The PAU Survey: The quasar UV and Lyα luminosity functions at $2.7<z<5.3$

We present the Lyman-α (Lyα) 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 $2.7<z<5.3$ within an effective area of ~ 36 deg² observed in 40 narrow-band filters (NB; FWHM ~ 120 {A}). We cover the intermediate-bright luminosity regime of the LF (1043.5<(L_ Lyα/ erg\,s⁻¹)<1045.5; -29<MUV<-24). The continuous wavelength coverage of the PAUS NB set allows a very efficient target identification and precise redshift measurements. We show that our method is able to retrieve a fairly complete (C~ 85%) and pure (P~ 90%) sample of Lyα emitting quasars for L_ Lyα>10⁴⁴ 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$α$ 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$α$ LF becomes steeper with redshift, suggesting that the number density of Ly$α$-bright quasars declines faster than that of fainter emitters. By integrating the Ly$α$ LF we find that the total Ly$α$ 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 $z~ 4$. 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-α forest as a function of redshift.