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Multi-wavelength observations of protoplanetary disks in the sub-millimetercontinuum have measured spectral indices values which are significantly lowerthan what is found in the diffuse interstellar medium. Under the assumptionthat mm-wave emission of disks is mostly optically thin, these data have beengenerally interpreted as evidence for the presence of mm/cm-sized pebbles inthe disk outer regions. In this work we investigate the effect of possiblelocal optically thick regions on the mm-wave emission of protoplanetary diskswithout mm/cm-sized grains. A significant local increase of the optical depthin the disk can be caused by the concentration of solid particles, as predictedto result from a variety of proposed physical mechanisms. We calculate thefilling factors and implied overdensities these optically thick regions wouldneed to significantly affect the millimeter fluxes of disks, and we discusstheir plausibility. We find that optically thick regions characterized byrelatively small filling factors can reproduce the mm-data of young diskswithout requesting emission from mm/cm-sized pebbles. However, these opticallythick regions require dust overdensities much larger than what predicted by anyof the physical processes proposed in the literature to drive the concentrationof solids. We find that only for the most massive disks it is possible andplausible to imagine that the presence of optically thick regions in the diskis responsible for the low measured values of the mm spectral index. For themajority of the disk population, optically thin emission from a population oflarge mm-sized grains remains the most plausible explanation. The results ofthis analysis further strengthen the scenario for which the measured lowspectral indices of protoplanetary disks at mm wavelengths are due to thepresence of large mm/cm-sized pebbles in the disk outer regions.

The effect of local optically thick regions in the long-wave emission of young circumstellar disks