A physical model for the hard X-ray background

We combine a semi-analytic galaxy formation model with a prescription for the obscured growth of massive black holes, to reproduce the hard X-ray background (XRB), the local 2–10 keV active galactic nuclei (AGN) luminosity function and the source counts, including recent Chandra results. The model also complies with constraints on the AGN contribution to the far-infrared and submillimetre backgrounds. The comoving density of luminous AGN [L(2-10keV) > 1044 erg s-1, in the unabsorbed rest-frame] in the model declines sharply since z=2, mimicking the observed evolution of the quasar population. The abundance of lower luminosity AGN simultaneously increases, and we identify such objects with the Seyfert galaxies. These features reflect an epoch-dependent rate of Bondi accretion from the hot, cooling atmosphere: at z < 2.5 most AGN are fed at much less than 10 per cent of the Eddington rate, whilst at z > 2.5 most accrete at 10–50 per cent Eddington. Unlike other models for quasar and galaxy formation, we do not consider major mergers between normal galaxies. The model produces an excess soft XRB below 4 keV which can be removed by modifying the wind expulsion model of Fabian to incorporate anisotropic ejection.