The 12CO/13CO ratio in turbulent molecular clouds

The (CO)-C-13 molecule is often used as a column density tracer in regions where the (CO)-C-12 emission saturates. The (CO)-C-13 column density is then related to that of (CO)-C-12 by a uniform isotopic ratio. A similar approximation is frequently used when deriving (CO)-C-13 emission maps from numerical simulations of molecular clouds. To test this assumption, we calculate the (CO)-C-12/(CO)-C-13 ratio self-consistently, taking the isotope-selective photodissociation and the chemical fractionation of CO into account. We model the coupled chemical, thermal and dynamical evolution and the emergent (CO)-C-13 emission of isolated, starless molecular clouds in various environments. Selective photodissociation has a minimal effect on the ratio, while the chemical fractionation causes a factor of 2-3 decrease at intermediate cloud depths. The variation correlates with both the (CO)-C-12 and the (CO)-C-13 column densities. Neglecting the depth dependence results in <= 60 per cent error in (CO)-C-12 column densities derived from (CO)-C-13. The same assumption causes <= 50 per cent disparity in the (CO)-C-13 emission derived from simulated clouds. We show that the discrepancies can be corrected by a fitting formula. The formula is consistent with millimetre-wavelength isotopic ratio measurements of densemolecular clouds, but underestimates the ratios from the ultraviolet absorption of diffuse regions.