Constraints on the dust size distributions in the HD 163296 disk from the difference of the apparent dust ring widths between two ALMA Bands

TL;DR

This paper introduces a novel method to constrain dust size distributions in protoplanetary disks by analyzing the differences in dust ring widths at different ALMA wavelengths, applied to HD 163296.

Contribution

The study develops a new approach linking dust spatial distribution to size distribution, providing constraints on maximum dust size and size distribution exponent in specific disk rings.

Findings

Outer ring's width narrows at longer wavelengths, indicating larger grains.

Inner ring shows consistent width across wavelengths, suggesting smaller grains.

Constraints on dust size parameters imply spatial variation in dust growth processes.

Abstract

The dust size in protoplanetary disks is a crucial parameter for understanding planet formation, while the observational constraints on dust size distribution have large uncertainties. In this study, we present a new method to constrain the dust size distribution from the dust spatial distribution, utilizing the fact that larger dust grains are more spatially localized. We analyze the ALMA Band 6 (1.25 mm) and Band 4 (2.14 mm) high-resolution images and constrain the dust size distribution in the two rings of the HD 163296 disk. We find that the outer ring at 100 au appears narrower at the longer wavelengths, while the inner ring at 67 au appears to have similar widths across the two wavelengths. We model dust rings trapped at gas pressure maxima, where the dust grains follow a power-law size distribution, and the dust grains of a specific size follow a Gaussian spatial distribution with the width depending on the grain size. By comparing the observations with the models, we constrain the maximum dust size $a_{\mathrm{max}}$ and the exponent of the dust size distribution $p$. We constrain that $0.9 \ \mathrm{mm} < a_{\mathrm{max}} < 5 \ \mathrm{mm}$ and $p < 3.3$ in the inner ring, and $a_{\mathrm{max}} > 3 \times 10^1 \ \mathrm{mm}$ and $3.4 < p < 3.7$ in the outer ring. The larger maximum dust size in the outer ring implies a spatial dependency in dust growth, potentially influencing the formation location of the planetesimals. We further discuss the turbulence strength $\alpha$ derived from the constrained dust spatial distribution, assuming equilibrium between turbulent diffusion and accumulation of dust grains.