Discovery of the wavelength dependency of apparent ring widths and constraints on the dust size distributions in the HD 163296 disk

Kiyoaki Doi

Observational constraints on the dust size distribution in the disks provide a clue to understanding planet formation. Previous studies have estimated the dust size distribution using the spectral index derived from multi-wavelength observations or dust polarization observations. However, these studies give different results depending on their methods and model assumptions and do not reach a consensus.
In this work, we propose a new method to constrain the dust size distribution from the wavelength dependency of the dust ring widths. Many disks have dust and gas rings, and larger dust grains are more effectively trapped in the gas rings, forming narrower dust rings. As a result, the dust rings are expected to appear narrower at longer wavelengths since the observations are sensitive to the dust grains whose size is comparable to the observed wavelength.
We analyze high-resolution Band 4 (2.1 mm) and Band 6 (1.3 mm) images of the HD 163296 disk. We find for the first time that the width of the outer dust ring (100 au) appears 1.2 times narrower at the longer wavelength, while the width of the inner ring (67 au) is similar between the two bands. The difference in the ring width depending on the observed wavelength is consistent with the dust trapping scenario in a gas ring. We constrain the maximum dust size a_max and the exponent of the dust size distribution p from the difference in dust ring width between the two bands, together with the spectral index, and found that 1 mm < a_max < 20 mm and p < 3.5 in the inner ring, and a_max > 30 mm and 3.4 < p < 3.6 in the outer ring. The slope p ? 3.5 may imply the dust collisional cascade of already formed planetesimal in the outer ring.