2016A&A...594A..85M

Context. Despite intensive studies of protoplanetary disks, there is still no reliable way to determine their total (gast+dust) mass and their surface density distribution, quantities that are crucial for describing both the structure and the evolution of disks up to the formation of planets.
Aims. The goal of this work is to use less-abundant CO isotopologues, such as ¹³CO, C¹⁸O and C¹⁷O, detection of which is routine for ALMA, to infer the gas mass of disks. Isotope-selective effects need to be taken into account in the analysis, because they can significantly modify CO isotopologues' line intensities.
Methods. CO isotope-selective photodissociation has been implemented in the physical-chemical code DALI (Dust And LInes) and more than 800 disk models have been run for a range of disk and stellar parameters. Dust and gas temperature structures have been computed self-consistently, together with a chemical calculation of the main atomic and molecular species. Both disk structure and stellar parameters have been investigated by varying the parameters in the grid of models. Total fluxes have been ray-traced for different CO isotopologues and for various low J-transitions for different inclinations.
Results. A combination of ¹³CO and C¹⁸O total intensities allows inference of the total disk mass, although with non-negligible uncertainties. These can be overcome by employing spatially resolved observations, that is the disk's radial extent and inclination. Comparison with parametric models shows differences at the level of a factor of a few, especially for extremely low and high disk masses. Finally, total line intensities for different CO isotopologue and for various low-J transitions are provided and are fitted to simple formulae. The effects of a lower gas-phase carbon abundance and different gas-to-dust ratios are investigated as well, and comparison with other tracers is made.
Conclusions. Disk masses can be determined within a factor of a few by comparing CO isotopologue lines observations with the simulated line fluxes provided in this paper, modulo the uncertainties in the volatile elemental abundances.