Competing ⍺-effects in the solar dynamo

Abstract

The large-scale magnetic field in the Sun varies with a period of approximately 22 years, although the amplitude of the cycle is subject to long-term modulation with recurrent phases of significantly reduced magnetic activity. It is believed that a hydromagnetic dynamo is responsible for producing this large-scale field, although this dynamo process is not well understood. Any dynamo that is responsible for the generation and maintenance of a large scale magnetic field requires mechanisms that are able to convert poloidal field lines into toroidal field lines and vice versa. Differential rotation is widely accepted to generate toroidal field however the converse process that is required for poloidal field regeneration is still a topic of some debate. This thesis aims to investigate how competing mechanisms for poloidal field regeneration (namely a time delayed Babcock-Leighton surface α-effect and an interface-type α-effect) interact with each other, leading to the modulation of the dynamo wave. Initially, the study completed by Jouve et al. (2010) is expanded upon to include both sources for poloidal field regeneration. This requires solving the standard αω dynamo equations in one spatial dimension, including source terms corresponding to both competing α-effects in the evolution equation for the poloidal field. In addition to solving the one-dimensional PDEs directly, using numerical techniques, a local approximation is used to reduce the governing equations to a set of coupled ODEs, which are studied using a combination of analytical and numerical methods. In the ODE model, it is straightforward to find parameters such that a series of bifurcations can be identified as the time delay is increased, with the dynamo transitioning from periodic states to chaotic states via multiply periodic solutions. Similar transitions can be observed in the full model, with the chaotically modulated solutions exhibiting solar-like behaviour. Further refinements to this model produce similar results albeit in a smaller region of parameter space. In order to impose more realistic physical properties of the system, the αω dynamo equations with both mechanisms for poloidal field regeneration are then solved numerically in two spatial dimensions. Upon retaining a parametrised time delayed field, the 2D code is able to produce modulation that is similar to that found in the 1D system. Removing the parametrised time delayed field, a shallow flow is imposed and the equations are solved in full. Modulation is found when the relative strength of the competing α-effects are varied and it is also apparent that the parity of the dynamo wave is dependent upon the strength of the meridional flow.