A Detailed Gravitational Lens Model Based on Submillimeter Array and
  Keck Adaptive Optics Imaging of a Herschel-ATLAS Sub-millimeter Galaxy at
  z=4.243
  We present high-spatial resolution imaging obtained with the Submillimeter
Array (SMA) at 880um and the Keck Adaptive Optics (AO) system at Ks-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 ~0.6") resolve the dust emission into multiple lensed images, while
the Keck AO Ks-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 mu = 4.1 +/- 0.2 and has an intrinsic infrared (IR) luminosity of
L_IR = (2.1 +/- 0.2) x 10^13 Lsun. 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 Sigma_IR = (3.4 +/- 0.9) x 10^11 Lsun 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 theta_E1 = 0.57 +/- 0.01 and theta_E2 = 0.40 +/- 0.01 that
imply masses of M_lens1 = (7.4 +/- 0.5) x 10^10 Msun and M_lens2 = (3.7 +/-
0.3) x 10^10 Msun. 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.
