The bright sub-mm galaxy MM 18423+5938 at redshift 3.9296 has been predicted from mid-infrared and millimetre photometry to have an exceptionally large total infrared ( IR ) luminosity .
We present new radio imaging at 1.4 GHz with the Westerbork Synthesis Radio Telescope that is used to determine a radio-derived total IR luminosity for MM 18423+5938 via the well established radio–far-infrared correlation .
The flux density is found to be S _ { 1.4 ~ { } GHz } = 217 \pm 37 \mu Jy , which corresponds to a rest-frame luminosity density of L _ { 1.4 ~ { } GHz } = 2.32 \pm 0.40 \times 10 ^ { 25 } \mu ^ { -1 } W Hz ^ { -1 } , where \mu is the magnification from a probable gravitational lens .
The radio-derived total IR luminosity and star-formation rate are L _ { 8 - 1000 ~ { } \mu m } = 5.6 ^ { +4.1 } _ { -2.4 } \times 10 ^ { 13 } \mu ^ { -1 } L _ { \odot } and SFR = 9.4 ^ { +7.4 } _ { -4.9 } \times 10 ^ { 3 } \mu ^ { -1 } M _ { \odot } yr ^ { -1 } , respectively , which are \sim 9 times smaller than those previously reported .
These differences are attributed to the IR spectral energy distribution of MM 18423+5938 being poorly constrained by the limited number of reliable photometric data that are currently available , and from a previous misidentification of the object at 70 \mu m. Using the radio derived total IR luminosity as a constraint , the temperature of the cold dust component is found to be T _ { d } \sim 24 ^ { +7 } _ { -5 } K for a dust emissivity of \beta = 1.5 \pm 0.5 .
The radio-derived properties of this galaxy are still large given the low excitation temperature implied by the CO emission lines and the temperature of the cold dust .
Therefore , we conclude that MM 18423+5938 is probably gravitationally lensed .