7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Modeling Convection and Transport in the Sun
Youhei Masada 11
Department of Applied physics, Fukuoka Universitye-mail: ymasada@fukuoka-u.ac.jp
What physical mechanism primarily drives the thermal
convection in the Sun? Two physical mechanisms arediscussed as possible candidate: one is the locally-driven
convection, which is fueled by a local (negative) entropy
gradient, and the other is cooling-driven convection
triggered by surface radiative cooling. The solar interior
physics is constructed conventionally based on the
mixing-length theory, with assuming the locally-driven
convection as the dominant mechanism of momentum
and energy transports. However, it has become evident inrecent years that a significant disparity exists between
theory and observation of the solar convection, known as
the "convection conundrum". To address this discrepancy,
the concept of cooling-driven convection, characterizedby spontaneously-generated downflow plumes at theconvection zone (CZ) surface, is being reevaluated.
Which model (cooling- or locally-driven) provides abetter description of the Sun's thermal convection? To
answer this question, we employ MHD simulations tostudy distinctions in the physical characteristics of thepossible two convection models. From the stability pointof view, the only difference between the models lies in aslight difference in the super-adiabaticity. While thecooling-driven model has an adiabatic entropy profile
except the CZ surface in the radial direction, thelocally-driven one has a radially super-adiabatic profile.
Our analysis of the simulation data reveals two primary
insights: First, there exist substantial difference in thespectra of the convective kinetic energy between models.
Second, there exist a significant difference in 2nd-ordercorrelations of physical parameters, particularly turbulent
mass, momentum, and energy fluxes, between models.

Fig.1. Entropy distributions at the CZ surface for models.

Fig.1 shows the entropy distribution (deviation from themean value) at the CZ surface for two models. While theblack tone denotes the region consisting of cool and fast
downflows, white tone is corresponding to hot and slow
upflow region. The typical size of the convective cell
apparently differs between the models. This dissimilarity
in the spatial structure of the convection becomes clearer
in the power spectra, as shown in Fig.2. While thecooling-driven model exhibits a remarkable peak at thehigh-frequency regime (k ~ 8kL) and diminishing its
intensity on the low-frequency side, the locally-driven

one shows a broad spectrum with a robust intensity evenon the low-frequency side.

Fig.2. Spectra of convective energy for two models.

The difference that can be found in the turbulent flux iseven more pronounced. In Fig.3 (left top), the vertical(radial) distributions of turbulent internal energy fluxes
for the cooling-driven (red) and locally-driven (blue)
models are shown. The difference is particularly striking
near the CZ surface: the cooling-driven model has asharp peak around the CZ surface. The turbulent energy
flux in the locally-driven convection is well-described bya gradient-diffusion model (left bottom in Fig.3), whilethat in the cooling-driven convection is not, necessitating
an alternative theory (model) for its description.

Fig.3. (a)Turbulent energy fluxes for models. (b)Predicted
turbulent energy fluxes based on the gradient diffusion model.
(c)Fitting of the turbulent flux in the cooling-driven convection
by the modified (our developed) gradient-diffusion model withconsidering a non-equilibrium effect.

In our talk, we show that one of the prominent featuresof the cooling-driven convection, the enhanced transportof the turbulent energy just below the CZ surface, whichcannot be reproduced by the gradient diffusion model, iswell reproduced by the (our developed) modified modelwith considering the non-equilibrium effect. We will alsodelve into disparities between two convection models
through higher-order correlation analysis. Furthermore,
the results of analyses using machine learning techniques
and a comparison of the numerical model with the actual
solar convection will be discussed.
References[1] Masada & Sano (2022) in review (arXiv:2206.06566)[2] Yokoi, Masada, Takiawki (2022), MNRAS, 51, 2[3] Ishikawa et al. (2022), A&A, 658, A142