The 5-10 keV AGN luminosity function at 0.01 < z < 4.0

The active galactic nuclei (AGN) X-ray luminosity function traces actively accreting supermassive black holes and is essential for the study of the properties of the AGN population, black hole evolution, and galaxy-black hole coevolution. Up to now, the AGN luminosity function has been estimated several times in soft (0.5-2 keV) and hard X-rays (2-10 keV). AGN selection in these energy ranges often suffers from identification and redshift incompleteness and, at the same time, photoelectric absorption can obscure a significant amount of the X-ray radiation. We estimate the evolution of the luminosity function in the 5-10 keV band, where we effectively avoid the absorbed part of the spectrum, rendering absorption corrections unnecessary up to N_H ~ 10²³ cm^-2. Our dataset is a compilation of six wide, and deep fields: MAXI, HBSS, XMM-COSMOS, Lockman Hole, XMM-CDFS, AEGIS-XD, Chandra-COSMOS, and Chandra-CDFS. This extensive sample of ~1110 AGN (0.01 < z < 4.0, 41 < log L_x < 46) is 98% redshift complete with 68% spectroscopic redshifts. For sources lacking a spectroscopic redshift estimation we use the probability distribution function of photometric redshift estimation specifically tuned for AGN, and a flat probability distribution function for sources with no redshift information. We use Bayesian analysis to select the best parametric model from simple pure luminosity and pure density evolution to more complicated luminosity and density evolution and luminosity-dependent density evolution (LDDE). We estimate the model parameters that describe best our dataset separately for each survey and for the combined sample. We show that, according to Bayesian model selection, the preferred model for our dataset is the LDDE. Our estimation of the AGN luminosity function does not require any assumption on the AGN absorption and is in good agreement with previous works in the 2-10 keV energy band based on X-ray hardness ratios to model the absorption in AGN up to redshift three. Our sample does not show evidence of a rapid decline of the AGN luminosity function up to redshift four.