Early Grain Growth in the Young Protostellar Disk HH 212 Supported by Dust Self-Scattering Modeling

Abstract: Grain growth in disks around young stars plays a crucial role in the formation of planets. Early grain growth has been suggested in the HH 212 protostellar disk by previous polarization observations. To confirm it and to determine the grain size, we analyze high-resolution multi-band observations of the disk obtained with Atacama Large Millimeter/submillimeter Array (ALMA) in Bands 9 (0.4 mm), 7 (0.9 mm), 6 (1.3 mm), 3 (3 mm) as well as with Very Large Array (VLA) in Band Ka (9 mm) and present new VLA data in Bands Q (7 mm), K (1.3 cm), and X (3 cm). We adopt a parameterized flared disk model to fit the continuum maps of the disk in these bands and derive the opacities, albedos, and opacity spectral index $\mathrm{\beta}$ of the dust in the disk, taking into account the dust scattering ignored in the previous work modeling the multi-band data of this source. For the VLA bands, we only include the Band Q data in our modeling to avoid free-free emission contamination. The obtained opacities, albedos, and opacity spectral index $\beta$ (with a value of $\sim$ 1.2) suggest that the upper limit of maximum grain size in the disk be $\sim$ 130 $\mu$m, consistent with that implied in the previous polarization observations in Band 7, supporting the grain growth in this disk. The values of the absorption opacities further highlight the need for a new dust composition model for Class 0/I disks.