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
500μm by the SPIRE instrument on Herschel. From a sample of 63
previously identified mm sources with reliable radio identifications in
the Great Observatories Origins Deep Survey North 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 τ=
(ν/nu0)β, where β=+1.8 and
ν0=c/100 μm. 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 |Δz|/(1 +z) = 0.16 (=
0.51). Including constraints from the radio-far-IR correlation, the
accuracy is improved to |Δz|/(1 +z) = 0.15 (=
0.45). We estimate the redshift distribution of mm-selected sources
finding a significant excess at z > 3 when compared to ˜ 850
μm selected samples.