Nonlinear Mean-Field Dynamos With Magnetic Helicity Transport and Solar Activity: Sunspot Number and Tilt

In this chapter, we discuss a mean field solar dynamo model with algebraic and dynamic nonlinearities, various mechanisms of sunspot formation, and prediction of solar activity. The algebraic nonlinearity describes the quenching of the alpha effect, turbulent magnetic diffusion, and the effective pumping velocity due to feedback from the growing large-scale magnetic field on the fluid motion. The dynamic nonlinearity is due to the evolution of the magnetic helicity of the small-scale magnetic field during the nonlinear stage of the dynamo; it is derived from conservation of the total (large-scale plus small-scale) magnetic helicity for very small microscopic magnetic diffusivity.We discuss observations of magnetic helicity in the Sun and their connection with the nonlinear mean field dynamo. We derive a budget equation for sunspot numbers taking into account sunspot formation mechanism due to the negative effective magnetic pressure instability. To predict solar activity, we use dynamo simulations as input to an artificial neural network that learns sunspot dynamics from available observations. Finally, we analyze the contribution of magnetic helicity transport to the formation of tilt in sunspot bipolar regions and compare the results with available observational data over the last 10 solar cycles (15-24).