Three-dimensional non-kinematic simulation of the post-emergence evolution of bipolar magnetic regions and the Babcock-Leighton dynamo of the Sun

Context. The Babcock-Leighton flux-transport model is a widely accepted dynamo model of the Sun that can explain many observational aspects of solar magnetic activity. This dynamo model has been extensively studied in a two-dimensional (2D) mean-field framework in both kinematic and non-kinematic regimes. Recent three-dimensional (3D) models have been restricted to the kinematic regime. In these models, the surface poloidal flux is produced by the emergence of bipolar magnetic regions (BMRs) that are tilted according to Joy's law. Aims. We investigate the prescription for emergence of a BMR in 3D non-kinematic simulations. In particular, we examine the effect of the radial extent of the BMR. We also report our initial results based on a cyclic Babcock-Leighton dynamo simulation. Methods. We extended a conventional 2D mean-field model of the Babcock-Leighton flux-transport dynamo into 3D non-kinematic regime, in which a full set of magnetohydrodynamic (MHD) equations are solved in a spherical shell using a Yin-Yang grid. The large-scale mean flows, such as differential rotation and meridional circulation, are not driven by rotationally constrained convection, but rather by the parameterized A-effect in this model. For the induction equation, we used a Babcock-Leighton alpha-effect source term by which the surface BMRs are produced in response to the dynamo-generated toroidal field inside the convection zone. Results. We find that in the 3D non-kinematic regime, the tilt angle of a newly-emerged BMR is very sensitive to the prescription for the subsurface structure of the BMR (particularly, its radial extent). Anti-Joy tilt angles are found unless the BMR is deeply embedded in the convection zone. We also find that the leading spot tends to become stronger (higher field strengths) than the following spot. The anti-Joy's law trend and the morphological asymmetry of the BMRs can be explained by the Coriolis force acting on the Lorentz-force-driven flows. Furthermore, we demonstrate that the solar-like magnetic cycles can be successfully obtained if Joy's law is explicitly given in the Babcock-Leighton alpha-effect. In these cyclic dynamo simulations, a strong Lorentz force feedback leads to cycle modulations in the differential rotation (torsional oscillation) and meridional circulation. The simulations, however, do not include radiative effects (e.g., enhanced cooling by faculae) that are required to properly model the torsional oscillations. The non-axisymmetric components of the flows are found to exist as inertial modes such as the equatorial Rossby modes.