Compact disks: An explanation to faint CO emission in Lupus disks

Context. ALMA disk surveys have shown that a large fraction of observed protoplanetary disks in nearby star-forming regions (SFRs) are fainter than expected in CO isotopolog emission. Disks not detected in 13CO line emission are also faint and often unresolved in the continuum emission at an angular resolution of around 0.2 arcsec. Aims. Focusing on the Lupus SFR, the aim of this work is to investigate whether this population comprises radially extended and low-mass disks - as commonly assumed so far - or intrinsically radially compact disks, an interpretation that we propose in this paper. The latter scenario was already proposed for individual sources or small samples of disks, while this work targets a large population of disks in a single young SFR for which statistical arguments can be made. Methods. We ran a new grid of physical-chemical models of compact disks with the physical-chemical code DALI in order to cover a region of the parameter space that has not been explored before with this code. We compared these models with 12CO and 13CO ALMA observations of faint disks in the Lupus SFR, and report the simulated integrated continuum and CO isotopolog fluxes of the new grid of compact models. Results. Lupus disks that are not detected in 13CO emission and have faint or undetected 12CO emission are consistent with compact disk models. For disks with a limited radial extent, the emission of CO isotopologs is mostly optically thick and scales with the surface area, that is, 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 12CO and 13CO at a moderate angular resolution will allow us to distinguish whether faint disks are intrinsically compact or extended but faint, without the need to resolve 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.