Starburst galaxies and structure in the submillimetre background towards the Hubble Deep Field

We use an 850-micron SCUBA map of the HDF to study the dust properties of optically-selected starburst galaxies at high redshift. Although the 850-micron map does not allow detection of the majority of individual sources, we show that the galaxies with the highest UV star-formation rates are detected statistically, with a flux density of about S_{850}=0.2 mJy for an apparent UV star-formation rate of 1 h^{-2} msun yr^{-1}. This level of submillimetre output indicates that the total star-forming activity is on average a factor of approximately 6 times larger than the rate inferred from the UV output of these galaxies. The general population of optical starbursts is then predicted to contribute at least 25 per cent of the 850-micron background. We carry out a power-spectrum analysis of the map, which yields some evidence for angular clustering of the background source population, but at a level lower than that seen in Lyman-break galaxies. Together with other lines of argument, particularly from the NICMOS HDF data, this suggests that the 850-micron background originates over an extremely wide range of redshifts -- perhaps 1 < z < 6.