Interpreting ALMA Multi-wavelength Continuum Observations of PDS 70 c: An Optically Thick Dust Ring in the Circumplanetary Disk

Giant planets form small gas disks, called circumplanetary disks (CPDs), during gas accretion. The CPD of PDS 70 c has been detected by ALMA in (sub)millimeter continuum emission, which is interpreted as thermal emission from dust in the CPD. The resulting spectral index suggests that the disk is optically thick over a wide range of wavelengths. However, this is inconsistent with previous CPD dust models, which predict that the disk is optically thin because of radial dust drift. Here, we present a new interpretation of the multi-wavelength observations: the CPD hosts an optically thick dust ring, whose existence has been discussed in the context of satellite formation. We demonstrate that a dust-ring model that incorporates gas accretion, dust evolution, and dust thermal emission, is consistent with the observations under reasonable conditions, whereas a conventional ring-less model requires more stringent conditions. We also show that the dust ring inferred from the observations potentially satisfies the conditions for exomoon formation via streaming instability and subsequent gravitational instability.