We have compiled a complete extragalactic sample based on ～25,000 deg~2 to a limiting flux of 3 x 10~(-11) ergs cm~(-2) s~(-1) (～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 α = 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 γ_1 =0.8 below and γ_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 W_(20-40) 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.
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机译：我们已根据〜25,000 deg〜2到3 x 10〜（-11）ergs cm〜（-2）s〜（-1）的极限通量（〜7000 deg〜2的通量极限）编译了完整的河外样本使用INTEGRAL在20-40 keV波段中的10〜（-11）ergs cm〜（-2）s〜（-1））。我们构建了详细的曝光图以补偿不均匀曝光的影响。磁通数关系最好由幂定律描述，斜率α= 1.66±0.11。单位面积累积通量的积分导致f_（20-40）keV = 2.6 x 10〜（-10）ergs cm〜（-2）s〜（-1）sr〜（-1），约为1％的已知20-40 keV X射线背景。我们基于INTEGRAL板上的成像器IBIS-ISGRI检测到的38个河外物体，提出了AGNs在20-40 keV能量范围内的第一个发光度函数。发光度函数显示出平滑连接的双幂律形式，其折射率L_ * = 2.4 x 10〜（43）ers s〜（-1）低于γ_1= 0.8，高于γ_2= 2.1。每单位体积所有积分AGN的发射率是W_（20-40）keV（> 10〜（41）ergs s〜（-1））= 2.8 x 10〜（38）ergs s〜（-1）h_（70 ）〜3 Mpc〜（-3）。这些结果与在2-20 keV的能带中得出的结果一致，并且未显示Compton厚物体的显着贡献。由于本研究中使用的样本确实是局部的（z = 0.022），因此对于该能带中AGN的演化只能得出有限的结论。
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