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The growth of solids from sub-micron to millimeter and centimeter sizes isthe early step toward the formation of planets inside protoplanetary disks(PPDs). However, such processes and their potential impact on the later stagesof solid growth are still poorly understood. In this work, we test thehypothesis that most disks contain at least one ringed structure with arelative small radius. We have carried out a large family of 1D two-fluid(gas+dust) hydrodynamical simulations by evolving the gas and dust motionself-consistently while allowing dust size to evolve via coagulation andfragmentation. We investigate the joint effects of ringed structures and dustsize growth on the overall sub-millimeter and millimeter (mm) flux and spectralindex of PPDs. Ringed structures slow down the dust radial drift and speed upthe dust growth. In particular, we find that those unresolved disks with a highfragmentation velocity ($\sim10\ {\rm m~s^{-1}}$) and a high dust surfacedensity ($\sim10\ {\rm g\ cm^{-2}}$ in the ring) can have mm spectral indicesas low as $\sim2.0$, consistent with mm observations of faint disks in nearbystar forming regions. Furthermore, disks with more than one ringed structurecan potentially reproduce brighter disks with spectral indices lower than$\sim2.5$. Future multi-wavelength high-resolution observations of these lowspectral index sources can be used to test the existence of the ringedstructures in the unresolved disks and differentiate the effects of dust sizegrowth from optical depth.

Effects of Ringed Structures and Dust Size Growth on Millimeter Observations of Protoplanetary Disks