Nonthermal Velocity Dispersion in the Outer Disk of HL Tau

Abstract

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.

Figures (12)

• Figure 1: (a) Moment 0 and 1 maps of the H_2CO ($3_{1,2}\hbox{--}2_{1,1}$) emission, shown with contours and color, respectively. Contour levels are $-3\sigma$, $3\sigma$, $6\sigma$, and $12\sigma$, where $\sigma= 2.37 ~\mjypbm~\kmps$. (b) The 1.3 mm dust continuum emission (orange color) overlaid with the peak intensity map of the H_2CO emission (contours and light blue color). Contours start from $5\sigma$ and increase in steps of $5\sigma$, where $\sigma= 1.68~\mjypbm$. (c) Moment 0 and 1 maps of the HCO^+ ($3\hbox{--}2$) emission, shown with contours and color, respectively. Contour levels are $-3\sigma$, $3\sigma$, $6\sigma$, and $12\sigma$, where $\sigma= 4.90 ~\mjypbm~\kmps$. The filled ellipses at the bottom left corners denote the beam size of each image.
• Figure 2: Velocity channel maps of the H_2CO ($3_{1,2}\hbox{--}2_{1,1}$) data, the best-fit model, and residuals after subtracting the best-fit model from the data. The label at the top left corner of each panel denotes the LSR velocity. The velocity channels are presented in steps of three times original channel spacing. Contour levels are $-6\sigma$, $-3\sigma$, $3\sigma$, $6\sigma$, $12\sigma$ and $24\sigma$, where $\sigma= 1.68 ~\mjypbm$. Dashed and solid contours indicate negative and positive values, respectively. The filled ellipses at the bottom left corners denote the beam size. Gray scales indicate the channels that are excluded from the parametric model fitting because of absorption by foreground envelope gas or contamination of emission from the main streamer.
• Figure 3: A schematic picture illustrating the concept of the channel-based three-layer approximation.
• Figure 4: Radial profiles of the best-fit local line width, the thermal velocity component estimated using temperature distributions derived in Okuzumi2016a and Yen2019a, and the nonthermal velocity dispersion obtained by subtracting the thermal component from the best-fit local line width. The color shaded regions indicate the $1\sigma$ uncertainty of $\Delta V$, derived from the posterior distributions of $\Delta V_0$ and $l$, the error of the thermal velocity given the temperature range, and the uncertainty of the nonthermal velocity dispersion, derived from above two uncertainties.
• Figure 5: (a, b) Total line width maps of the data and best-fit model, including Keplerian shear motions. (c) The residual map after subtracting the total line widths of the best-fit model from those of the data. Contours indicate $\pm3\sigma$ and $\pm6\sigma$, where $\sigma$ is the fitting uncertainty derived in the Gaussian fitting. The central region, which shows large residuals due to absorption by foreground gas against the optically thick dust continuum in the data, is masked for better visualization.