Spatially Resoved 12CO(2-1)/12CO(1-0) in the Starburst Galaxy NGC 253:
  Assessing Optical Depth to Constrain the Molecular Mass Outflow Rate
  We present Atacama Large Millimeter/submillimeter Array (ALMA) observations
of 12CO(1-0) and 12CO(2-1) in the central 40" (680 pc) of the nuclear starburst
galaxy NGC 253, including its molecular outflow. We measure the ratio of
brightness temperature for CO(2-1)/CO(1-0), r_21, in the central starburst and
outflow-related features. We discuss how r_21 can be used to constrain the
optical depth of the CO emission, which impacts the inferred mass of the
outflow and consequently the molecular mass outflow rate. We find r_21 less
than or equal to 1 throughout, consistent with a majority of the CO emission
being optically-thick in the outflow, as it is in the starburst. This suggests
that the molecular outflow mass is 3-6 times larger than the lower limit
reported for optically thin CO emission from warm molecular gas. The implied
molecular mass outflow rate is 25-50 solar masses per year, assuming that
conversion factor for the outflowing gas is similar to our best estimates for
the bulk of the starburst. This is a factor of 9-19 times larger than the star
formation rate in NGC 253. We see tentative evidence for an extended, diffuse
CO(2-1) component.
