Estimate on dust scale height from 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 variation of the intensity. 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 hd/hg > 0.55 at the inner ring and hd/hg < 0.44 at the outer ring in the 2 ? error range, where hd is the dust scale height and hg 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 ? to gas-to-dust-coupling parameter St from the derived dust scale height; ?/St > 0.48 at the inner ring, and ?/St < 0.19 at the outer ring. This results show that the turbulence is stronger or the dust is smaller at the inner ring than at the outer ring.