Abstract

Solar magnetic activities show an about 11-year cycle period with the variations of the amplitudes. The increasing technological advancement induces the stronger influence of the solar magnetic cycle on humans. The magnetic cycle is believed to be caused by a magnetohydrodynamic (MHD) dynamo process in the solar interior, where the flows and the magnetic fields interact in the strongly turbulent convective zone. The intrinsic features of the solar interior, e.g., the stratification, the turbulence and the nonlinearities, make the global MHD simulations of solar convection with the realistic parameters of the Sun extremely hard. The past substantial progress in understanding the solar magnetic cycle benefitted from the simplified models, e.g., the axisymmetric kinematic ones. The mean field electrodynamics and the helioseismology laid the foundation of the progress. Under the effects of the large-scale flows, the poloidal and the toroidal components of the magnetic field sustain each other, which persists the cycle variations of the solar magnetic field. The key ingredients in the dynamo process include the mechanism and the location of the toroidal field generation, the mechanism and the location of the poloidal field generation, the rising of toroidal field to form the sunspots with tilts and the mechanism for the equatorward migration of the sunspots. So far, only the generation of the toroidal field by differential rotations is less controversial. The current dynamo models usually do not include the toroidal flux tube emergence, which was investigated as a separated topic. As the workhorse to understand the solar cycle during the past decade, the Babcock-Leighton (BL) type flux transport dynamos is a popular paradigm for explaining the cyclic nature of solar magnetic activity. They were even used to predict future solar cycles by assimilating observed surface flows and fields into the models. Recently the flux transport dynamos faces some challenges, such as the depth variation of the equatorward flow, the strong turbulent diffusivity, and so on. But the BL mechanism which is due to the decay of the tilt sunspot groups on the solar surface to regenerate the poloidal field, is most probably at the heart of the solar cycle. The further understanding of the solar magnetic cycle will benefit from the constraints of the solar historical data, the helioseismology, the different magnetic cycles of different types of stars, and the global MHD numerical simulations. These fields will be developed in parallel with the kinematic dynamo and fertilize each other. The three dimensional Babcock-Leighton type dynamo models coupled with the toroidal flux tube emergence is expected to be the workhorse of the next generation of solar dynamo.

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