X-ray Luminosity Function of Quasars at 3 < z < 5 from XMM-Newton Serendipitous Survey Data

Abstract

The X-ray luminosity function of distant (3<z<5.1) unabsorbed quasars has been measured. A sample of distant high-luminosity quasars ($10^{45} \leq L_{{\rm X},2-10} < 7.5 \times 10^{45}$ erg/s in the 2--10 keV energy band) from the catalog given in Khorunzhev et al. (2016) compiled from the data of the 3XMM-DR4 catalog of the XMM-Newton serendipitous survey and the Sloan Digital Sky Survey (SDSS) has been used. This sample consists of 101 sources. Most of them (90) have spectroscopic redshifts $z_{spec}\geqslant 3$. The remaining ones are quasar candidates with photometric redshift estimates $z_{phot}\geqslant 3$. The spectroscopic redshifts of eight sources have been measured with AZT-33IK and BTA telescopes. Owing to the record sky coverage area ($\simeq 250$ sq. deg at X-ray fluxes $\sim 10^{-14}$ erg/s/cm$^{2}$ in the 0.5-2 keV), from which the sample was drawn, we have managed to obtain reliable estimates of the space density of distant X-ray quasars with luminosities $L_{{\rm X},2-10} > 2 \times 10^{45}$ erg/s for the first time. Their comoving space density remains constant as the redshift increases from z=3 to z=5 to within a factor of 2. The power-law slope of the X-ray luminosity function of high-redshift quasars in its bright end (above the break luminosity) has been reliably constrained for the first time. The range of possible slopes for the quasar luminosity and density evolution model is $\gamma_2=2.78^{+0.00}_{-0.04}\pm0.20$, where initially the lower and upper boundaries of $\gamma_2$ with the remaining uncertainty in the detection completeness of X-ray sources in SDSS, and subsequently the statistical error of the slope are specified.