The hard X-ray 20-40 keV AGN luminosity function

We have compiled a complete extragalactic sample based on similar to 25,000 deg(2) to a limiting flux of 3; 10(-11) ergs cm(-2) s(-1) (similar to 7000 deg(2) to a flux limit of 10(-11) ergs cm(-2) s(-1)) in the 20-40 keV band with INTEGRAL. We have constructed a detailed exposure map to compensate for effects of nonuniform exposure. The flux-number relation is best described by a power law with a slope of alpha = 1.66 +/- 0.11. The integration of the cumulative flux per unit area leads to f(20-40) (keV) = 2.6 x 10(-10) ergs cm(-2) s(-1) sr(-1), which is about 1% of the known 20-40 keV X-ray background. We present the first luminosity function of AGNs in the 20-40 keV energy range, based on 38 extragalactic objects detected by the imager IBIS-ISGRI on board INTEGRAL. The luminosity function shows a smoothly connected double-power-law form with an index of gamma(1) = 0.8 below and gamma(2) = 2.1 above the turnover luminosity of L-* = 2.4 x 10(43) ergs s(-1). The emissivity of all INTEGRAL AGNs per unit volume is W20-40 (keV)(> 10(41) ergs s(-1)) = 2.8 x 10(38) ergs s(-1) h(70)(3) Mpc(-3). These results are consistent with those derived in the 2-20 keV energy band and do not show a significant contribution by Compton-thick objects. Because the sample used in this study is truly local (z = 0.022), only limited conclusions can be drawn for the evolution of AGNs in this energy band.