The Role of Temperature and Density Variations in Vortex Formation in Protoplanetary Disks.

Research Period
February 2024 – May 2024

Research Guidance
Guidance under Professor Richard Teague, Massachusetts Institute of Technology (MIT)

Hypothesis
The central hypothesis proposed that specific temperature and density variations within protoplanetary disks play a crucial role in driving vortex formation, a key process in planetary formation. Furthermore, the evolution of these variations can be effectively modeled through numerical simulations and corroborated with observational data. 

Motivation
My interest in planetary formation stems from its ability to bridge my fascination with geological formations and planetary science. I am particularly intrigued by the immense diversity of planets and the processes that led to their formation. What factors caused such a variety of planetary types to emerge?

Specifically, I am fascinated by planetary vortices, which play a critical role in forming different kinds of planets by serving as dust and gas traps within protoplanetary disks. These vortices facilitate the accumulation of material essential for planetesimal formation—a fundamental step in the planetary formation process. Observations from ALMA (Atacama Large Millimeter/submillimeter Array) have captured detailed images of protoplanetary disks, revealing structures consistent with vortex activity. These observations underscore the importance of vortices as observable phenomena in planet formation, making them a compelling area for further study. 

Problem Breakdown
The research was divided into the following key objectives to systematically address the central hypothesis:

1. Density Evolution Analysis: Plotted density over time to observe its evolution. The results demonstrated the transformation of the disk from a homogeneous state to a highly structured configuration.
2. Density Visualization: Created a time-lapse movie of density evolution. The visualization revealed the presence of a vortex, observed at different positions as it rotated around the disk’s center. This rotation was evident due to the changing position of the density anomaly.
3. Velocity Structure Analysis: Plotted graphs to analyze how the velocity structure changed over time.
4. Intrinsic Vortex Rotation: Developed a method to distinguish between the intrinsic rotation of the vortex and its apparent rotation due to projection effects, using matrix-based calculations. This clarified that the intrinsic rotation is the key factor of interest.
5. Validation of Numerical Simulations: Compared simulation-generated data with observational evidence, such as velocity graphs, to validate the accuracy of the models and confirm their ability to replicate the physical processes observed in protoplanetary disks.

Quantifiable Outcomes
1. Data Analysis Results: The research identified a strong correlation between temperature gradients, density variations, and vortex rotation within the protoplanetary disk. The simulations revealed that vortices exhibited a stable counterclockwise rotation, with uniform patterns maintained over time. These findings were instrumental in understanding vortex stability and evolution, highlighting their role in gas and dust accretion processes that contribute to planet formation.
2. Model Validation: Comparative analysis of simulation-generated graphs with observational data confirmed the accuracy of the numerical models. Structural similarities between the two datasets validated the models’ ability to replicate the essential dynamics of protoplanetary disks, ensuring their reliability for future research applications.
3. Visualization Outputs: Detailed graphs and charts were produced to illustrate the relationships between temperature, density, and vortex dynamics. These visualizations were critical in communicating complex disk behaviors and supported the validation and refinement of the simulation models.

These outcomes significantly advanced the understanding of protoplanetary disk dynamics and the early stages of gas giant formation. The research not only validated existing numerical models but also established a foundation for future enhancements in simulation accuracy and predictive capabilities.

Skills Acquired

1. Advanced Data Analysis: Gained expertise in processing and interpreting numerical simulation data, particularly focusing on temperature, density, and velocity correlations.
2. Numerical Model Validation: Developed proficiency in assessing simulation accuracy through detailed comparisons with observational data.
3. Astrophysical Visualization: Enhanced ability to produce and interpret detailed graphs and charts for effective communication of complex dynamics.
4. Velocity Component Analysis: Learned to analyze and interpret radial and azimuthal velocity (v_ϕ​) data, gaining insights into vortex dynamics and disk evolution.
5. Research Tools and Techniques: Acquired skills in using computational tools for data-driven insights and generating high-quality visual outputs.

Key Learnings

1. Protoplanetary Disk Dynamics: Deepened understanding of how non-uniform temperature and density variations lead to vortex formation and their role in planetary formation.
2. Astrophysical Contexts: Gained insights into how the collapse of molecular clouds and conservation of angular momentum shape protoplanetary disk dynamics.
3. Scientific Validation: Learned the importance of rigorous model validation by aligning simulation data with observable phenomena.
4. Research Methodology: Developed a systematic approach to addressing complex scientific questions, enhancing problem-solving and analytical strategies.
5. Collaboration in Research: Recognized the importance of integrating theoretical knowledge, simulations, and data analysis within a broader research framework.

Graphs and Visualization