Connecting the cosmic infrared background to the X-ray background

We estimate the contribution of active galactic nuclei (AGN) and of their host galaxies to the infrared background. We use the luminosity function and evolution of AGN recently determined by the hard X-ray surveys, and new spectral energy distributions connecting the X-ray and the infrared emission, divided in intervals of absorption. These two ingredients allow us to determine the contribution of AGN to the infrared background by using mostly observed quantities, with only minor assumptions. We find that AGN emission contributes little to the infrared background (<5 per cent over most of the infrared bands), implying that the latter is dominated by star formation. However, AGN host galaxies may contribute significantly to the infrared background, and more specifically 10-20 per cent in the 1-20 mum range and similar to5 per cent at lambda < 60 mum. We also give the contribution of AGN and of their host galaxies to the source number counts in various infrared bands, focusing on those which will be observed with Spitzer. We also report a significant discrepancy between the expected contribution of AGN hosts to the submillimetre background and bright submillimetre number counts with the observational constraints. We discuss the causes and implications of this discrepancy and the possible effects on the Spitzer far-infrared bands.