Bright and Faint Ends of Ly$\alpha$ Luminosity Functions at $\textit{z} = 2$ Determined by the Subaru Survey: Implications for AGN, Magnification Bias, and ISM HI Evolution

We present the Lya luminosity functions (LFs) derived by our deep Subaru narrowband survey that identifies a total of 3,137 Lya emitters (LAEs) at $z = 2.2$ in five independent blank fields. The sample of these LAEs is the largest, to date, and covers a very wide Lya luminosity range of $\log L_{Ly\alpha} = 41.7-44.4$ erg s$^{-1}$. We determine the Lya LF at $z = 2.2$ with unprecedented accuracies, and obtain the best-fit Schechter parameters of $L^{*}_{Ly\alpha} = 5.29^{+1.67}_{-1.13} \times 10^{42}$ erg s$^{-1}$, $\phi^{*}_{Ly\alpha} = 6.32^{+3.08}_{-2.31} \times 10^{-4}$ Mpc$^{-3}$, and $\alpha = -1.75^{+0.10}_{-0.09}$ showing a steep faint-end slope. We identify a significant hump at the LF bright end ($\log L_{Ly\alpha} > 43.4$ erg s$^{-1}$). Because all of the LAEs in the bright-end hump have (a) bright counterpart(s) either in the X-ray, UV, or radio data, this bright-end hump is not made by gravitational lensing magnification bias but AGNs. These AGNs allow us to derive the AGN UV LF at $z \sim 2$ down to the faint magnitude limit of $M_{UV} \simeq -22.5$, and to constrain the faint-end slope of AGN UV LF, $\alpha_{AGN}=-1.2 \pm 0.1$, that is flatter than those at $z > 4$. Based on the Lya and UV LFs from our and previous studies, we find the increase of Lya escape fraction $f^{Ly\alpha}_{esc}$ from $z \sim 0$ to $6$ by two orders of magnitude. This large $f^{Ly\alpha}_{esc}$ increase can be explained neither by the evolution of stellar population nor outflow alone, but the evolution of neutral hydrogen HI density in inter-stellar medium that enhances dust attenuation for Lya by resonance scattering. Our uniform expanding shell models suggest that the typical HI column density decreases from $N_{HI} \sim 7 \times 10^{19}$ ($z \sim 0$) to $\sim 1 \times 10^{18}$ cm$^{-2}$ ($z \sim 6$) to explain the large $f^{Ly\alpha}_{esc}$ increase.