Estimate on dust scale height from ALMA dust continuum image of the HD 163296 protoplanetary disk

We aim at estimating the dust scale height of protoplanetary disks from millimeter continuum observations. First, we present a general expression of intensity of a ring in a protoplanetary disk, and show that we can constrain the dust scale height by the azimuthal intensity variation. Then, we apply the presented methodology to the two distinct rings at 68 au and at 100 au of the protoplanetary disk around HD 163296. We constrain the dust scale height by comparing the DSHARP high-resolution millimeter dust continuum image with radiative transfer simulations using RADMC-3D. We find that h_d/h_g > 0.84 at the inner ring and h_d/h_g < 0.11 at the outer ring with the 3 sigma uncertainties, where h_d is the dust scale height and h_g is the gas scale height. This indicates that the dust is flared at the inner ring and settled at the outer ring. We further constrain the ratio of turbulence parameter alpha to gas-to-dust-coupling parameter St from the derived dust scale height; alpha/St > 2.4 at the inner ring, and alpha/St < 1.1*10^{-2} at the outer ring. This result shows that the turbulence is stronger or the dust is smaller at the inner ring than at the outer ring.