Herschel and Hubble study of a lensed massive dusty starbursting galaxy
  at $z\sim3$
  We present the results of combined deep Keck/NIRC2, HST/WFC3 near-infrared
and Herschel far infrared observations of an extremely star forming dusty
lensed galaxy identified from the Herschel Astrophysical Terahertz Large Area
Survey (H-ATLAS J133542.9+300401). The galaxy is gravitationally lensed by a
massive WISE identified galaxy cluster at $z\sim1$. The lensed galaxy is
spectroscopically confirmed at $z=2.685$ from detection of $\rm {CO (1
\rightarrow 0)}$ by GBT and from detection of $\rm {CO (3 \rightarrow 2)}$
obtained with CARMA. We use the combined spectroscopic and imaging observations
to construct a detailed lens model of the background dusty star-forming galaxy
(DSFG) which allows us to study the source plane properties of the target. The
best-fit lens model provide magnification of $\mu_{\rm star}=2.10\pm0.11$ and
$\mu_{\rm dust}=2.02\pm0.06$ for the stellar and dust components respectively.
Multi-band data yields a magnification corrected star formation rate of
$1900(\pm200)\,M_{\odot}{\rm yr^{-1}}$ and stellar mass of
$6.8_{-2.7}^{+0.9}\times10^{11}\,M_{\odot}$ consistent with a main sequence of
star formation at $z\sim2.6$. The CO observations yield a molecular gas mass of
$8.3(\pm1.0)\times10^{10}\,M_{\odot}$, similar to the most massive star-forming
galaxies, which together with the high star-formation efficiency are
responsible for the intense observed star formation rates. The lensed DSFG has
a very short gas depletion time scale of $\sim40$ Myr. The high stellar mass
and small gas fractions observed indicate that the lensed DSFG likely has
already formed most of its stellar mass and could be a progenitor of the most
massive elliptical galaxies found in the local Universe.
