Mid-J CO Shock Tracing Observations of Infrared Dark Clouds III: SLED
  fitting
  Giant molecular clouds contain supersonic turbulence that can locally heat
small fractions of gas to over 100 K. We run shock models for low-velocity,
C-type shocks propagating into gas with densities between 10^3 and 10^5 cm^(-3)
and find that CO lines are the most important cooling lines. Comparison to
photodissociation region (PDR) models indicates that mid-J CO lines (J = 8-7
and higher) should be dominated by emission from shocked gas. In Papers I and
II we presented CO J = 3-2, 8-7, and 9-8 observations toward four primarily
quiescent clumps within infrared dark clouds. Here we fit PDR models to the
combined spectral line energy distributions and show that the PDR models that
best fit the low-J CO emission underpredict the mid-J CO emission by orders of
magnitude, strongly hinting at a hot gas component within these clumps. The
low-J CO data clearly show that the integrated intensities of both the CO J =
8-7 and 9-8 lines are anomalously high, such that the line ratio can be used to
characterize the hot gas component. Shock models are reasonably consistent with
the observed mid-J CO emission, with models with densities near 10^(4.5)
cm^(-3) providing the best agreement. Where this mid-J CO is detected, the mean
volume filling factor of the hot gas is 0.1%. Much of the observed mid-J CO
emission, however, is also associated with known protostars and may be due to
protostellar feedback.
