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The dust size in protoplanetary disks is a crucial parameter forunderstanding planet formation, while the observational constraints on dustsize distribution have large uncertainties. In this study, we present a newmethod to constrain the dust size distribution from the dust spatialdistribution, utilizing the fact that larger dust grains are more spatiallylocalized. 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 tworings of the HD 163296 disk. We find that the outer ring at 100 au appearsnarrower at the longer wavelengths, while the inner ring at 67 au appears tohave similar widths across the two wavelengths. We model dust rings trapped atgas pressure maxima, where the dust grains follow a power-law sizedistribution, and the dust grains of a specific size follow a Gaussian spatialdistribution with the width depending on the grain size. By comparing theobservations with the models, we constrain the maximum dust size$a_{\mathrm{max}}$ and the exponent of the dust size distribution $p$. Weconstrain 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 theouter ring implies a spatial dependency in dust growth, potentially influencingthe formation location of the planetesimals. We further discuss the turbulencestrength $\alpha$ derived from the constrained dust spatial distribution,assuming equilibrium between turbulent diffusion and accumulation of dustgrains.

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