The Hard X-ray 20-40 keV AGN Luminosity Function
  We have compiled a complete extragalactic sample based on 25,000 deg^2 to a limiting flux of 3E-11 ergs/cm**2/sec (7,000 deg^2 to a flux limit of 1E-11 ergs/cm**2/sec) 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+-0.11. The integration of the cumulative flux per unit area leads to f = 2.6E-10 ergs/cm**2/sec/sr, 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 two power-law form, with an index of gamma_1 = 0.8 below, and gamma_2 = 2.1 above the turn-over luminosity of L* = 2.4E43 ergs/sec. The emissivity of all INTEGRAL AGNs per unit volume is W(> 1E41 ergs/sec) = 2.8E38 ergs/sec/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 (average z = 0.022), only limited conclusions can be drawn for the evolution of AGNs in this energy band. 
V. Beckmann (1,2), S. Soldi (3), C. R. Shrader (1), N. Gehrels (1), N.   Produit (3) ((1) NASA/GSFC, (2) Univ. Maryland Balt...