A complete distribution of redshifts for sub-millimetre galaxies in the SCUBA-2 Cosmology Legacy Survey UDS field

Sub-milllimetre galaxies (SMGs) are some of the most luminous star-forming galaxies in the Universe, however their properties remain hard to determine due to the difficulty of identifying their optical\slash near-infrared counterparts. One of the key steps to determining the nature of SMGs is measuring a redshift distribution representative of the whole population. We do this by applying statistical techniques to a sample of 761 850$\mu$m sources from the SCUBA-2 Cosmology Legacy Survey observations of the UKIDSS Ultra-Deep Survey (UDS) Field. We detect excess galaxies around $> 98.4$ per cent of the 850$\mu$m positions in the deep UDS catalogue, giving us the first 850$\mu$m selected sample to have virtually complete optical\slash near-infrared redshift information. Under the reasonable assumption that the redshifts of the excess galaxies are representative of the SMGs themselves, we derive a median SMG redshift of $z = 2.05 \pm 0.03$, with 68 per cent of SMGs residing between $1.07