The Magellan M2FS Spectroscopic Survey of High-$z$ Galaxies: Ly{\alpha} Emitters at $z\approx6.6$ and the Evolution of Ly{\alpha} Luminosity Function over $z\approx5.7-6.6$

We present a sample of Ly{\alpha} emitters (LAEs) at $z\approx6.6$ from our spectroscopic survey of high-redshift galaxies using the multi-object spectrograph M2FS on the Magellan Clay telescope. The sample consists of 36 LAEs selected by the narrow-band (NB921) technique over nearly 2 deg$^2$ in the sky. These galaxies generally have high Ly{\alpha} luminosities spanning a range of ${\sim}3\times10^{42}{-}7\times10^{43}$ erg s$^{-1}$, and include some of the most Ly{\alpha}-luminous galaxies known at this redshift. They show a positive correlation between the Ly{\alpha} line width and Ly{\alpha} luminosity, similar to the relation previously found in $z\approx5.7$ LAEs. Based on the spectroscopic sample, we calculate a sophisticated sample completeness correction and derive the Ly{\alpha} luminosity function (LF) at $z\approx6.6$. We detect a density bump at the bright end of the Ly{\alpha} LF that is significantly above the best-fit Schechter function, suggesting that very luminous galaxies tend to reside in overdense regions that have formed large ionized bubbles around them. By comparing with the $z\approx5.7$ Ly{\alpha} LF, we confirm that there is a rapid LF evolution at the faint end, but a lack of evolution at the bright end. The fraction of the neutral hydrogen in the intergalactic medium at $z\approx6.6$ estimated from such a rapid evolution is about $\sim0.3\pm0.1$, supporting a rapid and rather late process of cosmic reionization.