We present a source-plane reconstruction of a Herschel and Planck -detected gravitationally-lensed dusty star-forming galaxy ( DSFG ) at z = 1.68 using Hubble , Sub-millimeter Array ( SMA ) , and Keck observations .
The background sub-millimeter galaxy ( SMG ) is strongly lensed by a foreground galaxy cluster at z = 0.997 and appears as an arc of length \sim 15 ^ { \prime \prime } in the optical images .
The continuum dust emission , as seen by SMA , is limited to a single knot within this arc .
We present a lens model with source plane reconstructions at several wavelengths to show the difference in magnification between the stars and dust , and highlight the importance of a multi-wavelength lens models for studies involving lensed DSFGs .
We estimate the physical properties of the galaxy by fitting the flux densities to model SEDs leading to a magnification-corrected star formation rate of 390 \pm 60 M _ { \odot } yr ^ { -1 } and a stellar mass of 1.1 \pm 0.4 \times 10 ^ { 11 } M _ { \odot } .
These values are consistent with high-redshift massive galaxies that have formed most of their stars already .
The estimated gas-to-baryon fraction , molecular gas surface density , and SFR surface density have values of 0.43 \pm 0.13 , 350 \pm 200 M _ { \odot } pc ^ { -2 } , and \sim 12 \pm 7 ~ { } M _ { \odot } yr ^ { -1 } kpc ^ { -2 } , respectively .
The ratio of star formation rate surface density to molecular gas surface density puts this among the most star-forming systems , similar to other measured SMGs and local ULIRGS .