2019ApJ...878...39L

The growth of solids from submicron to millimeter and centimeter sizes is the early step toward the formation of planets inside protoplanetary disks (PPDs). However, such processes and their potential impact on the later stages of solid growth are still poorly understood. In this work, we test the hypothesis that most disks contain at least one ringed structure with a relatively small radius. We have carried out a large family of 1D two-fluid (gas+dust) hydrodynamical simulations by evolving the gas and dust motion self-consistently while allowing dust size to evolve via coagulation and fragmentation. We investigate the joint effects of ringed structures and dust size growth on the overall submillimeter and millimeter flux and spectral index of PPDs. Ringed structures slow down the dust radial drift and speed up the dust growth. In particular, we find that those unresolved disks with a high fragmentation velocity (∼10 m s^–1) and a high dust surface density (∼10 g cm^–2 in the ring) can have millimeter spectral indices as low as ∼2.0, consistent with millimeter observations of faint disks in nearby star-forming regions. Furthermore, disks with more than one ringed structure can potentially reproduce brighter disks with spectral indices lower than ∼2.5. Future multiwavelength high-resolution observations of these low-spectral-index sources can be used to test the existence of the ringed structures in the unresolved disks and differentiate the effects of dust size growth from optical depth.