Thermal Structure Determines Kinematics: Vertical Shear Instability in Stellar Irradiated Protoplanetary Disks

Abstract: Turbulence is crucial for protoplanetary disk dynamics, and Vertical Shear Instability (VSI) is a promising mechanism in outer disk regions to generate turbulence. We use Athena++ radiation module to study VSI in full and transition disks, accounting for radiation transport and stellar irradiation. We find that the thermal structure and cooling timescale significantly influence VSI behavior. The inner rim location and radial optical depth affect disk kinematics. Compared with previous vertically-isothermal simulations, our full disk and transition disks with small cavities have a superheated atmosphere and cool midplane with long cooling timescales, which suppresses the corrugation mode and the associated meridional circulation. This temperature structure also produces a strong vertical shear at $\mathrm{\tau_}$ = 1, producing an outgoing flow layer at $\tau_ < 1$ on top of an ingoing flow layer at $\tau_* \sim 1$. The midplane becomes less turbulent, while the surface becomes more turbulent with effective $\alpha$ reaching $\sim10^{-2}$ at $\tau_* \lesssim$1. This large surface stress drives significant surface accretion, producing substructures. Using temperature and cooling time measured/estimated from radiation-hydro simulations, we demonstrate that less computationally-intensive simulations incorporating simple orbital cooling can almost reproduce radiation-hydro results. By generating synthetic images, we find that substructures are more pronounced in disks with larger cavities. The higher velocity dispersion at the gap edge could also slow particle settling. Both properties are consistent with recent Near-IR and ALMA observations. Our simulations predict that regions with significant temperature changes are accompanied by significant velocity changes, which can be tested by ALMA kinematics/chemistry observations.

• The paper finds that thermal structure, particularly radial optical depth, suppresses Vertical Shear Instability (VSI) in the midplane of irradiated protoplanetary disks but not in the atmosphere.
• Thermal stratification leads to stratified accretion flows with opposing directions in the atmosphere and midplane, resulting in significant surface accretion.
• Long cooling timescales suppress classical corrugation modes and promote zonal flows, providing an explanation for observed disk substructures like gaps and rings.

Analysis of "Thermal Structure Determines Kinematics: Vertical Shear Instability in Stellar-Irradiated Protoplanetary Disks"

The paper "Thermal Structure Determines Kinematics: Vertical Shear Instability in Stellar-Irradiated Protoplanetary Disks" investigates the intricate dynamics of turbulence within protoplanetary disks, specifically focusing on the role of Vertical Shear Instability (VSI) in the outer regions of these disks. Through the use of the Athena++ radiation module, the authors, Zhang, Zhu, and Jiang, explore the effects of thermal structure and radiation transport on VSI in both full and transition disks. The significant influence of thermal structure and cooling timescales on VSI behavior is highlighted, offering insights into protoplanetary disk dynamics and turbulence.

Key Findings and Methodology

The study relies on radiation hydrodynamic simulations, utilizing Athena++ with a built-in radiation module to simulate and analyze the VSI's impact on protoplanetary disks. It considers both full disks and transition disks, taking into account variables like the inner rim location and radial optical depth. The research underscores how a disk's thermal structure profoundly influences its kinematic properties. Key outcomes from these simulations include:

1. Thermal Structure's Impact on Disk Dynamics: The study emphasizes that the radial optical depth due to stellar irradiation plays a crucial role in shaping the disk's thermal profile. Disks with a cool midplane and a superheated atmosphere, delineated by the $\tau_* = 1$ surface, exhibit suppressed VSI activity in the midplane, resulting in reduced turbulence. In contrast, the atmosphere remains turbulent.
2. Stratified Accretion Flows: The thermal stratification leads to unique accretion dynamics characterized by stratified accretion flows. An outgoing flow is observed in the atmosphere, overlaying an ingoing flow in the midplane transition region. This results in significant surface stress contributing to notable surface accretion.
3. Suppressed Corrugation Mode: The long cooling timescales in certain disk areas lead to the suppression of the classical n=1 corrugation mode typically associated with VSI. This inhibition is evident in disks with significant thermal structuring.
4. Zonal Flows and Substructures: The presence of zonal flows, along with the resultant substructures such as gaps and rings, align with observations from instruments like ALMA. The study predicts that larger cavities within disks exacerbate these substructures, a hypothesis which aligns with both Near-IR and ALMA observations.

Theoretical and Practical Implications

From a theoretical standpoint, this study advances our understanding of how thermodynamics and radiation transport in protoplanetary disks govern the emergence and characteristics of VSI and resulting turbulence. The authors establish theoretical links between temperature structures and kinematic changes that may be validated through observational data.

On a practical level, the study raises intriguing possibilities for future observational campaigns. The identified correlations between thermal structures and kinematic changes offer a predictive tool for understanding the physical conditions within observed protoplanetary disks. Such insights are vital for interpreting ALMA observations and other future instruments designed to study the formative processes of planetary systems.

Future Directions

The study sets the groundwork for further exploration into VSI's role in turbulence generation and the complex interaction of thermal dynamics, suggesting multiple pathways for future research:

• 3D Simulations: Expanding the current 2D setup to three dimensions will enable predictions concerning VSI-driven kinematic features that may be testable via detailed ALMA observations, enhancing the validation process for these models.
• Integration with Chemical Models: Future work incorporating VSI turbulence models with chemical distribution studies could provide comprehensive insights into material transport and its implications on observed chemical abundances within protoplanetary disks.
• Exploring Other Instabilities: Investigating how VSI interacts with or even suppresses other instabilities like Magnetorotational Instability (MRI) could offer a more nuanced understanding of the interplay between different turbulence sources.

In summary, this paper highlights the pivotal role of thermal structure in shaping the kinematics of protoplanetary disks through VSI. The research provides a crucial stepping stone toward resolving the complex disk dynamics that underpin planet formation, thus fostering advancements in both theoretical models and observational techniques in astrophysics.