1999ApJ...513..275B

We present a simple, semianalytical approach to compute the line emission of C⁺, C⁰, and CO in photodissociation regions of varying metallicity that depends on very few parameters and naturally incorporates the clumpiness of the interstellar medium into the calculations. We use it to study the dependence of the I_[CII]/I_CO and I_[CI]/I_CO line ratios on the metallicity. We show how to modify it to include the effects of density and radiation field, and we have compared it with observational data. We find that the model explains the observed trend of enhanced [C II]/CO line ratio with decreasing metallicity as the natural result of the augmented fraction of photodissociated gas in a clump. We show that enhanced [C II]/CO ratios can be produced by lowering the upper limit of the clump size distribution, as may happen in 30 Doradus. We also find that the available data favor a [C I]/CO intensity ratio essentially independent of metallicity, albeit the paucity of observations does not exclude other possibilities. This is difficult to understand if most of the C⁰ is produced by UV photons as is the case with C⁺. Finally, we study the prediction of the model for the trend of the X_CO factor with metallicity. Comparison with previous observational studies yields good agreement.