The 12CO/13CO ratio in turbulent molecular clouds

The ¹³CO molecule is often used as a column density tracer in regions where the ¹²CO emission saturates. The ¹³CO column density is then related to that of ¹²CO by a uniform isotopic ratio. A similar approximation is frequently used when deriving ¹³CO emission maps from numerical simulations of molecular clouds. To test this assumption, we calculate the ¹²CO/¹³CO 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 ¹³CO 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 ¹²CO and the ¹³CO column densities. Neglecting the depth dependence results in ≤60 per cent error in ¹²CO column densities derived from ¹³CO. The same assumption causes ≤50 per cent disparity in the ¹³CO 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 dense molecular clouds, but underestimates the ratios from the ultraviolet absorption of diffuse regions.