One Solution to the Mass Budget Problem for Planet Formation: Optically Thick Disks with Dust Scattering.

ALMA surveys have suggested that the dust in Class II disks may not be enough to explain the averaged solid mass in exoplanets. This suggestion stems from an assumption that the mm continuum emission is optically thin, which seems to be supported by recent DSHARP observations where the measured optical depths of spatially resolved disks are mostly less than one. However, we point out that dust scattering can considerably reduce the emission from an optically thick region. If that scattering is ignored, the optical depth will be considerably underestimated. An optically thick disk with scattering can be misidentified as an optically thin disk. Dust scattering in more inclined disks can reduce the intensity even further, making the disk look even fainter. The measured optical depth of ~0.6 in several DSHARP disks can be naturally explained by optically thick dust with an albedo of ~0.9 at 1.25 mm. Using the DSHARP opacity, this albedo corresponds to a dust population with the maximum grain size ($s_{max}$) of 0.1-1 mm. For optically thick scattering disks, the measured spectral index $\alpha$ can be either larger or smaller than 2 depending on if the dust albedo increases or decreases with wavelength. Using the DSHARP opacity, $\alpha<2$ corresponds to $s_{max}$ of 0.03-0.3 mm. Furthermore, when the disk changes from optically thick to optically thin, $\alpha$ should change suddenly. We describe how this optical thick scattering scenario could explain the observed scaling between submm continuum sizes and luminosities, and might help ease the tension between the dust size constraints from polarization and dust continuum measurements. We suggest that longer wavelength observations (e.g. ngVLA or SKA) are desired to probe the dust mass in disks. When the disk is optically thick, the measured 1) emssion reduction and 2) the spectral index provide stringent constraints on the dust properties.