Ingeniería Civil Matemática certificada por 3 años hasta Diciembre de 2026
Omar Jesús Guerra Villalón
Bachelor’s Thesis
Incidence of Rotation Speed Ω and Ionization δ in a Numerical Study of Stellar Winds.
Thesis Advisor
Rodrigo Meneses
Co-Advisor
Michel Curé
Sumary
The study of stellar winds emitted by massive stars is crucial for understanding stellar evolution and the enrichment of their surrounding environments. These winds, driven by the interaction between radiation and stellar gas, determine key observable properties such as terminal velocity and mass-loss rate. This thesis addresses the complexity of modeling these winds through an analytical approach, numerically solving nonlinear equations that describe the dynamics of the wind velocity profile and the mass-loss rate.
A preliminary construction of the model has been presented based on elementary equations and appropriate variable transformations, allowing for a detailed physical description of stellar winds. Through a numerical procedure, favorable numerical solutions were identified for parametric analysis, focusing on the wind velocity profile, the eigenvalues of the physical problem, and the location of critical points.
In this work, using a viscosity model, it is shown that the ionization parameter δ and the rotational velocity Ω are fundamental to the characteristics of stellar winds. It is found that decreasing Ω leads to higher terminal velocities, while increasing δ smooths the velocity profile, indicating a more monotonic evolution. Additionally, a relationship is identified between the mass-loss rate and singular points through the interpretation of eigenvalues: as the eigenvalues increase, the singular points move farther from the stellar surface.
Finally, based on the results presented in this thesis, these can be interpreted as a preliminary study for future analyses focused on a joint study of the parameters k, α, γ_vis, δ, and Ω, as well as considering the sensitivity of numerical solutions to variations in the aforementioned parameters. A qualitative mathematical analysis could be useful for better understanding how these changes affect the behavior of the stellar wind model.
