutral HI fraction inthe intergalactic medium suppresses Lyman-$\alpha$, with an estimated neutralfraction $\chi_{HI}\sim0.5$, in agreement with other estimates.

Spectroscopy of z ~ 7 candidate galaxies: Using Lyman-alpha to constrain the neutral fraction of hydrogen in the high-redshift universe