ALMA Imaging and Gravitational Lens Models of South Pole
  Telescope-Selected Dusty, Star-Forming Galaxies at High Redshifts
  The South Pole Telescope has discovered one hundred gravitationally lensed,
high-redshift, dusty, star-forming galaxies (DSFGs). We present 0.5" resolution
870um Atacama Large Millimeter/submillimeter Array imaging of a sample of 47
DSFGs spanning z=1.9-5.7, and construct gravitational lens models of these
sources. Our visibility-based lens modeling incorporates several sources of
residual interferometric calibration uncertainty, allowing us to properly
account for noise in the observations. At least 70% of the sources are strongly
lensed by foreground galaxies (mu_870um > 2), with a median magnification
mu_870um = 6.3, extending to mu_870um > 30. We compare the intrinsic size
distribution of the strongly lensed sources to a similar number of unlensed
DSFGs and find no significant differences in spite of a bias between the
magnification and intrinsic source size. This may indicate that the true size
distribution of DSFGs is relatively narrow. We use the source sizes to
constrain the wavelength at which the dust optical depth is unity and find this
wavelength to be correlated with the dust temperature. This correlation leads
to discrepancies in dust mass estimates of a factor of 2 compared to estimates
using a single value for this wavelength. We investigate the relationship
between the [CII] line and the far-infrared luminosity and find that the same
correlation between the [CII]L_FIR ratio and Sigma_FIR found for low-redshift
star-forming galaxies applies to high-redshift galaxies and extends at least
two orders of magnitude higher in Sigma_FIR. This lends further credence to the
claim that the compactness of the IR-emitting region is the controlling
parameter in establishing the "[CII] deficit."
