We present detection and analysis of faint X-ray sources in the Chandra deep field south (CDFS) using the 4 Msec Chandra observation and adopting a new detection algorithm, based on a targeted search at the position of known high-z galaxies. This optimized technique results in the identification of 54 z>3 AGNs, 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 join 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 best modeled by pure luminosity evolution with L* decreasing from 6x10^44 ergs/s at z=3 to L*=2x10^44 ergs/s at z=6. We compare the high-z luminosity function with the prediction 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. A better agreement is found assuming a minimum Dark Matter halo mass for black hole formation and growth. We compare our AGN luminosity functions with galaxy mass functions to derive 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 10-30 from z=0.25 to z=4-5. We also report on the detection of a large fraction of highly obscured, Compton thick AGN at z>3 (18+17-10%). Their optical counterparts are not strongly reddened 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. If confirmed, this would be one of the farthest objects in which stellar sources are detected in X-rays.
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