The BeppoSAX High-Energy Large-area Survey.: V.: The nature of the hard X-ray source population and its evolution

We present optical spectroscopic identifications of hard X-ray (5-10 keV) selected sources belonging to the High-Energy Large-Area Survey sample obtained with BeppoSAX down to a 5-10 keV flux limit of f(5-10 keV) similar to 3 x 10(14) ergs cm(-2) s(-1). The sample consists of 118 sources. There are 25 sources that have been identified through correlations with catalogs of known sources. A spectroscopic identification for 49 more has been searched for with the telescope. The results of 13 fields were empty down to R = 21. There were 37 sources identified as type 1 active galactic nuclei (AGNs) and nine as type 2 AGNs. The remaining sources are five narrow emission-line galaxies, six clusters, two BL Lac objects, one radio galaxy, and one star. Combining these objects with other hard X-ray selected AGNs from ASCA and HEAO1, we find that the local luminosity function of type 1 AGNs (AGN 1s) in the 2-10 keV band is fairly well represented by a double power law function. There is evidence for significant cosmological evolution according to a pure luminosity evolution (PLE) model [L-X(z) proportional to (1+ z)(k)], with k = 2.12 and 2.22 (sigma(k) similar or equal to 0.14) in a (Omega(m), Omega(lambda)) = (1.0; 0.0) and a (Omega(m), Omega(lambda)) = (0.3; 0.7) cosmology, respectively. The data show an excess of faint high-redshift type AGN 1s, which is well modeled by a luminosity-dependent density evolution (LDDE), similar to what is observed in soft X-rays. However, in both cosmologies, the statistics are not significant enough to distinguish between the PLE and LDDE models. The fitted models imply a contribution of AGN 1s to the 2 10 keV X-ray background from 35% up to 60%.