In this paper we have presented model computations of low-J 12CO/13CO/C18O emission from spherical clouds exposed to isotropic FUV radiation fields. The principal results of our investigations can be summarized as follows:
1. The 12CO 21/10 line ratio is insensitive to the cloud gas density and column density . This line ratio varies from values of 0.6 to 1.4 for low large clouds to high small clouds. The behavior of the 13CO 21/10 line ratio is similar, with values ranging from 0.6 to 2.4.
2. Similarly, the 12CO 32/21 line ratio ranges from 0.6 to 1.1, and the 13CO 32/21 ratio ranges from 0.5 to 1.4.
3. The isotopic ratio of the 12CO 21 and the 13CO 21 line ranges from 1.8 for low large clouds to 7.0 for high small clouds. The 12CO/12C18O 21 line ratio varies from 3 to .
4. For a fixed FUV field strength the 12CO 21 line center brightness temperature (averaged over the cloud surface) ranges from 1.1 K for a model with and to 53 K for a model with and . The 13CO 21 line intensities range from 0.5 K to 24 K. For small clouds C18O is nearly fully photodissociated, and reaches a maximum value of K when and are large.
5. For clouds with the absolute and relative CO line intensities are insensitive to in the range 100 to .
6. Taken together, these statements show that the low-J 12CO/13CO line ratios in particular (but also the C18O line ratios) are rather insensitive to the physical parameters of the UV-embedded clumps (density, column density, and UV-field strength). This implies on one hand, that the low-J isotopomeric CO line ratios are not useful diagnostics of these conditions. On the other hand, it is very satisfying that the models reproduce the narrow range of observed line ratios over a large range of realistic clump parameters. Thus, the scenario of clumpy molecular clouds, penetrated by UV-radiation through the diffuse interclump medium, provides a natural explanation for the narrow range of observed low-J CO line ratios, despite the large variation of physical paramters of those clumps within a molecular cloud.
Molecular cloud geometry is, of course, much more complex than spherical. The observed, fractal distribution of the observed line emission can, however, be modelled as a superposition of the emission from many clumps with a power law mass and size distribution over a large range in clump masses (Stutzki et al. 1998). Although superimposing the emission from many clumps will certainly change the resulting line ratios for the clump ensemble, condidering different beam filling factors and optical depth effects, it will keep the line ratios of the clump ensemble near the narrow range of line ratios found for the single clumps. The variation in the observed line ratios between different sources and regions within a source would then, in addition to systematic gradients e.g. in the average UV-field, result from the difference in the distribution of clumps along the particular sources or lines-of-sight: high total column density lines-of-sight will be dominated by a few, large and massive clumps, low column density lines-of-sight see mainly many small, unresolved clumps.
In a more detailed model clumps of different masses and sizes, embedded in a lower density interclump medium, will be illuminated by a UV field decreasing systematically from outside into the cloud. Such a model and its application to interpreting the emission distribution observed for particular sources will the topic of subsequent papers.
© European Southern Observatory (ESO) 2000
Online publication: June 8, 2000