The cosmological properties of AGN in the XMM-Newton Hard Bright Survey

Aims. We investigate here the X-ray luminosity function (XLF) of absorbed ($N_{\rm H}$ between 4 $\times$ 1021 and 1024 cm-2) and unabsorbed ($N_{\rm H}$ < 4 $\times$ 1021 cm-2) AGN, the fraction of absorbed AGN as a function of $L_{\rm X}$ (and z), the intrinsic $N_{\rm H}$ distribution of the AGN population, and the XLF of Compton thick ($N_{\rm H}$ > 1024 cm-2) AGN. Methods. To carry out this investigation, we have used the XMM-Newton Hard Bright Serendipitous Sample (HBSS), a complete sample of bright X-ray sources ($f_{\rm x}$ $\ga$ 7 $\times$ 10-14 erg cm-2 s-1) at high galactic latitude (|b| > 20°) selected in the 4.5-7.5 keV energy band. The HBSS sample is now almost completely identified (97% spectroscopic identifications) and it can be safely used for a statistical investigation. The HBSS contains 62 AGN out of which 40 are unabsorbed (or marginally absorbed; $N_{\rm H}$ < 4 $\times$ 1021 cm-2) and 22 are absorbed ($N_{\rm H}$ between 4 $\times$ 1021 and ~1024 cm-2). Results. Absorbed and unabsorbed AGN are characterised by two different XLF with the absorbed AGN population being described by a steeper XLF, if compared with the unabsorbed ones, at all luminosities. The intrinsic fraction F of absorbed AGN (i.e., the fraction of sources with $N_{\rm H}$ between 4 $\times$ 1021 and 1024 cm-2 divided the sources with $N_{\rm H}$ below 1024 cm-2, corrected for the bias due to the photoelectric absorption) with $L_{2{-}10~{\rm keV}}$ $\ga$ 3 $\times$ 1042 erg s-1 is 0.57 $\pm$ 0.11; we find that F decreases with the intrinsic luminosity, and probably, increases with the redshift. Our data are consistent with a flat Log $N_{\rm H}$ distribution for $N_{\rm H}$ between 1020 and 1024 cm-2. Finally, by comparing the results obtained here with those obtained using an optically-selected sample of AGN we derive, in an indirect way, the XLF of Compton thick AGN; the latter is well described by a XLF similar, in shape, to that of absorbed AGN, but having a normalization of about a factor of 2 above. The density ratio between Compton thick AGN ($N_{\rm H}$ $\geq$ 1024 cm-2) and Compton thin AGN ($N_{\rm H}$ $\leq$ 1024 cm-2) decreases from 1.08 $\pm$ 0.44 at ~1043 erg s-1 to 0.57 $\pm$ 0.22 at ~1044 erg s-1 to 0.23 $\pm$ 0.15 at ~1045 erg s-1. Conclusions. The results presented here on the anti-correlation between F and $-L_{\rm x}$ are fully consistent with the hypothesis of a reduction of the covering factor of the gas as a function of the luminosity and are clearly inconsistent with the simplest unified scheme of AGN. These results strongly support the recently proposed radiation-limited clumpy dust torus model although alternative physical models are also consistent with the observations.