Solar dynamo

Builds on Dynamo theory Magnetohydrodynamics Cowling's antidynamo theorem

Definition

The solar dynamo is the dynamo that maintains the large-scale magnetic field of the Sun in its convection zone, against ohmic decay. In the mean-field formulation, split the velocity and the magnetic field into averages over longitude and fluctuations, $u = U + u'$ and $B = \bar B + b'$ . The mean field $\bar B$ obeys the mean-field induction equation of magnetohydrodynamics: $\frac{\partial \bar B}{\partial t} = \nabla \times \left( U \times \bar B + \alpha \bar B \right) + \eta_T \nabla^2 \bar B, \qquad \nabla \cdot \bar B = 0.$ Here the mean flow $U$ contains the differential rotation and the meridional circulation of the Sun. The scalar $\alpha$ describes the mean electromotive force of the helical small-scale motions. The constant $\eta_T > 0$ is the turbulent magnetic diffusivity. A solar dynamo model is a solution of this equation in a spherical shell, with $U$ close to the observed rotation of the Sun. The solution must not decay and must oscillate in time.

Remarks

The mean field splits into a toroidal part, along circles of latitude, and a poloidal part, in meridional planes. The shear of $U$ turns poloidal field into toroidal field, the $\Omega$ -effect, and the term $\alpha \bar B$ turns toroidal field into poloidal field, the $\alpha$ -effect. Models with both effects are called $\alpha\Omega$ dynamos.

Example: take a local Cartesian model with constant $\alpha$ and constant shear. The $\alpha\Omega$ equations have travelling wave solutions, which grow when the product of $\alpha$ and the shear is large enough. Parker called these dynamo waves, and they model the migration of the sunspot belts toward the equator.

Non-example: take an axisymmetric flow acting on an axisymmetric field, with $\alpha = 0$ and molecular diffusivity in place of $\eta_T$ . By Cowling's antidynamo theorem, it cannot sustain the field. So the non-axisymmetric fluctuations behind $\alpha$ are essential.

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Tag	`PGC8JZ6XYS`
URI	`m2://PGC8JZ6XYS`
Kind	definition
Writing	W0 stub
MSC	85A30, 76W05
Defines	Solar dynamo
Uses	Dynamo theory, Magnetohydrodynamics, Cowling's antidynamo theorem
Changed	3 November 2026

Solar dynamo

Definition

Remarks

Reading path

Further reading

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