Oscillator models of the solar cycle: Towards the development of inversion methods

This article reviews some of the leading results obtained in solar dynamo physics by using temporal oscillator models as a tool to interpret observational data and dynamo model predictions. We discuss how solar observational data such as the sunspot number is used to infer the leading quantities responsible for the solar variability during the last few centuries. Moreover, we discuss the advantages and difficulties of using inversion methods (or backward methods) over forward methods to interpret the solar dynamo data. We argue that this approach could help us to have a better insight about the leading physical processes responsible for solar dynamo, in a similar manner as helioseismology has helped to achieve a better insight on the thermodynamic structure and flow dynamics in the Sun's interior.Comment: 28 pages; 16 figures, ISSI Workshop 11-15 November 2013 - The Solar Cycle, http://www.issibern.ch/program/workshops.htm

On the compatibility of a flux transport dynamo with a fast tachocline scenario

The compatibility of the fast tachocline scenario with a flux transport dynamo model is explored. We employ a flux transport dynamo model coupled with simple feedback formulae relating the thickness of the tachocline to the amplitude of the magnetic field or to the Maxwell stress. The dynamo model is found to be robust against the nonlinearity introduced by this simplified fast tachocline mechanism. Solar-like butterfly diagrams are found to persist and, even without any parameter fitting, the overall thickness of the tachocline is well within the range admitted by helioseismic constraints. In the most realistic case of a time and latitude dependent tachocline thickness linked to the value of the Maxwell stress, both the thickness and its latitude dependence are in excellent agreement with seismic results. In the nonparametric models, cycle related temporal variations in tachocline thickness are somewhat larger than admitted by helioseismic constraints; we find, however, that introducing a further parameter into our feedback formula readily allows further fine tuning of the thickness variations.Comment: Accepted in Solar Physic

Surface Flux Transport on the Sun

We review the surface flux transport model for the evolution of magnetic flux patterns on the Sun's surface. Our underlying motivation is to understand the model's prediction of the polar field (or axial dipole) strength at the end of the solar cycle. The main focus is on the "classical" model: namely, steady axisymmetric profiles for differential rotation and meridional flow, and uniform supergranular diffusion. Nevertheless, the review concentrates on recent advances, notably in understanding the roles of transport parameters and - in particular - the source term. We also discuss the physical justification for the surface flux transport model, along with efforts to incorporate radial diffusion, and conclude by summarizing the main directions where researchers have moved beyond the classical model.Comment: 35 pages, 11 figures, accepted for publication in Space Science Review