The Herschel-ATLAS: magnifications and physical sizes of
  $500\,\mu$m-selected strongly lensed galaxies
  We perform lens modelling and source reconstruction of Submillimeter Array
(SMA) data for a sample of 12 strongly lensed galaxies selected at 500$\mu$m in
the Herschel Astrophysical Terahertz Large Area Survey H-ATLAS. A previous
analysis of the same dataset used a single S\`ersic profile to model the light
distribution of each background galaxy. Here we model the source brightness
distribution with an adaptive pixel scale scheme, extended to work in the
Fourier visibility space of interferometry. We also present new SMA
observations for seven other candidate lensed galaxies from the H-ATLAS sample.
Our derived lens model parameters are in general consistent with previous
findings. However, our estimated magnification factors, ranging from 3 to 10,
are lower. The discrepancies are observed in particular where the reconstructed
source hints at the presence of multiple knots of emission. We define an
effective radius of the reconstructed sources based on the area in the source
plane where emission is detected above 5$\sigma$. We also fit the reconstructed
source surface brightness with an elliptical Gaussian model. We derive a median
value $r_{eff}\,\sim 1.77\,$kpc and a median Gaussian full width at half
maximum $\sim1.47\,$kpc. After correction for magnification, our sources have
intrinsic star formation rates SFR$\,\sim900-3500\,M_{\odot}yr^{-1}$, resulting
in a median star formation rate surface density
$\Sigma_{SFR}\sim132\,M_{\odot}$ yr$^{-1}$ kpc$^{-2}$ (or $\sim 218\,M_{\odot}$
yr$^{-1}$ kpc$^{-2}$ for the Gaussian fit). This is consistent with what
observed for other star forming galaxies at similar redshifts, and is
significantly below the Eddington limit for a radiation pressure regulated
starburst.
