The Hard X-Ray Luminosity Function of High-Redshift ($3<z\lesssim 5$) Active Galactic Nuclei

We present the hard-band ($2-10\mathrm{k}\mathrm{e}\mathrm{V}$) X-ray luminosity function (HXLF) of $0.5-2\mathrm{k}\mathrm{e}\mathrm{V}$ band selected AGN at high redshift. We have assembled a sample of 141 AGN at $3<z\lesssim 5$ from X-ray surveys of different size and depth, in order to sample different regions in the $L_X-z$ plane. The HXLF is fitted in the range $\mathrm{l}\mathrm{o}\mathrm{g}{\mathrm{L}}_{\mathrm{X}}\sim 43-45$ with standard analytical evolutionary models through a maximum likelihood procedure. The evolution of the HXLF is well described by a pure density evolution, with the AGN space density declining by a factor of $\sim 10$ from $z=3$ to 5. A luminosity-dependent density evolution model which, normally, best represents the HXLF evolution at lower redshift, is also consistent with the data, but a larger sample of low-luminosity ($\mathrm{l}\mathrm{o}\mathrm{g}{\mathrm{L}}_{\mathrm{X}}<44$), high-redshift AGN is necessary to constrain this model. We also estimated the intrinsic fraction of AGN obscured by a column density $\mathrm{l}\mathrm{o}\mathrm{g}{\mathrm{N}}_{\mathrm{H}}\ge 23$ to be $0.54\pm 0.05$, with no strong dependence on luminosity. This fraction is higher than the value in the Local Universe, suggesting an evolution of the luminous (${\mathrm{L}}_{\mathrm{X}}>{10}^{44}\mathrm{e}\mathrm{r}\mathrm{g}{\mathrm{s}}^{-1}$) obscured AGN fraction from $z=0$ to $z>3$.