A Detailed Gravitational Lens Model Based on Submillimeter Array and Keck Adaptive Optics Imaging of a Herschel-ATLAS Submillimeter Galaxy at z = 4.243

We present high-spatial resolution imaging obtained with the Submillimeter Array (SMA) at 880 μm and the Keck adaptive optics (AO) system at the KS-band of a gravitationally lensed submillimeter galaxy (SMG) at z = 4.243 discovered in the Herschel Astrophysical Terahertz Large Area Survey. The SMA data (angular resolution ≈0". 6) resolve the dust emission into multiple lensed images, while the Keck AO K_S-band data (angular resolution ≈0". 1) resolve the lens into a pair of galaxies separated by 0". 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 ± 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 μ = 4.1 ± 0.2 and has an intrinsic infrared (IR) luminosity of L_(IR) = (2.1 ± 0.2) × 10_(13) L_☉. We measure a half-light radius of the background source of r_s = 4.4 ± 0.5 kpc which implies an IR luminosity surface density of Σ_(IR) = (3.4 ± 0.9) × 10^(11) L_☉ kpc^(−2), a value that is typical of z > 2 SMGs but significantly lower than IR luminous galaxies at z ∼ 0. The two lens galaxies are compact (r_(lens) ≈ 0.9 kpc) early-types with Einstein radii of θ_(E1) = 0.57 ± 0.01 and θ_(E2) = 0.40 ± 0.01 that imply masses of M_(lens1) = (7.4 ± 0.5) × 10^(10)M_☉ and M_(lens2) = (3.7 ± 0.3) × 10^(10) M_☉. 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 ∼ 0.6. This work highlights the importance of high spatial resolution imaging in developing models of strongly lensed galaxies discovered by Herschel