A robust method for investigating galactic evolution in the submillimetre waveband .2. The submillimetre background and source counts

This is the second of two papers describing a model of galactic evolution in the submillimetre waveband. The model incorporates a self-consistent treatment of the evolution of dust and stars, is normalized to the submillimetre properties of galaxies in the local Universe, and can be used to make predictions for both disc and elliptical galaxies and for 'closed-box', 'inflow', and 'outflow' models of galactic evolution. The model does not include the effects of hierarchical clustering, but we show that the variation in the predictions produced by the different dust-evolution models is so large that it is premature to include the effects of an even more uncertain process. In Paper I we investigated whether it is possible to explain the extremely high dust masses of high-redshift quasars and radio galaxies by galactic evolution. In this paper we use the model to make predictions about the submillimetre background and source counts. All our disc galaxy models exceed at short wavelengths (lambda < 200 mu m) the submillimetre background recently measured by Puget et al. (1996), suggesting either that there is a problem with our models, or that the background measurement at the shorter wavelengths is inaccurate, or a combination of the two. However, the two models in which we assume the rapidly evolving star formation rate found from optical studies predict backgrounds that are so much greater than the measured background that we do not believe that this discrepancy can be the result of an inaccurate background measurement. We therefore conclude that there is no evidence in the submillimetre waveband for the rapid evolution found from optical studies. At longer wavelengths, most of the disc galaxy models predict backgrounds that are less than the observed background. Our elliptical galaxy models are more uncertain because they are less securely tied to the observed submillimetre properties of the local Universe. We find that it is relatively easy to produce models that predict backgrounds similar to that observed, but ale caution that our disc galaxy models show that a significant fraction of the observed background must be coming from disc galaxies. The main weaknesses in our models are the lack of a direct measurement of the submillimetre luminosity function for galaxies and the fact that we have been forced to assume that all local disc galaxies have the same far-infrared-submillimetre spectral energy distribution and the same ratio of gas mass to stellar mass. Observations with the SCUBA submillimetre array should remove both of these weaknesses, as well as providing measured source counts with which to confront the models.