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

Atacama Large Millimeter Array (ALMA) surveys have suggested that the dust in Class II disks may not be enough to explain the averaged solid mass in exoplanets, under the assumption that the mm disk continuum emission is optically thin. This optically thin assumption seems to be supported by recent Disk Substructures at High Angular Resolution Project (DSHARP) observations where the measured optical depths 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, 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 similar to 0.6 in several DSHARP disks can be naturally explained by optically thick dust with an albedo of similar to 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 whether the dust albedo increases or decreases with wavelength. We describe how this optically 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 a significant amount of disk mass can be hidden from ALMA observations and longer wavelength observations (e.g., Very Large Array or Square Kilometre Array) are desired to probe the dust mass in disks.