Faint high-redshift AGN in the Chandra deep field south: the evolution of the AGN luminosity function and black hole demography

Context. We present detection and analysis of faint X-ray sources in the Chandra deep field south (CDFS) using the 4 Ms Chandra observation. Aims. We place constraints on active galactic nuclei (AGN) luminosity functions at z = 3-7, its cosmological evolution, and high-redshift black hole and AGN demography. Methods. We use a new detection algorithm, using the entire three-dimensional data-cube (position and energy), and searching for X-ray counts at the position of high-z galaxies in the GOODS-South survey. Results. This optimized technique results in the identification of 54 AGN at z > 3, 29 of which are new detections. Applying stringent completeness criteria, we derive AGN luminosity functions in the redshift bins 3-4, 4-5, and >5.8 and for 42.75 < log L(2-10 keV) < 44.5. We combine this data with the luminous AGN luminosity functions from optical surveys and find that the evolution of the high-z, wide luminosity range luminosity function can be modeled by pure luminosity evolution with L* decreasing from 6.6 x 10(44) erg/s at z = 3 to L* = 2 x 10(44) erg/s at z = 6. We compare the high-z luminosity function with the predictions of theoretical models using galaxy interactions as AGN triggering mechanism. We find that these models are broadly able to reproduce the high-z AGN luminosity functions. Closer agreement is found when we assume a minimum dark matter halo mass for black hole formation and growth. We compare our AGN luminosity functions with galaxy mass functions to derive the high-z AGN duty cycle, using observed Eddington ratio distributions to derive black hole masses. We find that the duty cycle increases with galaxy stellar mass and redshift by a factor of 10-30 from z = 0.25 to z = 4-5. We also report the detection of a large fraction of highly obscured, Compton thick AGN at z > 3 (18(-10)(+17)%). Their optical counterparts do not show any reddening and we thus conclude that the size of the X-ray absorber is likely smaller than the dust sublimation radius. We finally report the discovery of a highly star-forming galaxy at z = 3.47, arguing that its X-ray luminosity is likely dominated by stellar sources. If confirmed, this would be one of the farthest objects in which stellar sources have been detected in X-rays.