Breaking the 'redshift deadlock' -: II.: The redshift distribution for the submillimetre population of galaxies

Ground-based submillimetre and millimetre wavelength blank-field surveys have identified more than 100 sources, the majority of which are believed to be dusty optically obscured starburst galaxies. Colours derived from various combinations of far-infrared, submillimetre, millimetre and radio fluxes provide the only currently available means to determine the redshift distribution of this new galaxy population. In this paper we apply our Monte Carlo photometric redshift technique, introduced recently by Hughes et al. in Paper I, to the multiwavelength data available for 77 galaxies selected at 850 mum and 1.25 mm. We calculate a probability distribution for the redshift of each galaxy, which includes a detailed treatment of the observational errors and uncertainties in the evolutionary model. The cumulative redshift distribution of the submillimetre galaxy population that we present in this paper, based on 50 galaxies found in wide-area SCUBA surveys, is asymmetric, and broader than those published elsewhere, with a significant high-z tail for some of the evolutionary models considered. Approximately 40 to 90 per cent of the submillimetre population is expected to have redshifts in the interval 2 less than or equal toz less than or equal to 4. Whilst this result is completely consistent with earlier estimates for the submillimetre galaxy population, we also show that the colours of many (less than or similar to50 per cent) individual submillimetre sources, detected only at 850 mum with non-detections at other wavelengths, are consistent with those of starburst galaxies that lie at extreme redshifts, z > 4. Spectroscopic confirmation of the redshifts, through the detection of rest-frame far-infrared-millimetre wavelength molecular transition lines, will ultimately calibrate the accuracy of this technique. We use the redshift probability distribution of HDF850.1 to illustrate the ability of the method to guide the choice of possible frequency tunings on the broad-band spectroscopic receivers that equip the large-aperture single-dish millimetre and centimetre wavelength telescopes.