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 submillimeter (submm) source, SMMJ163555.5+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 ± 0.001 if we attribute the single emission line detected at λ = 6140 Å to Lyα. 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 24 μm to 850 μm 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 1.3 × 10 ¹² L _⊙, which implies a star formation rate (SFR) of 230 M _Oṡ yr^-1. This makes it the lowest-luminosity submillimeter galaxy (SMG) known at z>4 to date. Previous CO(4-3) emission line observations yielded a non-detection, for which we derived an upper limit of the CO line luminosity of L_CO = 0.3 × 10¹⁰K km s^-1 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 1.6 × 10¹⁰ M _⊙. The optical morphology is compact and in the source plane the galaxy has an extent of ∼ 6 × 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 × 3 kpc, which implies a lower limit on the SFR surface density of 12 M _⊙ yr^-1 kpc². 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.