We derive photometric redshifts from 17-band optical to mid-infrared photometry of 74 robust radio , 24 \mu m and Spitzer IRAC counterparts to 68 of the 126 submillimetre galaxies ( SMGs ) selected at 870 \mu m by LABOCA observations in the Extended Chandra Deep Field South ( ECDFS ) .
We test the photometric redshifts of the SMGs against the extensive archival spectroscopy in the ECDFS .
The median photometric redshift of identified SMGs is z = 2.2 \pm 0.1 , the interquartile range is z = 1.8 –2.7 and we identify 10 ( \sim 15 \% ) high-redshift ( z \geq 3 ) SMGs .
We derive a simple redshift estimator for SMGs based on the IRAC 3.6 and 8 \mu m fluxes which is accurate to \Delta z \sim 0.4 for SMGs at z < 4 .
A statistical analysis of sources around unidentified SMGs identifies a population of likely counterparts with a redshift distribution peaking at z = 2.5 \pm 0.3 , which likely comprises \sim 60 \% of the unidentified SMGs .
This confirms that the bulk of the undetected SMGs are co-eval with those detected in the radio/mid-infrared .
We conclude that at most \sim 15 \% of all the SMGs are below the flux limits of our IRAC observations and lie at z \ga 3 and hence around \sim 30 \% of all SMGs have z \ga 3 .
We estimate that the full S _ { 870 \mu m } > 4 mJy SMG population has a median redshift of 2.5 \pm 0.6 .
In contrast to previous suggestions we find no significant correlation between submillimetre flux and redshift .
The median stellar mass of the SMGs derived from SED fitting is ( 9.2 \pm 0.9 ) \times 10 ^ { 10 } M _ { \sun } and the interquartile range is ( 4.7–14 ) \times 10 ^ { 10 } M _ { \sun } , although we caution that the uncertainty in the star-formation histories results in a factor of \sim 5 uncertainty in these stellar masses .
Using a single temperature modified blackbody fit with \beta = 1.5 the median characteristic dust temperature of SMGs is 35.9 \pm 1.4 K and the interquartile range is 28.5 –43.3 K. The infrared luminosity function shows that SMGs at z = 2 –3 typically have higher far-infrared luminosities and luminosity density than those at z = 1 –2 .
This is mirrored in the evolution of the star-formation rate density ( SFRD ) for SMGs which peaks at z \sim 2 .
The maximum contribution of bright SMGs to the global SFRD ( \sim 5 \% for SMGs with S _ { 870 \mu m } \ga 4 mJy ; \sim 50 \% for SMGs with S _ { 870 \mu m } > 1 mJy ) also occurs at z \sim 2 .