  Despite intensive studies of protoplanetary disks, there is still no reliable
way to determine their total 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. The goal of this work is to use less
abundant CO isotopologues, whose detection 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. CO isotope-selective photodissociation has been implemented in the
physical-chemical code DALI and 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
species. Both disk structure and stellar parameters have been investigated.
Total fluxes have been ray-traced for different CO isotopologues and for
various transitions for different inclinations. 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, i.e. the disk's radial extent and inclination.
Comparison with parametric models shows differences at the factor of a few
level, 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/dust ratios are investigated as well, and
comparison with other tracers is made. Disk masses can be determined within a
factor of a few by comparing CO isotopologue lines observations with the
simulated line fluxes, modulo the uncertainties in the volatile elemental
abundances.
