Protoplanetary disk masses from CO isotopologue line emission

Context. One of the methods for deriving disk masses relies on direct observations of the gas, whose bulk mass is in the outer cold regions (T less than or similar to 30 K). This zone can be well traced by rotational lines of less abundant CO isotopologues such as (CO)-C-13, (CO)-O-18, and (CO)-O-17, which probe the gas down to the midplane. The total CO gas mass is then obtained with the isotopologue ratios taken to be constant at the elemental isotope values found in the local interstellar medium. This approach is imprecise, however, because isotope-selective processes are ignored. Aims. The aim of this work is an isotopologue-selective treatment of CO isotopologues, to obtain a more accurate determination of disk masses. Methods. The isotope-selective photodissociation, the main process controlling the abundances of CO isotopologues in the CO-emissive layer, is properly treated for the first time in a full-disk model. The chemistry, thermal balance, line, and continuum radiative transfer are all considered together with a chemical network that treats (CO)-C-13, (CO)-O-18 and (CO)-O-17, isotopes of all included atoms and molecules as independent species. Results. Isotope selective processes lead to regions in the disk where the isotopologue abundance ratios of (CO)-O-18/(CO)-C-12, for example, are considerably different from the elemental O-18/O-16 ratio. The results of this work show that considering CO isotopologue ratios as constants can lead to underestimating disk masses by up to an order of magnitude or more if grains have grown to larger sizes. This may explain observed discrepancies in mass determinations from different tracers. The dependence of the various isotopologue emission on stellar and disk parameters is investigated to set the framework for the analysis of ALMA data. Conclusions. Including CO isotope selective processes is crucial for determining the gas mass of the disk accurately (through ALMA observations) and thus for providing the amount of gas that may eventually form planets or change the dynamics of forming planetary systems.