🔭 astrophysics

Nonthermal Velocity Dispersion in the Outer Disk of HL Tau

Using ALMA archival data of H₂CO emission, this study presents the first direct measurement of significant nonthermal velocity dispersion in the outer disk of HL Tau, suggesting that gravitational instability or infall from the envelope drives strong turbulence with a Mach number of ~0.4 and an alpha viscosity of ~0.16.

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

Published 2026-04-01

📖 5 min read🧠 Deep dive

CC BY 4.0

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

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a giant, swirling cosmic whirlpool made of gas and dust, waiting to birth a new solar system. This is HL Tau, a baby star surrounded by a protoplanetary disk. For years, astronomers have been trying to figure out how "calm" or "chaotic" the water in this whirlpool is.

Why does it matter? Think of the dust grains in the disk as tiny building blocks for planets. If the water is too calm, the blocks sink to the bottom and stack up neatly to form planets. If the water is too turbulent (like a raging storm), the blocks get tossed around, collide, and break apart, making it hard for planets to form.

This paper is like a new, high-tech speedometer that finally measured the "turbulence" in the outer edges of HL Tau's disk, a place that was previously too foggy and messy to study clearly.

Here is the breakdown of what they found, using some everyday analogies:

1. The Challenge: Seeing Through the Fog

HL Tau is a "Class I" star, meaning it's very young and still wrapped in a thick blanket of falling gas (an envelope). It's like trying to hear a whisper in a room where a heavy rainstorm is battering the windows.

The Problem: Most molecules used to measure speed (like CO) trace the falling rain (the envelope) or the wind blowing out (outflows), not the disk itself.
The Solution: The team used a specific molecule called Formaldehyde (H₂CO). Think of this molecule as a "ghost" that only lives in the calm, flat middle of the disk, ignoring the falling rain and the wind. It allowed them to see the disk's true motion clearly.

2. The Measurement: Separating the Spin from the Shake

The disk is spinning around the star (Keplerian motion), like a figure skater spinning. But the gas inside also has its own internal "shaking" or jittering (turbulence).

The Analogy: Imagine a spinning merry-go-round. The whole thing is moving fast, but if you look closely at a single horse, it's also bouncing up and down.
The Method: The astronomers built a complex computer model to calculate exactly how fast the merry-go-round should be spinning at every point. Then, they subtracted that "spin speed" from the actual observed speed. What was left over was the "bouncing" (the nonthermal velocity).

3. The Big Discovery: A Storm in the Outer Ring

They found that the outer part of the disk (between 80 and 180 times the distance from the Earth to the Sun) is much more turbulent than expected.

The Numbers: The gas is moving chaotically at about 0.15 km/s (roughly 335 mph).
The Scale: This is like a "turbulent Mach number" of 0.4. In plain English, the gas is moving at nearly half the speed of sound within that gas cloud. It's not a gentle breeze; it's a strong gale.
The Contrast: This is a huge difference from the inner disk (closer to the star), which is very calm and settled, like a still pond. The outer disk is a choppy sea.

4. Why is it so Chaotic? (The Culprits)

The authors propose two main suspects for this stormy weather:

Suspect A: Gravitational Instability (The Heavy Blanket)
The outer disk is so massive that its own gravity is starting to fight against the spin. Imagine a heavy blanket being spun around; if it's too heavy, it starts to wrinkle and buckle. These "wrinkles" (spiral arms) create turbulence. The math suggests the disk is heavy enough to be unstable, creating a self-regulating cycle of chaos.
Suspect B: The Falling Envelope (The Rain on the Roof)
HL Tau is still being fed by gas falling in from the surrounding cloud. Imagine rain falling onto a spinning trampoline. The impact of the falling rain creates ripples and waves. The team suggests that this constant "rain" hitting the disk is stirring up the gas, creating the turbulence they measured.

5. What Does This Mean for Planet Formation?

This discovery changes the story of how planets are born in young systems.

The Inner Disk: Calm and settled. Dust grains can sink to the middle and clump together easily. This is where planets might be forming now.
The Outer Disk: Chaotic and turbulent. The "storm" keeps dust grains from settling. It's like trying to build a sandcastle in a hurricane; the grains are constantly being kicked apart.
The Takeaway: Planet formation isn't uniform. It's a "calm center, stormy edge" scenario. The turbulence in the outer disk might actually be preventing planets from forming there right now, or it might be the very mechanism that eventually triggers the formation of giant planets by compressing the gas.

Summary

In simple terms, this paper is the first time we've successfully measured the "wind speed" inside the outer ring of a baby star's disk. We found that while the inner ring is a calm nursery for planets, the outer ring is a turbulent storm, likely caused by the disk's own heavy weight or the rain of gas falling onto it. This helps us understand that the universe is a much more dynamic and violent place during the birth of stars than we previously thought.

1. Problem Statement

Turbulence is a fundamental parameter governing the evolution of protoplanetary disks and the planet formation process. It influences dust settling, planetesimal formation via streaming instability, and chemical mixing. While turbulence strength ( $\alpha$ ) has been constrained in older, Class II disks (ages $\sim$ 1–5 Myr) using dust scale heights and molecular line widths, the turbulence in younger, embedded disks (Class 0/I, ages $\lesssim$ 0.5 Myr) remains poorly understood. These younger systems are often surrounded by infalling envelopes and outflows, making it difficult to isolate the disk gas and measure nonthermal motions. HL Tau, a nearby protostar with a massive, structured disk still embedded in an infalling envelope, serves as a critical test case to determine if turbulence is weak (as in settled inner rings) or strong in these early evolutionary stages.

2. Methodology

The authors utilized ALMA archival data of the H $_2$ CO (3 $_{1,2}$ –2 $_{1,1}$ ) emission line to measure nonthermal velocity dispersion in the outer disk ( $r \gtrsim 80$ au) of HL Tau.

Tracer Selection: H $_2$ CO was chosen because previous studies indicate it traces the Keplerian disk and is less contaminated by the infalling envelope compared to other tracers like CO or HCO $^+$ .
Data Reduction: High-resolution imaging was performed using CASA. The data were self-calibrated, and channel maps were generated with a velocity resolution of $\sim$ 0.187 km s $^{-1}$ .
Parametric Modeling:
- A viscous disk model was employed to fit the velocity channel maps.
- The model accounts for Keplerian shear motion, which dominates line broadening at limited spatial resolutions.
- A channel-based three-layer approximation was introduced to handle radiative transfer efficiently. This method divides the gas along the line of sight into cells corresponding to velocity channels, treating them as thin layers to analytically solve radiative transfer while accounting for disk thickness and dust continuum subtraction.
- The local line width ( $\Delta V$ ) was parameterized as a power law of radius: $\Delta V(R) = \Delta V_0 (R/100 \text{ au})^l$ .
Derivation of Nonthermal Dispersion:
- The total line width was decomposed into thermal ( $v_{th}$ ) and nonthermal ( $v_{nth}$ ) components: $\Delta V = \sqrt{v_{th}^2 + v_{nth}^2}$ .
- Thermal velocities were estimated using temperature profiles from previous studies (dust continuum and HCO $^+$ lines) as lower and upper bounds ( $T \approx 20\text{--}30$ K).
- The nonthermal component was derived by subtracting the thermal contribution from the best-fit local line width.
Emission Height Analysis: The authors compared observed channel maps with modeled isovelocity curves to constrain the vertical emission height ( $z/R$ ) of the H $_2$ CO layer.

3. Key Contributions

First Direct Measurement in an Embedded Disk: This study presents the first direct measurement of nonthermal velocity dispersion specifically within the embedded disk of a Class I/II protostar (HL Tau), overcoming the challenge of envelope contamination.
Novel Modeling Technique: The development and application of the channel-based three-layer approximation allows for efficient radiative transfer modeling that accounts for disk thickness and Keplerian shear without the computational cost of full 3D radiative transfer, enabling robust parameter fitting via MCMC.
Radial Variation of Turbulence: The study provides evidence for a pronounced radial variation in turbulence, contrasting the weak turbulence in the inner dusty rings with strong turbulence in the outer gas disk.

4. Key Results

Nonthermal Velocity Dispersion: The average nonthermal velocity dispersion in the outer disk (80–180 au) is $\sim$ 0.15 km s $^{-1}$ .
- This value slightly increases with radius, ranging from $\sim$ 0.10 km s $^{-1}$ at 80 au to $\sim$ 0.20 km s $^{-1}$ at 180 au.
- This corresponds to approximately 0.6 times the isothermal sound speed ( $c_s$ ) assuming $T=20$ K.
Turbulence Parameters:
- Assuming the nonthermal motion is entirely turbulent, the turbulent Mach number is $\mathcal{M} \sim 0.4$ .
- Using the relation $\alpha \sim \mathcal{M}^2$ , the viscous parameter is estimated as $\alpha \sim 0.16$ .
Emission Height: Analysis of the channel map morphology (single isovelocity curves vs. double curves) indicates that H $_2$ CO emission originates near the disk midplane, specifically at heights $z/R \lesssim 0.1$ .
Model Validation: The parametric model successfully reproduces the azimuthally averaged line widths of the data within $\sim$ 10 m s $^{-1}$ . Residuals on the northwest side (associated with an infalling streamer) show larger line widths, confirming the streamer was successfully excluded from the disk analysis.

5. Significance and Physical Interpretation

Driving Mechanisms: The measured high turbulence ( $\alpha \sim 0.16$ $α \sim 0.16$ ) is too strong to be explained by standard Magnetorotational Instability (MRI) or Vertical Shear Instability (VSI) near the midplane, which typically predict much weaker turbulence in this region.
- Gravitational Instability (GI): The results strongly suggest GI as the primary driver. The outer disk mass and infall rates imply a Toomre $Q$ parameter $< 1.7$ , making the disk gravitationally unstable. GI can drive turbulence of $\mathcal{M} \sim 0.4$ near the midplane.
- Envelope Infall: The dynamical perturbation from gas infalling from the envelope (streamers) can also generate spiral density waves and Reynolds stress, potentially driving $\alpha \sim 0.1$ in the outer disk.
Radial Stratification of Turbulence: The findings highlight a stark contrast between the inner and outer disk. The inner dusty rings ( $r < 40$ au) show settled dust and weak turbulence ( $\alpha \sim 10^{-4}$ ), while the outer gas disk is highly turbulent. This suggests that turbulence is not uniform but varies significantly with radius and potentially with height.
Implications for Planet Formation: Strong turbulence in the outer disk may inhibit dust settling and planetesimal formation via the streaming instability in that region, whereas the settled inner rings remain conducive to these processes. The results emphasize that planet formation in young, embedded systems is a complex process governed by spatially varying turbulence driven by gravitational instability and external accretion.

Conclusion

The paper demonstrates that the outer disk of HL Tau is a site of vigorous turbulence ( $\alpha \sim 0.16$ ), likely driven by gravitational instability and/or infall from the envelope. This contrasts sharply with the quiescent inner disk, indicating that the physical conditions for planet formation evolve rapidly and vary significantly across the disk during the early embedded phase.