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We aim at estimating the dust scale height of protoplanetary disks frommillimeter continuum observations. First, we present a general expression ofintensity of a ring in a protoplanetary disk, and show that we can constrainthe dust scale height by the azimuthal intensity variation. Then, we apply thepresented methodology to the two distinct rings at 68 au and at 100 au of theprotoplanetary disk around HD 163296. We constrain the dust scale height bycomparing the DSHARP high-resolution millimeter dust continuum image withradiative transfer simulations using RADMC-3D. We find that h_d/h_g > 0.84 atthe inner ring and h_d/h_g < 0.11 at the outer ring with the 3 sigmauncertainties, where h_d is the dust scale height and h_g is the gas scaleheight. This indicates that the dust is flared at the inner ring and settled atthe outer ring. We further constrain the ratio of turbulence parameter alpha togas-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. Thisresult shows that the turbulence is stronger or the dust is smaller at theinner ring than at the outer ring.

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