Source structure and molecular gas properties from high-resolution CO
  imaging of SPT-selected dusty star-forming galaxies
  We present Atacama Large Millimeter/submillimeter Array (ALMA) observations
of high-J CO lines ($J_\mathrm{up}=6$, 7, 8) and associated dust continuum
towards five strongly lensed, dusty, star-forming galaxies (DSFGs) at redshift
$z = 2.7$-5.7. These galaxies, discovered in the South Pole Telescope survey,
are observed at $0.2''$-$0.4''$ resolution with ALMA. Our high-resolution
imaging coupled with the lensing magnification provides a measurement of the
structure and kinematics of molecular gas in the background galaxies with
spatial resolutions down to kiloparsec scales. We derive visibility-based lens
models for each galaxy, accurately reproducing observations of four of the
galaxies. Of these four targets, three show clear velocity gradients, of which
two are likely rotating disks. We find that the reconstructed region of CO
emission is less concentrated than the region emitting dust continuum even for
the moderate-excitation CO lines, similar to what has been seen in the
literature for lower-excitation transitions. We find that the lensing
magnification of a given source can vary by 20-50% across the line profile,
between the continuum and line, and between different CO transitions. We apply
Large Velocity Gradient (LVG) modeling using apparent and intrinsic line ratios
between lower-J and high-J CO lines. Ignoring these magnification variations
can bias the estimate of physical properties of interstellar medium of the
galaxies. The magnitude of the bias varies from galaxy to galaxy and is not
necessarily predictable without high resolution observations.
