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Physical properties and morphology of a newly identified compact z=4.04 lensed submillimeter galaxy in Abell 2218

We present the identification of a bright submm source, SMMJ163555.5+661300, detected in the lensing cluster Abell2218, 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+-0.001 if we attribute the single emission line detected at lambda=6140AA 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_850~1.6, the radio-submm flux ratio S_1.4/S_850 < 0.004, and the 24um to 850um flux ratio S_24/S_850 < 0.005. Correcting for the gravitational lensing amplification of ~5.5, we find that the source has a far-infrared luminosity of 1.3x10^12 Lsun, which implies a star formation rate of 230 Msun/yr. 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 = 0.3x10^10 K km/s/pc^2, which is not inconsistent with the L'_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 1.6x10^10 Msun. The optical morphology is compact and in the source plane the galaxy has an extent of ~6kpc x 3kpc 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 8kpc x 3kpc, which implies a lower limit on the star formation rate surface density of 12 Msun/yr/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.