The X-ray luminosity function of active galactic nuclei in the redshift interval z=3-5

We combine deep X-ray survey data from the Chandra observatory and the wide-area/shallow XMM-XXL field to estimate the active galactic nuclei (AGN) X-ray luminosity function in the redshift range z = 3-5. The sample consists of nearly 340 sources with either photometric (212) or spectroscopic (128) redshift in the above range. The combination of deep and shallow survey fields also provides a luminosity baseline of three orders of magnitude, L_X(2-10 keV) ≈ 10⁴³-10⁴⁶ erg s^{- 1} at z > 3. We follow a Bayesian approach to determine the binned AGN space density and explore their evolution in a model-independent way. Our methodology properly accounts for Poisson errors in the determination of X-ray fluxes and uncertainties in photometric redshift estimates. We demonstrate that the latter is essential for unbiased measurement of space densities. We find that the AGN X-ray luminosity function evolves strongly between the redshift intervals z = 3-4 and z = 4-5. There is also suggestive evidence that the amplitude of this evolution is luminosity dependent. The space density of AGN with L_X(2-10 keV) < 10⁴⁵ erg s^{- 1} drops by a factor of 5 between the redshift intervals above, while the evolution of brighter AGN appears to be milder. Comparison of our X-ray luminosity function with that of ultraviolet (UV)/optical selected quasi-stellar objects at similar redshifts shows broad agreement at bright luminosities, L_X(2-10 keV) > 10⁴⁵ erg s^{- 1}. At fainter luminosities X-ray surveys measure higher AGN space densities. The faint-end slope of UV/optical luminosity functions, however, is steeper than for X-ray selected AGN. This implies that the Type I AGN fraction increases with decreasing luminosity at z > 3, opposite to trends established at lower redshift. We also assess the significance of AGN in keeping the hydrogen ionized at high redshift. Our X-ray luminosity function yields ionizing photon rate densities that are insufficient to keep the Universe ionized at redshift z > 4. A source of uncertainty in this calculation is the escape fraction of UV photons for X-ray selected AGN.