Context :

Aims : We study the hard X-ray luminosity function and absorption distribution of local ( z \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ < $ } } } 0.1 ) active galactic nuclei ( AGN ) and discuss the implications for AGN cosmological evolution and for the cosmic X-ray background ( CXB ) .

Methods : We use the INTEGRAL all-sky hard X-ray survey to perform a statistical study of a representative sample of nearby AGN .
Our entire all-sky sample consists of 127 AGN , of which 91 are confidently detected ( > 5 \sigma ) on the time-averaged map obtained with the IBIS/ISGRI instrument and 36 are detected only during single observations .
Among the former there are 66 non-blazar AGN located at |b| > 5 ^ { \circ } , where the survey ’ s identification completeness is \sim 93 % , which we use for calculating the AGN luminosity function and X-ray absorption distribution .

Results : In broad agreement with previous studies , we find that the fraction f _ { a } of obscured ( \log N _ { H } > 22 ) objects is much higher ( \sim 70 % ) among the low-luminosity AGN ( L _ { hx } < 10 ^ { 43.6 } erg s ^ { -1 } ) than among the high-luminosity ones ( L _ { hx } > 10 ^ { 43.6 } erg s ^ { -1 } ) , f _ { a } \sim 25 % , where L _ { hx } is the luminosity in the 17–60 keV energy band .
We also find that locally the fraction of Compton-thick AGN is less than 20 % unless there is a significant population of AGN that are so strongly obscured that their observed hard X-ray luminosities fall below \sim 10 ^ { 40 } – 10 ^ { 41 } erg s ^ { -1 } , the effective limit of our survey .
The constructed hard X-ray luminosity function has a canonical , smoothly broken power-law shape in the range 40 < \log L _ { hx } < 45.5 with a characteristic luminosity of \log L _ { \ast } = 43.40 \pm 0.28 .
The estimated local luminosity density due to AGN with \log L _ { hx } > 40 is ( 1.4 \pm 0.3 ) \times 10 ^ { 39 } erg s ^ { -1 } Mpc ^ { -3 } ( 17–60 keV ) .
We demonstrate that the spectral shape and amplitude of the CXB are consistent with the simple scenario in which the N _ { H } distribution of AGN ( for a given L _ { hx } / L _ { \ast } ( z ) ratio ) has not changed significantly since z \sim 1.5 , while the AGN luminosity function has experienced pure luminosity evolution .

Conclusions :