We present high-spatial resolution imaging obtained with the Submillimeter Array ( SMA ) at 880 \mu m and the Keck Adaptive Optics ( AO ) system at K _ { S } -band of a gravitationally lensed sub-millimeter galaxy ( SMG ) at z = 4.243 discovered in the Herschel Astrophysical Terahertz Large Area Survey .
The SMA data ( angular resolution \approx 0 \farcs 6 ) resolve the dust emission into multiple lensed images , while the Keck AO K _ { S } -band data ( angular resolution \approx 0 \farcs 1 ) resolve the lens into a pair of galaxies separated by 0 \farcs 3 .
We present an optical spectrum of the foreground lens obtained with the Gemini-South telescope that provides a lens redshift of z _ { lens } = 0.595 \pm 0.005 .
We develop and apply a new lens modeling technique in the visibility plane that shows that the SMG is magnified by a factor of \mu = 4.1 \pm 0.2 and has an intrinsic infrared ( IR ) luminosity of L _ { IR } = ( 2.1 \pm 0.2 ) \times 10 ^ { 13 } ~ { } L _ { \sun } .
We measure a half-light radius of the background source of r _ { s } = 4.4 \pm 0.5 ~ { } kpc which implies an IR luminosity surface density of \Sigma _ { IR } = ( 3.4 \pm 0.9 ) \times 10 ^ { 11 } ~ { } L _ { \sun } ~ { } kpc ^ { − 2 } , a value that is typical of z > 2 SMGs but significantly lower than IR luminous galaxies at z \sim 0 .
The two lens galaxies are compact ( r _ { lens } \approx 0.9 ~ { } kpc ) early-types with Einstein radii of \theta _ { E 1 } = 0.57 \pm 0.01 and \theta _ { E 2 } = 0.40 \pm 0.01 that imply masses of M _ { lens 1 } = ( 7.4 \pm 0.5 ) \times 10 ^ { 10 } ~ { } M _ { \sun } and M _ { lens 2 } = ( 3.7 \pm 0.3 ) \times 10 ^ { 10 } ~ { } M _ { \sun } .
The two lensing galaxies are likely about to undergo a dissipationless merger , and the mass and size of the resultant system should be similar to other early-type galaxies at z \sim 0.6 .
This work highlights the importance of high spatial resolution imaging in developing models of strongly lensed galaxies discovered by Herschel .