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The reader may verify that ACO, when multiplied by the cloud volume, yields a luminosity which matches that implied by equation (7.34) to within a factor of order unity.

In summary, the volumetric cooling rate from a cloud with given NH, Tg, and Ay may be found by first estimating J* from equation (7.32). We then obtain the radiative emission from the dominant J* + 1 ^ J* line by using equation (7.35). For a more accurate assessment of ACO, the total CO cooling, one should add the emission from several optically thick lines, i. e., those with J < J*. Here one needs to specify the cloud surface area. Figure 7.9 plots, in addition to J*, ACO as a function of gas temperature for the same cloud parameters. Notice how the cooling rate increases exponentially with Tg, as radiative trapping excites more molecules into the critical J -level.

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