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3. AGN POPULATION SYNTHESIS MODELS

In 1989, when the resolved XRB fraction was just a few percent, Setti & Woltjer (1989) proposed that the flat slope of the 2-10 keV XRB was due to a population of obscured AGN in addition to the bright unobscured AGN with steep spectra observed at that time. Since then, a number of models have been worked out and refined constantly (Madau, Ghisellini & Fabian 1994; Comastri et al. 1995; Pompilio, La Franca & Matt 2000; Wilman & Fabian 1999). With the increasing sensitivity of recent X-ray surveys, the population of obscured AGN emerged (see e.g. Mushotzky et al. 2000), and the main prediction of the AGN synthesis models was then confirmed. However, given the large number of uncertain parameters involved, it is crucial to check synthesis models against the largest number of observational constraints. The main uncertainties are related to unobscured AGN. While the X-ray luminosity function (XLF) and evolution of unobscured AGN are rather well known (e.g. Miyaji, Hasinger & Schmidt 2000), nothing is known about obscured AGN. Comastri et al. (1995) showed that, assuming for the obscured AGN a distribution of absorbing columns and the same evolution and XLF (upscaled by a factor of a few) of unobscured ones, it was possible to fit the full XRB spectrum in the ~ 1 - 100 keV band, as well as the integral counts (logN-logS relation) in the 0.5-2 keV and 2-10 keV energy bands. Also, the redshift distribution of AGN detected in ROSAT and HEAO-1 samples (at limiting fluxes of f0.5-2 ~ 10-14 erg cm-2 s-1 and f2-10 ~ 3 × 10-11 erg cm-2 s-1 , respectively) were in good agreement with the model expectations. Later, more constraints became available. The local ratio between obscured and unobscured AGN (in the Seyfert luminosity regime) was found to be ~ 4 (Maiolino & Rieke 1995), and the column density distribution of local Seyfert 2s was determined (Risaliti et al. 1999). Using these new constraints it was shown (Gilli, Risaliti & Salvati 1999) that, if the column density distribution in obscured AGN is the same at all redshifts and luminosities, then additional obscured sources at moderate/high redshifts are required to match the XRB constraints. Gilli, Salvati & Hasinger (2001, hereafter GSH01) proposed that obscured sources evolve slightly faster than unobscured ones. In particular they favored a model (model B) where the ratio between obscured and unobscured AGN increases from 4 at z = 0 to 10 at z = 1.3, where both populations stop evolving. This model was able to reproduce the broad set of observational constraints used by Comastri et al., furthermore extending the agreement to lower fluxes. In particular, the redshift distribution of soft X-ray selected AGN in the ROSAT Ultra Deep Survey (UDS, Lehmann et al. 2001) at a limiting flux of f0.5-2 ~ 10-15 erg cm-2 s-1 was nicely reproduced, as well as that of hard X-ray selected AGN in the ASCA Large Sky Survey (Akiyama et al. 2000) at a limiting flux of f2-10 ~ 10-13 erg cm-2 s-1 . Moreover, AGN synthesis models showed that, while the XRB spectrum can be simply fitted with a population of Seyfert 2 galaxies in addition to unobscured AGN, the ASCA and BeppoSAX source counts in the hard band are matched only by assuming a population of luminous obscured AGN, the so-called QSO2s (GSH01; Comastri et al. 2001). It is here noted that the main contribution to the source counts is expected to be produced by QSO2s with column densities in the range logNH = 22 - 23, while the contribution of Compton thick QSO2s is expected to be negligible.

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