Lupus disks with faint CO isotopologues: low gas/dust or high carbon depletion?

Context. An era has started in which gas and dust can be observed independently in protoplanetary disks, thanks to the recent surveys with the Atacama Large Millimeter/sub-millimeter Array (ALMA). The first near-complete high-resolution disk survey in both dust and gas in a single star-forming region has been carried out in Lupus, finding surprisingly low gas-to-dust ratios. Aims. The goal of this work is to fully exploit CO isotopologue observations in Lupus, comparing them with physical-chemical model results, in order to obtain gas masses for a large number of disks and compare gas and dust properties. Methods. We have employed the grid of physical-chemical models presented previously to analyze continuum and CO isotopologue ((CO)-C-13 J = 3-2 and (CO)-O-18 J = 3-2) observations of Lupus disks, including isotope-selective processes and freeze-out. We also employed the ALMA (CO)-C-13-only detections to calculate disk gas masses for a total of 34 sources, which expands the sample of 10 disks reported earlier, where (CO)-O-18 was also detected. Results. We confirm that overall gas-masses are very low, often lower than 1M(J), when volatile carbon is not depleted. Accordingly, global gas-to-dust ratios are much lower than the expected interstellar-medium value of 100, which is predominantly between 1 and 10. Low CO-based gas masses and gas-to-dust ratios may indicate rapid loss of gas, or alternatively chemical evolution, for example, through sequestering of carbon from CO to more complex molecules, or carbon locked up in larger bodies. Conclusions. Current ALMA observations of (CO)-C-13 and continuum emission cannot distinguish between these two hypotheses. We have simulated both scenarios, but chemical model results do not allow us to rule out one of the two, pointing to the need to calibrate CO-based masses with other tracers. Assuming that all Lupus disks have evolved mainly as a result of viscous processes over the past few Myr, the previously observed correlation between the current mass accretion rate and dust mass implies a constant gas-to-dust ratio, which is close to 100 based on the observed M-disk/M-acc ratio. This in turn points to a scenario in which carbon depletion is responsible for the low luminosities of the CO isotopologue line.