Far-infrared continuum data from the COBE / DIRBE instrument were combined with Nagoya 4-m { } ^ { 13 } \kern - 0.8 ptCO J = 1 \rightarrow 0 spectral line data to infer the multiparsec-scale physical conditions in the Orion A and B molecular clouds , using 140 \mu m /240 \mu m dust color temperatures and the 240 \mu m / { } ^ { 13 } \kern - 0.8 ptCO J = 1 \rightarrow 0 intensity ratios .
In theory , the ratio of far-IR , submillimeter , or millimeter continuum to that of a { } ^ { 13 } \kern - 0.8 ptCO ( or C { } ^ { 18 } \kern - 0.8 ptO ) rotational line can place reliable upper limits on the temperature of the dust and molecular gas on multi-parsec scales ; on such scales , both the line and continuum emission are optically thin , resulting in a continuum-to-line ratio that suffers no loss of temperature sensitivity in the high-temperature limit as occurs for ratios of CO rotational lines or ratios of continuum emission in different wavelength bands .

Two-component models fit the Orion data best , where one has a fixed-temperature and the other has a spatially varying temperature .
The former represents gas and dust towards the surface of the clouds that are heated primarily by a very large-scale ( i.e . \sim 1 kpc ) interstellar radiation field .
The latter represents gas and dust at greater depths into the clouds and are shielded from this interstellar radiation field and heated by local stars .
The inferred physical conditions are consistent with those determined from previously observed maps of { } ^ { 12 } \kern - 0.8 ptCO J = 1 \rightarrow 0 and J = 2 \rightarrow 1 that cover the entire Orion A and B molecular clouds .
The models require that the dust-gas temperature difference is 0 \pm 2 K. If this surprising result applies to much of the Galactic ISM , except in unusual regions such as the Galactic Center , then there are a number implications .
These include dust-gas thermal coupling that is commonly factors of 5 to 10 stronger than previously believed , Galactic-scale molecular gas temperatures closer to 20 K than to 10 K , an improved explanation for the N ( H _ { 2 } ) /I ( CO ) conversion factor ( a full discussion of this is deferred to a later paper ) , and ruling out at least one dust grain alignment mechanism .
The simplest interpretation of the models suggests that about 40–50 % of the Orion clouds are in the form of cold ( i.e . \sim 3 -10 K ) dust and gas , although alternative explanations are not ruled out .
These alternatives include the contribution to the 240 \mu m continuum by dust associated with atomic hydrogen and reduced { } ^ { 13 } \kern - 0.8 ptCO abundance towards the clouds ’ edges .
Even considering these alternatives , it is still likely that cold material with temperatures of \sim 7 -10 K still exists .
If this cold gas and dust are common in the Galaxy , then mass estimates of the Galactic ISM must be revised upwards by up to 60 % .

The feasibility of submillimeter or millimeter continuum to { } ^ { 13 } \kern - 0.8 ptCO line ratios constraining estimates of dust and molecular gas temperatures was tested .
The model fits allowed the simulation of the necessary millimeter-continuum and { } ^ { 13 } \kern - 0.8 ptCO J = 1 \rightarrow 0 maps used in the test .
In certain “ hot spots ” — that have continuum-to-line ratios above some threshold value — the millimeter continuum to { } ^ { 13 } \kern - 0.8 ptCO ratio can estimate the dust temperature to within a factor of 2 over large ranges of physical conditions .
Nevertheless , supplemental observations of the { } ^ { 13 } \kern - 0.8 ptCO J = 2 \rightarrow 1 line or of shorter wavelength continuum are advisable in placing lower limits on the estimated temperature .
Even without such supplemental observations , this test shows that the continuum-to-line ratio places reliable upper limits on the temperature .