2014A&A...564A..95P

Most Class II sources (of nearby star-forming regions) are surrounded by disks with weak millimeter continuum emission. These ``faint'' disks may hold clues to the disk dissipation mechanism. However, the physical properties of protoplanetary disks have been directly constrained by imaging only the brightest sources. We attempt to determine the characteristics of such faint disks around classical T Tauri stars and to explore the link between disk faintness and the proposed disk dispersal mechanisms (accretion, viscous spreading, photo-evaporation, planetary system formation). We performed high angular resolution (0.3'') imaging of a small sample of disks (9 sources) with low 1.3mm continuum flux (mostly <30mJy) with the IRAM Plateau de Bure interferometer and simultaneously searched for <sup>13</sup>CO (or CO) J=2-1 line emission. Using a simple parametric disk model, we determined characteristic sizes for the disks in dust and gas, and we constrained surface densities in the central 50AU. All disks are much smaller than the bright disks imaged so far, both in continuum and <sup>13</sup>CO lines (5 detections). In continuum, half of the disks are very small, with characteristic radii less than 10AU, but still have high surface density values. Small sizes appear to be the main cause of the low disk luminosity. Direct evidence for grain growth is found for the three disks that are sufficiently resolved. Low continuum opacity is attested in only two systems, but we cannot firmly distinguish between a low gas surface density and a lower dust emissivity resulting from grain growth. Finally, we report a tentative discovery of a ∼20AU radius cavity in DS Tau, which with the (unresolved) ``transition'' disk of CX Tau, brings the proportion of ``transitional'' disks to a similar value to that of brighter sources. The existence of cavities cannot by itself explain their observed low mm flux. This study highlights a category of very compact dust disks that still exhibit high surface densities, which may represent up to 25% of the whole disk population. While its origin is unclear with the current data alone, it may be related to the compact planetary systems found by the Kepler mission.