2023ApJ...954...41T

It remains unclear what mechanism is driving the evolution of protoplanetary disks. Direct detection of the main candidates, either turbulence driven by magnetorotational instabilities or magnetohydrodynamical disk winds, has proven difficult, leaving the time evolution of the disk size as one of the most promising observables able to differentiate between these two mechanisms. But to do so successfully, we need to understand what the observed gas disk size actually traces. We studied the relation between R_CO,90%, the radius that encloses 90% of the ¹²CO flux, and R_c, the radius that encodes the physical disk size, in order to provide simple prescriptions for conversions between these two sizes. For an extensive grid of thermochemical models, we calculate R_CO,90% from synthetic observations and relate properties measured at this radius, such as the gas column density, to bulk disk properties, such as R_c and the disk mass M_disk. We found an empirical correlation between the gas column density at R_CO,90% and disk mass: ${N}_{\mathrm{gas}}{({R}_{\mathrm{CO},90 \% })\approx 3.73\,\times \,{10}^{21}({M}_{\mathrm{disk}}/{M}_{\odot })}^{0.34}\ {\mathrm{cm}}^{-2}$. Using this correlation we derive an analytical prescription of R_CO,90% that only depends on R_c and M_disk. We derive R_c for disks in Lupus, Upper Sco, Taurus, and the DSHARP sample, finding that disks in the older Upper Sco region are significantly smaller (〈R_c〉 = 4.8 au) than disks in the younger Lupus and Taurus regions (〈R_c〉 = 19.8 and 20.9 au, respectively). This temporal decrease in R_c goes against predictions of both viscous and wind-driven evolution, but could be a sign of significant external photoevaporation truncating disks in Upper Sco.