Characterizing young protostellar disks with the CALYPSO IRAM-PdBI survey: large Class 0 disks are rare

Understanding the formation mechanisms of protoplanetary disks and multiple systems, and their pristine properties, is a key question for modern astrophysics. The properties of the youngest disks, embedded in rotating infalling protostellar envelopes, have largely remained unconstrained up to now. Observing the youngest protostars with high enough spatial resolution to resolve and characterize the progenitors of protoplanetary disks can only be achieved using sub-mm and mm interferometric facilities. In the framework of the IRAM-PdBI CALYPSO survey, we have obtained sub-arcsecond observations of the dust continuum emission at 231 GHz and 94 GHz, for a sample of 16 solar-type Class 0 protostars. In an attempt to identify disk-like structures embedded at small scales in the protostellar envelopes, we model the dust continuum emission visibility profiles using both Plummer-like envelope models and envelope models including additional Gaussian disk-like components. Our analysis shows that while most protostars might contain a disk-like structure, 60 au. Including all available literature providing constraints on Class 0 disks at sub-arcsecond scales, most (> 72% in a sample of 25 protostars) Class 0 protostellar disks are small and emerge only at radii < 60 au. Our multiplicity fraction at scales 100-5000 au is in global agreement with the multiplicity properties of Class I protostars at similar scales. We confront our observational constraints on the disk size distribution in Class 0 protostars to the typical disk properties from protostellar formation models. Because they reduce the centrifugal radius, and produce a disk size distribution peaking at radii <100 au during the main accretion phase, magnetized models of rotating protostellar collapse are favored by our observations.