Gas versus dust sizes of protoplanetary discs: Effects of dust evolution

Context. The extent of the gas in protoplanetary discs is observed to be universally larger than the extent of the dust. This is often attributed to radial drift and grain growth of the millimetre grains, but line optical depth produces a similar observational signature. Aims. We investigate in which parts of the disc structure parameter space dust evolution and line optical depth are the dominant drivers of the observed gas and dust size difference. Methods. Using the thermochemical model DALI with dust evolution included we ran a grid of models aimed at reproducing the observed gas and dust size dichotomy. Results. The relation between Rdust and dust evolution is non-monotonic and depends on the disc structure. The quantity Rgas is directly related to the radius where the CO column density drops below 1015 cm-2 and CO becomes photodissociated; Rgas is not affected by dust evolution but scales with the total CO content of the disc. While these cases are rare in current observations, Rgas/Rdust > 4 is a clear sign of dust evolution and radial drift in discs. For discs with a smaller Rgas/Rdust, identifying dust evolution from Rgas/Rdust requires modelling the disc structure including the total CO content. To minimize the uncertainties due to observational factors requires FWHMbeam < 1× the characteristic radius and a peak S/N > 10 on the 12CO emission moment zero map. For the dust outer radius to enclose most of the disc mass, it should be defined using a high fraction (90-95%) of the total flux. For the gas, any radius enclosing >60% of the 12CO flux contains most of the disc mass. Conclusions. To distinguish radial drift and grain growth from line optical depth effects based on size ratios requires discs to be observed at high enough angular resolution and the disc structure should to be modelled to account for the total CO content of the disc.