Comparison of 13CO Line and Far-Infrared Continuum Emission as a   Diagnostic of Dust and Molecular Gas Physical Conditions: I. Motivation and   Modeling
  Determining temperatures in molecular clouds from ratios of CO rotational lines or from ratios of continuum emission in different wavelength bands suffers from reduced temperature sensitivity in the high-temperature limit. In theory, the ratio of far-IR, submillimeter, or millimeter continuum to that of a 13CO (or C18O) rotational line can place reliable upper limits on the temperature of the dust and molecular gas. Consequently, far-infrared continuum data from the {\it COBE}/{\it DIRBE} instrument and Nagoya 4-m $\cOone$ spectral line data were used to plot 240$\um$/13CO J=1-0 intensity ratios against 140$\um$/240$\um$ dust color temperatures, allowing us to constrain the multiparsec-scale physical conditions in the Orion$ $A and B molecular clouds.   The best-fitting models to the Orion clouds consist of two components: a component near the surface of the clouds that is heated primarily by a very large-scale (i.e. $\sim 1 $kpc) interstellar radiation field and a component deeper within the clouds. The former has a fixed temperature and the latter has a range of temperatures that varies from one sightline to another. The models require a dust-gas temperature difference of 0$\pm 2 $K and suggest that 40-50% of the Orion clouds are in the form of dust and gas with temperatures between 3 and 10$ $K. These results have a number implications that are discussed in detail in later papers. These include stronger dust-gas thermal coupling and higher Galactic-scale molecular gas temperatures than are usually accepted, an improved explanation for the N(H$_2$)/I(CO) conversion factor, and ruling out one dust grain alignment mechanism. 
W. F. Wall