The synthesis of the cosmic X-ray background in the Chandra and XMM-Newton era

We present a detailed and self-consistent modeling of the cosmic X-ray background (XRB) based on the most up-to-date X-ray luminosity functions (XLF) and evolution of Active Galactic Nuclei (AGN). The large body of observational results collected by soft (0.5–2 keV) and hard (2–10 keV) X-ray surveys are used to constrain at best the properties of the Compton-thin AGN population and its contribution to the XRB emission. The number ratio R between moderately obscured (Compton-thin) AGN and unobscured AGN is fixed by the comparison between the soft and hard XLFs, which suggests that R decreases from 4 at low luminosities to 1 at high luminosities. From the same comparison there is no clear evidence of an evolution of the obscured AGN fraction with redshift. The distribution of the absorbing column densities in obscured AGN is determined by matching the soft and hard source counts. A distribution rising towards larger column densities is able to reproduce the soft and hard AGN counts over about 6 dex in flux. The model also reproduces with excellent accuracy the fraction of obscured objects in AGN samples selected at different X-ray fluxes. The integrated emission of the Compton-thin AGN population is found to underestimate the XRB flux at about 30 keV, calling for an additional population of extremely obscured (Compton-thick) AGN. Since the number of Compton-thick sources required to fit the 30 keV XRB emission strongly depends on the spectral templates assumed for unobscured and moderately obscured AGN, we explored the effects of varying the spectral templates. In particular, in addition to the column density distribution, we also considered a distribution in the intrinsic powerlaw spectral indices of variable width. In our baseline model a Gaussian distribution of photon indices with mean $\langle \Gamma \rangle=1.9$ and dispersion $\sigma_{\Gamma}=0.2$ is assumed. This increases the contribution of the Compton-thin AGN population to the 30 keV XRB intensity by ~$30\%$ with respect to the case of null dispersion (i.e. a single primary AGN powerlaw with $\Gamma=1.9$) but is not sufficient to match the 30 keV XRB emission. Therefore a population of heavily obscured -Compton-thick- AGN, as large as that of moderately obscured AGN, is required to fit the residual background emission. Remarkably, the fractions of Compton-thick AGN observed in the Chandra Deep Field South and in the first INTEGRAL and Swift catalogs of AGN selected above 10 keV are in excellent agreement with the model predictions.