Millimeter Gap Contrast as a Probe for Turbulence Level in Protoplanetary Disks

Turbulent motions are believed to regulate angular momentum transport and influence dust evolution in protoplanetary disks. Measuring the strength of turbulence is challenging through gas line observations because of the requirement for high spatial and spectral resolution data, and an exquisite determination of the temperature. In this work, taking the well-known HD 163296 disk as an example, we investigated the contrast of gaps identified in high angular resolution continuum images as a probe for the level of turbulence. With self-consistent radiative transfer models, we simultaneously analyzed the radial brightness profiles along the disk major and minor axes, and the azimuthal brightness profiles of the B67 and B100 rings. By fitting all the gap contrasts measured from these profiles, we constrained the gas-to-dust scale height ratio $\Lambda$ to be $3.0_{-0.8}^{+0.3}$, $1.2_{-0.1}^{+0.1}$ and ${\ge}\,6.5$ for the D48, B67 and B100 regions, respectively. The varying gas-to-dust scale height ratios indicate that the degree of dust settling changes with radius. The inferred values for $\Lambda$ translate into a turbulence level of $\alpha_{\rm turb}\,{<}\,3\times10^{-3}$ in the D48 and B100 regions, which is consistent with previous upper limits set by gas line observations. However, turbulent motions in the B67 ring are strong with $\alpha_{\rm turb}\,{\sim}1.2\,{\times}\,10^{-2}$. Due to the degeneracy between $\Lambda$ and the depth of dust surface density drops, the turbulence strength in the D86 gap region is not constrained.