Compact disks CO isotopologues line fluxes

The simulated integrated continuum and CO isotopologue fluxes of the new grid of compact models are reported. Lupus disks that are not detected in ^13^CO emission and with faint or undetected 12CO emission are consistent with compact disk models. For disks with a limited radial extent, the emission of CO isotopologues is mostly optically thick and it scales with the surface area: i.e., it is fainter for smaller objects.

The fraction of compact disks is potentially between roughly 50% and 60% of the entire Lupus sample. Deeper observations of ^12^CO and ^13^CO at a moderate angular resolution will allow us to distinguish whether faint disks are intrinsically compact, or if they are extended but faint, without the need of resolving them. If the fainter end of the disk population observed by ALMA disk surveys is consistent with such objects being very compact, this will either create a tension with viscous spreading or require MHD winds or external processes to truncate the disks.