This expression assumes that nearly all the carbon, with its number abundance of 3 x 10~4 relative to hydrogen, is in the form of CO.

Despite the very large value of t10 under typical cloud conditions, the optical depth for higher transitions, tj+1jJ , falls quickly with increasing J. The reason is the decline in NJ, the column density in the J-level. To quantify the trend, we generalize equation (7.29), utilizing the result for quantum mechanical rotators that Aj+1j scales as (J + 1)/(2J + 3) vj

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