We present the identification of a bright submillimeter ( submm ) source , SMM J163555.5+661300 , detected in the lensing cluster Abell 2218 , for which we have accurately determined the position using observations from the Submillimeter Array ( SMA ) .
The identified optical counterpart has a spectroscopic redshift of z = 4.044 \pm 0.001 if we attribute the single emission line detected at \lambda = 6140 Å to Lyman- \alpha .
This redshift identification is in good agreement with the optical/near-infrared photometric redshift as well as the submm flux ratio S _ { 450 } / S _ { 850 } \sim 1.6 , the radio-submm flux ratio S _ { 1.4 } / S _ { 850 } < 0.004 , and the 24 \mu m to 850 \mu m flux ratio S _ { 24 } / S _ { 850 } < 0.005 .
Correcting for the gravitational lensing amplification of \sim 5.5 , we find that the source has a far-infrared luminosity of 1.3 \times 10 ^ { 12 } L _ { \odot } , which implies a star formation rate of 230 M _ { \odot } yr ^ { -1 } .
This makes it the lowest-luminosity SMG known at z > 4 to date .
Previous CO ( 4-3 ) emission line obserations yielded a non-detection , for which we derived an upper limit of the CO line luminosity of L _ { CO } ^ { { } ^ { \prime } } = 0.3 \times 10 ^ { 10 } K km/s pc ^ { -2 } , which is not inconsistent with the L ^ { { } ^ { \prime } } _ { CO } - L _ { FIR } relation for starburst galaxies .
The best fit model to the optical and near-infrared photometry give a stellar population with an age of 1.4 Gyr and a stellar mass of 1.6 \times 10 ^ { 10 } M _ { \odot } .
The optical morphology is compact and in the source plane the galaxy has an extent of \sim 6 \times 3 kpc with individual star forming knots of < 500 pc in size .
J163556 is not resolved in the SMA data and we place a strict upper limit on the size of the starburst region of 8 { kpc } \times 3 { kpc } , which implies a lower limit on the star formation rate surface density of 12 M _ { \odot } yr ^ { -1 } kpc ^ { 2 } .
The redshift of J163556 extends the redshift distribution of faint , lensed SMGs , and we find no evidence that these have a different redshift distribution than bright SMGs .