The effect of local optically thick regions in the long-wave emission of   young circumstellar disks
  Multi-wavelength observations of protoplanetary disks in the sub-millimeter continuum have measured spectral indices values which are significantly lower than what is found in the diffuse interstellar medium. Under the assumption that mm-wave emission of disks is mostly optically thin, these data have been generally interpreted as evidence for the presence of mm/cm-sized pebbles in the disk outer regions. In this work we investigate the effect of possible local optically thick regions on the mm-wave emission of protoplanetary disks without mm/cm-sized grains. A significant local increase of the optical depth in the disk can be caused by the concentration of solid particles, as predicted to result from a variety of proposed physical mechanisms. We calculate the filling factors and implied overdensities these optically thick regions would need to significantly affect the millimeter fluxes of disks, and we discuss their plausibility. We find that optically thick regions characterized by relatively small filling factors can reproduce the mm-data of young disks without requesting emission from mm/cm-sized pebbles. However, these optically thick regions require dust overdensities much larger than what predicted by any of the physical processes proposed in the literature to drive the concentration of solids. We find that only for the most massive disks it is possible and plausible to imagine that the presence of optically thick regions in the disk is responsible for the low measured values of the mm spectral index. For the majority of the disk population, optically thin emission from a population of large mm-sized grains remains the most plausible explanation. The results of this analysis further strengthen the scenario for which the measured low spectral indices of protoplanetary disks at mm wavelengths are due to the presence of large mm/cm-sized pebbles in the disk outer regions. 
L. Ricci, F. Trotta, L. Testi, A. Natta, A. Isella, D. J. Wilner
astro-ph.GA astro-ph.EP