Carbon Monoxide and Dust Column Densities: The Dust-to-Gas Ratio and Structure of Three Giant Molecular Cloud Cores

We have observed emission in the three lowest rotational transitions of the optically thin species C¹⁸O and the dust continuum emission at three millimeter/submillimeter wavelengths. By employing the proper combination of the intensities of the three lowest rotational transitions of C¹⁸O, we can obtain the total molecular column density, with relatively little sensitivity to density and temperature variations along the line of sight. We use the line and continuum data to determine column densities of the dust and gas across three giant molecular cloud cores. We find that two of the three sources, M17 and Cepheus A, have the same gas column density-to-dust optical depth ratio, given by log [N(C¹⁸O)/τ(790 μm)] = 18.8. In the third source, the Orion molecular cloud, the gas-to-dust ratio is typically a factor of 3 lower than in the other two sources. The gas-to-dust ratio shows only a small (factor ≤ 3) variation across the region of M17 that we have mapped and a comparable reduction at the center of Cepheus A relative to the cloud edge.

We have good evidence for the correlation of the continuum emission in different bands for the Orion molecular cloud and find the frequency dependence of the optical depth in the densest regions near the embedded sources to be given by τ ∝ ν^1.9. For positions away from the embedded sources, there is a larger scatter in the data points, with a suggestion that the frequency dependence is steeper, such that τ ∝ ν^2.4. This may be an indication of a change in the grain properties between less dense and very dense regions and is consistent with the results of grain growth. Using standard values for the fractional abundance of C¹⁸O relative to H₂, the mean densities of the cloud cores are 3-5 × 10⁴ cm^-3 . These regions appear to be close to virial equilibrium. The dense gas [revealed by multiple transition studies of tracers such as CS and HC₃N to have n(H₂) ≃ 10⁶ cm^-3] has a volume filling factor of a few percent. Assuming a fractional abundance of C¹⁸O equal to 1.7 × 10^-7, we find that the 790 μm dust optical depth to mass column density ratio for M17 and Cepheus A is 0.0062 cm² g^-1, while the average value for the Orion molecular cloud is a factor of 3 larger.