A spectroscopic survey of Ly$α$ emitters and Ly$α$ luminosity function at Redshifts 3.7 and 4.8

Abstract: We present a spectroscopic survey of Ly$\alpha$ emitters (LAEs) at $z\sim3.7$ and $z\sim4.8$. The LAEs are selected using the narrowband technique based on the combination of deep narrowband and broadband imaging data in two deep fields, and then spectroscopically confirmed with the MMT multi-fiber spectrograph Hectospec. The sample consists of 71 LAEs at $z\sim3.7$ and 69 LAEs at $z\sim4.8$ over $\sim 1.5$ deg$^2$, making it one of the largest spectroscopically confirmed sample of LAEs at the two redshifts. Their Ly$\alpha$ luminosities are measured using the secure redshifts and deep photometric data, and span a range of $\sim 10^{42.5}$ - $10^{43.6} \,\rm erg\, s^{-1}$, so these LAEs represent the most luminous galaxies at the redshifts in terms of Ly$\alpha$ luminosity. We estimate and correct sample incompletenesses and derive reliable Ly$\alpha$ luminosity function (LF)s at $z\sim3.7$ and 4.8 based on the two spectroscopic samples. We find that our Ly$\alpha$ LFs are roughly consistent (within a factor of $2-3$) with previous measurements at similar redshifts that were derived from either photometric samples or spectroscopic samples. By comparing with previous studies in different redshifts, we find that the Ly$\alpha$ LFs decrease mildly from $z\sim3.1$ to $z\sim5.7$, supporting the previous claim of the slow LF evolution between $z\sim2$ and $z\sim6$. At $z>5.7$, the LF declines rapidly towards higher redshift, partly due to the effect of cosmic reionization.