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Modulated cycles in an illustrative solar dynamo model with competing α-effects

Lookup NU author(s): Laura Cole, Professor Paul BushbyORCiD



This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).


Context: 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. Aims: Within the framework of mean-field dynamo theory, our aim is to investigate how competing mechanisms for poloidal field regeneration (namely the Babcock-Leighton surface alpha-effect and an interface-type alpha-effect), can lead to the modulation of magnetic activity in a deep-seated solar dynamo model. Methods: We solve the standard alpha-omega dynamo equations in one spatial dimension, including source terms corresponding to both of the the competing alpha-effects in the evolution equation for the poloidal field. Following Jouve, Proctor & Lesur (2010), the surface alpha-effect is assumed to be proportional to a time-delayed toroidal field. This system is solved using two different methods. In addition to solving the one-dimensional partial differential equations directly, using numerical techniques, we also use a local approximation to reduce the governing equations to a set of coupled ordinary differential equations (ODEs), which are studied using a combination of analytical and numerical methods. Results: 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. Conclusions: Competing alpha-effects could explain the observed modulation in the solar cycle.

Publication metadata

Author(s): Cole LC, Bushby PJ

Publication type: Article

Publication status: Published

Journal: Astronomy & Astrophysics

Year: 2014

Volume: 563

Print publication date: 01/03/2014

Online publication date: 19/03/2014

Acceptance date: 17/02/2014

Date deposited: 02/10/2015

ISSN (print): 0004-6361

ISSN (electronic): 1432-0746

Publisher: EDP Sciences


DOI: 10.1051/0004-6361/201323285


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