1995A&A...300..890P

With a three dimensional Monte Carlo code, we have investigated how the clumpy structure of interstellar clouds would affect the excitation conditions of CO molecules and the resulting line profiles. The excitation conditions are shown to be sensitive to the volume filling factor f. For fixed n(H₂) the excitation temperature becomes generally higher in the cloud having large values of f than in the ones of small f. In completely filled cloud (f=1), the excitation temperature drops sharply near the cloud boundary, which would accompany self-absorption dips in the optically thick ¹²CO lines. As f approaches zero, the excitation condition becomes constant from the center to boundary. For the optically thin ¹³CO transitions, the excitation temperature attains uniform distribution at higher values of f than it does for the ¹²CO transitions. Macro-turbulence also tends to make the excitation conditions uniform throughout the cloud. For the optically thin transitions the radiation from adjacent clumps becomes unimportant, even at moderately low degree of clumpiness (i.e., f in order of 10^–1); while for the optically thick transitions, it does so only at f≲10^–2. When the total turbulence dispersion is kept the same for both models of turbulence, the macro-turbulence yields higher excitation temperatures than the micro-turbulence does. In the cloud with f≃0.1, the level population becomes thermalized at n(H₂)>2x10³cm^–3; whereas with f≃0.01, it does at much higher densities, n(H₂)>10⁴cm^–3. Higher degree of clumpiness (f->0), less trapping of radiation brought by small optical depth, and less frequency-coupling among the clumps due to macro-turbulence all make the excitation conditions be uniform throughout the clumpy cloud. Under the micro-turbulence condition, the synthesized ¹²CO lines exhibit the flat-top features only, without being accompanied by the self-absorption dips. For each of the J=1->0 and 2->1 transitions, the synthesized profiles from the macro-turbulence model put the ¹²CO-to-¹³CO ratios of the peak brightness temperature and of the line width right in their observed ranges. Clumpiness and macro-turbulence are the cloud attributes that are consistent with the observed profiles of CO lines from cold, dark, quiescent, molecular clouds.