The Hard X-ray 20-40 keV AGN Luminosity Function

We have compiled a complete, significance limited extragalactic sample based on approximately 25,000 deg(sup 2) to a limiting flux of 3 x 10(exp -11) ergs per square centimeter per second. (approximately 7,000 deg(sup 2)) to a flux limit of 10(exp -11) ergs per square centimeter per second)) in the 20 - 40 keV band with INTEGRAL. We have constructed a detailed exposure map to compensate for effects of non-uniform exposure. The flux-number relation is best described by a power-law with a slope of alpha = 1.66 plus or minus 0.11. The integration of the cumulative flux per unit area leads to f(sub 20-40 keV) = 2.6 x 10(exp -10) ergs per square centimeter per second per sr(sup -1) which is about 1% of the known 20-40 keV X-ray background. We present the first luminosity function of AGN in the 20-40 keV energy range, based on 68 extragalactic objects detected by the imager IBIS/ISGRI on-board INTEGRAL. The luminosity function shows a smoothly connected two power-law form, with an index of gamma (sub 1) = 0.9 below, and gamma (sub 2) = 2.2 above the turn-over luminosity of L(sub *), = 4.6 x 10(sup 43) ergs per second. The emissivity of all INTEGRAL AGNs per unit volume is W(sub 20-40keV)(greater than 10(sup 41) ergs per second) = 2.8 x 10(sup 38) ergs per second h(sup 3)(sub 70) Mpc(sup -3). These results are consistent with those derived in the 2-20keV energy band and do not show a significant contribution by Compton-thick objects. Because the sample used in this study is truly local (z(raised bar) = 0.022)), only limited conclusions can be drawn for the evolution of AGNs in this energy band. But the objects explaining the peak in the cosmic X-ray background are likely to be either low luminosity AGN (L(sub x) less than 10(sup 41) ergs per second) or of other type, such as intermediate mass black holes, clusters, and star forming regions.