Cosmological evolution of the hard X-ray active galactic nucleus luminosity function and the origin of the hard X-ray background

We investigate the cosmological evolution of the hard X-ray luminosity function (HXLF) of active galactic nuclei (AGNs) in the 2-10 keV luminosity range of 10(41.5)-10(46.5) ergs s(-1) as a function of redshift up to 3. From a combination of surveys conducted at photon energies above 2 keV with HEAO 1, ASCA, and Chandra, we construct a highly complete (>96%) sample consisting of 247 AGNs over the wide flux range of 10(-10) to 3.8 x 10(-15) ergs cm(-2) s(-1) (2-10 keV). For our purpose, we develop an extensive method of calculating the intrinsic (before absorption) HXLF and the absorption (N-H) function. This utilizes the maximum likelihood method, fully correcting for observational biases with consideration of the X-ray spectrum of each source. We find that (1) the fraction of X-ray absorbed AGNs decreases with the intrinsic luminosity and (2) the evolution of the HXLF of all AGNs (including both type I and type II AGNs) is best described with a luminosity-dependent density evolution (LDDE) where the cutoff redshift increases with the luminosity. Our results directly constrain the evolution of AGNs that produce a major part of the hard X-ray background, thus solving its origin quantitatively. A combination of the HXLF and the N-H function enables us to construct a purely "observation-based'' population synthesis model. We present basic consequences of this model and discuss the contribution of Compton-thick AGNs to the rest of the hard X-ray background.