Jinshi Sai, Shigehisa Takakuwa, Hsi-Wei Yen, Yusuke Tsukamoto, Yuya Fukuhara

Turbulence in protoplanetary disks plays a crucial role in the evolution of disk structures and the planet formation process therein. However, the strength of the turbulence remains unclear in young, embedded disks surrounded by infalling envelopes. In this paper, we present the first direct measurement of the nonthermal velocity dispersion within the embedded disk around HL Tau, which possesses a dusty disk with multiple rings and gap structures but is still associated with infalling gas flows from an envelope. Using ALMA archival data of the $\mathrm{H_2CO}$ emission, we measured the local line width through a parametric model fitting that accounts for the contribution of Keplerian shear motion. After subtracting the thermal component, the nonthermal velocity dispersion is $\sim\!\!0.15~\mathrm{km~s^{-1}}$ on average over radii of $80$-$180~\mathrm{au}$, and it slightly increases with radius. The estimated nonthermal motions correspond to a turbulent mach number of $\mathcal{M}\!\!\sim\!\!0.4$ or a viscous $α$ value of $α\!\!\sim\!\!0.16$, assuming that it is entirely caused by turbulence and $α\!\!\sim \!\! \mathcal{M}^2$. Our analysis also suggests that the $\mathrm{H_2CO}$ emission traces near the disk midplane ($z\lesssim 0.1 R$). Turbulence driven by the gravitational instability or infall from the envelope most naturally explains the large nonthermal motions, considering the large disk mass and associated infalling streamers. The strong turbulence measured in the outer disk, in contrast to the vertically settled inner dusty disk, suggests a pronounced radial variation in the turbulence strength and/or an anisotropic nature of the turbulence within the disk.