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First HETDEX Spectroscopic Determinations of Ly$α$ and UV Luminosity Functions at $z=2-3$: Bridging a Gap Between Faint AGN and Bright Galaxies

We present Ly$α$ and ultraviolet-continuum (UV) luminosity functions (LFs) of galaxies and active galactic nuclei (AGN) at $z=2.0-3.5$ determined by the un-targetted optical spectroscopic survey of the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX). We combine deep Subaru imaging with HETDEX spectra resulting in $11.4$ deg$^2$ of fiber-spectra sky coverage, obtaining $18320$ galaxies spectroscopically identified with Ly$α$ emission, $2126$ of which host type 1 AGN showing broad (FWHM$~>1000$ km s$^{-1}$) Ly$α$ emission lines. We derive the Ly$α$ (UV) LF over 2 orders of magnitude covering bright galaxies and AGN in $\log L_\mathrm{Lyα}/\mathrm{[erg~s^{-1}]}=43.3-45.5$ ($-27<M_\mathrm{UV}<-20$) by the $1/V_\mathrm{max}$ estimator. Our results reveal the bright-end hump of the Ly$α$ LF is composed of type 1 AGN. In conjunction with previous spectroscopic results at the faint end, we measure a slope of the best-fit Schechter function to be $α_\mathrm{Sch}=-1.70^{+0.13}_{-0.14}$, which indicates $α_\mathrm{Sch}$ steepens from $z=2-3$ towards high redshift. Our UV LF agrees well with previous AGN UV LFs, and extends to faint-AGN and bright-galaxy regimes. The number fraction of Ly$α$-emitting objects ($X_\mathrm{LAE}$) increases from $M_\mathrm{UV}^*\sim-21$ to bright magnitude due to the contribution of type 1 AGN, while previous studies claim that $X_\mathrm{Lyα}$ decreases from faint magnitude to $M_\mathrm{UV}^*$, suggesting a valley in the $X_\mathrm{Lyα}-$magnitude relation at $M_\mathrm{UV}^*$. Comparing our UV LF of type 1 AGN at $z=2-3$ with those at $z=0$, we find that the number density of faint ($M_\mathrm{UV}>-21$) type 1 AGN increases from $z\sim2$ to $z\sim0$ as opposed to the evolution of bright ($M_\mathrm{UV}<-21$) type 1 AGN, suggesting the AGN downsizing in the rest-frame UV luminosity.