Theory of Nonlinear Magnetoconvection and Its Application to Solar Convection Problems. II

Abstract Nonlinear magnetoconvection is discussed with the introduction of turbulent eddy diffusivities in the representative eddy simulation of the turbulent motion. It is found that the turbulent magnetoconvection is characterized by the effective Rayleigh number of about 4 times the critical Rayleigh number and by the effective Nusselt number of about 2. The solar convection zone is modelled into several representative zones, of which each zone has a characteristic scale such as shown by granule, supergranule and global convection cell. In the kinematic regime (the Chandrasekhar number Q < 1), the flux tube formation or the intensification of the magnetic field into thinner tubes results in the field strength as strong as about five times the imposed field strength at each zone. Thus, weak diffuse flux tubes ( ~ 50 G) in the deepest zone can account for 103-G fields at the supergranulation zone by the successive intensification in deeper zones. As a thermodynamical aspect of magnetoconvection, the sunspot darkness is shown to be a shallow layer (≲2 × 103 km) phenomenon, which is due to the decrease of the eddy diffusivities and the increased Chandrasekhar number, setting a larger superadiabatic temperature gradient in the presence of a strong field (≲ 2 × 103 G). Shallow layer convections such as penumbral grains, umbral oscillations and faculae are also discussed.