Protoplanetary disk masses from CO isotopologues line emission

One of the methods for deriving disk masses relies on direct observations of the gas, whose bulk mass is in the outer cold ($T\lesssim30$K) regions. This zone can be well traced by rotational lines of less abundant CO isotopologues, that 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 ISM. This approach is however imprecise, because isotope selective processes are ignored. The aim of this work is an isotopologue selective treatment of CO isotopologues, in order to obtain a more accurate determination of disk masses. 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 (DALI, Bruderer et al. 2012; Bruderer 2013). The chemistry, thermal balance, line and continuum radiative transfer are all considered together with a chemical network that treats $^{13}$CO, C$^{18}$O, C$^{17}$O, isotopes of all included atoms, and molecules, as independent species. Isotope selective processes lead to regions in the disk where the isotopologues abundance ratios are considerably different from the elemental ratio. The results of this work show that considering CO isotopologue ratios as constants can lead to an underestimate of disk masses by up to almost two orders of magnitude if grains have grown to larger sizes. This may explain observed discrepancies in mass determinations from different tracers. The dependence of the various isotopologues emission on stellar and disk parameters is investigated. Including CO isotope selective processes is crucial to determine the gas mass of the disk accurately (through ALMA observations) and thus to provide the amount of gas which may eventually form planets or change the dynamics of forming planetary systems.