Multi-wavelength Constraints on Dust Dynamics and Size Evolution in Protoplanetary Disk Rings. II. Observational Implications

Abstract: Spatially resolved dust rings in protoplanetary disks are widely used to infer disk and dust physics from multi-wavelength continuum observations. Their interpretation, however, often neglects grain growth and the evolution of the size distribution, limiting the connection between observed ring profiles and dust-evolution parameters. Building on a physical dust-ring model that includes coagulation and fragmentation, we develop a Bayesian inference framework that jointly incorporates radiative transfer and finite angular resolution. When applied to two rings in HD 163296 and two in LkCa 15, our framework yields gas-dependent estimates of the key dust-evolution parameters such as turbulence strength $α$ and the fragmentation velocity $v_{\rm frag}$ in a self-consistent way. Most rings admit both a low-$α$, low-$v_{\rm frag}$ branch with small grains, and a higher-$α$, higher-$v_{\rm frag}$ branch with larger grains. Typical low-$α$ branches have $α\sim10<sup>{-5}$--$10<sup>{-4}$ and fragmentation velocities of order cm s$<sup>{-1}$ level, whereas the higher-$α$ branches reach $α\sim10<sup>{-3}$--$10<sup>{-2}$ and fragmentation velocities of a few to $20$ m s$<sup>{-1}$. The observed broad and wavelength-dependent profiles near the ring peaks can be reproduced by intrinsically narrow dust rings. This new framework offers a more direct route from multi-wavelength continuum data to the microphysics of dust growth and trapping---a connection that can be robustly tested with future high-resolution observations at longer wavelengths.