The PAU Survey: The quasar UV and Ly$\alpha$ luminosity functions at $2.7<z<5.3$
We present the Lyman-$\alpha$ (Ly$\alpha$) and ultraviolet (UV) luminosity function (LF), in bins of redshift, of quasars selected in the Physics of the Accelerating Universe Survey (PAUS). A sample of 915 objects was selected at $2.7 10^{44}$ ${\rm erg\,s}$$^{-1}$. In order to obtain corrections for the LF estimation, and assess the accuracy of our selection method, we produced mock catalogs of $0<z<4.3$ quasars and galaxies that mimic our target population and their main contaminants. Our results show a clear evolution of the Ly$\alpha$ and UV LFs, with a declining tendency in the number density of quasars towards increasing redshifts. In addition, the faint-end power-law slope of the Ly$\alpha$ LF becomes steeper with redshift, suggesting that the number density of Ly$\alpha$-bright quasars declines faster than that of fainter emitters. By integrating the Ly$\alpha$ LF we find that the total Ly$\alpha$ emitted by bright quasars per unit volume rapidly declines with increasing redshift, being sub-dominant to that of star-forming galaxies by several orders of magnitude by $z\sim 4$. Finally, we stack the NB pseudo-spectra of a visually selected "golden sample" of 591 quasars to obtain photometric composite SEDs in bins of redshift, enabling to measure the mean IGM absorption by the Lyman-$\alpha$ forest as a function of redshift.