We investigate the potential of submm–mm and submm–mm–radio photometric redshifts using a sample of mm-selected sources as seen at 250 , 350 and 500 \mu m by the SPIRE instrument on Herschel .
From a sample of 63 previously identified mm-sources with reliable radio identifications in the GOODS-N and Lockman Hole North fields 46 ( 73 per cent ) are found to have detections in at least one SPIRE band .
We explore the observed submm/mm colour evolution with redshift , finding that the colours of mm-sources are adequately described by a modified blackbody with constant optical depth \tau = ( \nu / \nu _ { 0 } ) ^ { \beta } where \beta = +1.8 and \nu _ { 0 } = c / 100 \mu m. We find a tight correlation between dust temperature and IR luminosity .
Using a single model of the dust temperature and IR luminosity relation we derive photometric redshift estimates for the 46 SPIRE detected mm-sources .
Testing against the 22 sources with known spectroscopic , or good quality optical/near-IR photometric , redshifts we find submm/mm photometric redshifts offer a redshift accuracy of | \Delta z| / ( 1 + z ) = 0.16 ( < | \Delta z| > = 0.51 ) .
Including constraints from the radio-far IR correlation the accuracy is improved to | \Delta z| / ( 1 + z ) = 0.15 ( < | \Delta z| > = 0.45 ) .
We estimate the redshift distribution of mm-selected sources finding a significant excess at z > 3 when compared to \sim 850 \mu m selected samples .