2012A&A...546A..98A

This paper investigates which constraints can be placed on the fraction of Compton-thick active galactic nuclei (AGN) in the Universe from modelling the spectrum of the diffuse X-ray background (XRB). We present a model for the synthesis of the XRB that uses as input a library of AGN X-ray spectra generated by Monte Carlo simulations. This is essential to account for the Compton scattering of X-ray photons in a dense medium and the impact of that process on the spectra of heavily obscured AGN. We identify a small number of input parameters to the XRB synthesis code that encapsulate the minimum level of uncertainty in reconstructing the XRB spectrum. These are the power-law index and high-energy cutoff of the intrinsic X-ray spectra of AGN, the level of the reflection component in AGN spectra, and the fraction of Compton-thick AGN in the Universe. We then map the volume of the space allowed to these parameters by current observational determinations of the XRB spectrum in the range 3-100keV. One of the least-constrained parameters is the fraction of Compton-thick AGN. Statistically acceptable fits to the XRB spectrum at the 68% confidence level can be obtained for Compton-thick AGN fractions in the range 5-50%. This is because of degeneracies among input parameters to the XRB synthesis code and uncertainties in the modelling of AGN spectra (e.g. level of reflection fraction). The most promising route for constraining the fraction of Compton-thick AGN in the Universe is via the direct detection of those sources in high-energy (>10keV) surveys. We show that the observed fraction of Compton-thick sources identified in the Swift/BAT serendipitous survey limits the intrinsic fraction of Compton-thick AGN, at least at low redshift, to 10-20% (68% confidence level). We also make predictions on the number density of Compton-thick sources that current and future X-ray missions are expected to discover. Testing those predictions with data will place tight constraints on the intrinsic fraction of Compton-thick AGN as a function of redshift.