Description
The theoretical model for describing the Sun’s thermal convection remains incomplete. While the theory of stellar evolution is grounded in turbulent energy transport described by the gradient diffusion model and mixing length (ML) theory, recent research has increasingly called its validity into question. A notable example of this skepticism is the “convection conundrum”, a significant issue in solar physics (e.g., Hanasoge et al. 2013; Rast 2020; Hotta et al. 2023). According to ML theory, solar convection should display a hierarchical, multi-scale structure, yet there is a marked discrepancy between theoretical predictions and observations, particularly in the low-wavenumber modes where the observed convection power is notably weaker. The ultimate goal of our research is to achieve a comprehensive understanding of thermal convection and turbulent energy transport within the solar interior. There are at least two potential driving mechanisms for solar convection. One mechanism is driven by local entropy gradients (e.g., Kippenhahn & Weigert 1990), while the other is a non-local, non-equilibrium convection driven by surface radiative cooling (e.g., Spruit 1997; Yokoi et al. 2022). The former mechanism forms the basis of stellar evolution theory; however, due to the inconsistencies between ML theory and observations, such as the convection conundrum, the latter model is receiving renewed attention. To accurately model turbulent energy transport within the solar interior, we are currently investigating the driving mode of solar convection using various machine learning techniques. In our recent study (Masada et al. 2024, in prep.), we have examined the topological structure of the Sun’s granular convection using topological data analysis (TDA). Our analysis, utilizing persistence diagrams (PDs), has revealed that the solar granule is characterized by long-lived "topological defects”, suggesting greater compatibility with a cooling-driven convective structure. In my talk, I will present our recent efforts in studying solar convection, with a particular focus on our TDA analysis and its implications for modeling the convective transport inside the Sun.
