Modelling SCUBA sources in a Lambda-CDM cosmology: hot starbursts or cold extended galactic dust?

Previous modelling has demonstrated that it is difficult to reproduce the SCUBA source counts within the framework of standard hierarchical structure formation models if the sources are assumed to be the high-redshift counterparts of local ultra-luminous infrared galaxies with dust temperatures in the range 40-60 K. Here, we show that the counts are more easily reproduced in a model in which the bulk of the sub-millimetre emission comes from extended, cool (20-25 K) dust in objects with star formation rates of 50-100 solar masses per year. The low temperatures imply typical sizes of about 1 (S_{850}/1mJy})^{1/2} arcsec, a factor two to three larger than those predicted using starburst-like spectral energy distributions. Low dust temperatures also imply a ratio of optical/UV to 850-micron flux which is 30-100 times smaller, for the same optical depth, than expected for objects with a hot, starburst-like SED. This may help explain the small overlap between SCUBA sources and Lyman-break galaxies.