Solar Dynamo

Understanding the inner workings of the Sun's magnetic field requires an understanding of the motion of ionized gases under the influence of electromagnetic fields.  This merging of the sciences of ionized gases, fluid mechanics, and electromagnetism is called magnetohydrodynamics, or MHD.  Many of the founding principles of this field were discovered by Hannes Alfven (Alfven 1942). Alfven received the Nobel prize for this work in 1970.

Due to the complexity of the MHD equations, progress was slow in the days prior to easy access to computers.  In addition, some of the simplifications used to develop the models had problems of their own. The "Cowling antidynamo theorem" demonstrated that a pure axisymmetric model cannot produce a self-exciting dynamo (Cowling 1945, Cowling 1955).  Because of this, solar dynamo models had to include a component that 'breaks' this axial symmetry. The first major breakthrough towards a self-consistent dynamo model was due to E.N. Parker, who postulated that helical turbulent convection in stellar interiors would be able to circumvent the anti-dynamo theorem (Parker 1955). The first model integrating MHD concepts that successfully described many observed features of the solar magnetic cycle was presented by H.W. Babcock in 1961 (Babcock, 1961). More detailed models were developed as computational power increased.

The model used for these visualizations was developed by Andres Munoz-Jaramillo (Montana State University), Dibyendu Nandi (Indian Institute of Science Education and Research, Kolkata) and Petrus C.H. Martens (Harvard Smithsonian Center for Astrophysics) as part of a NASA Living With a Star funded research on solar-stellar magnetic fields. In this model, the toroidal component (fields and flows that are in the direction of rotation) are separated from the poloidal component (flows and field that are in the meridional plane perpendicular to the direction of rotation). This makes the model axisymmetric which simplifies some of the computations but means the model cannot be used to study non-axisymmetric features such as active-longitudes. Cowling's anti-dynamo theorem is bypassed through a phenomenological treatment of poloidal field creation through the buoyant eruption of tilted bipolar sunspot pairs. This model is described in detail in a recent research article (Munoz-Jaramillo, Nandy, Martens 2009).

In these models, the toroidal field is strongest deep in the solar interior, where it is produced by solar differential rotation and stored in a stable layer just beneath the convection zone. The poloidal field component, which is about 1000 times weaker than the toroidal field component, is strongest near the surface of the Sun. These dynamo models show that the toroidal and poloidal field components are regenerated from each other, creating alternating positive and negative signed field belts.

The poloidal field generated near the surface first moves poleward where it cancels the older polar field and creates the new cycle polar field (with opposite sign). In this poleward transport process the near-surface poleward meridional flow plays a crucial role. Subsequently the po

For more of the general technical and mathematical details of solar dynamo modeling, check out the review "Dynamo Models of the Solar Cycle" by Paul Charbonneau in Living Reviews in Solar Physics.

Frequently Asked Questions

Why does the field reverse?

The solar dynamo cycle involves the regeneration of the toroidal and poloidal components of the magnetic field driven by the energy of convective flows. In this dynamo model, a toroidal field of a particular cycle (say, n) generates a poloidal field for this cycle (n) with the same sign. However, the poloidal field of cycle (n) generates the toroidal field of the next cycle (n+1) which is opposite in sign to the previous cycle. This change in sign is due to the way the solar differential rotation is structured. Thus the orientation of the bipolar sunspot pairs, which are produced from the

Useful Links:

• The Sunspot Cycle (NASA/MSFC)
• The Sunspot Cycle (Windows to the Universe)

To generate these visualizations, the poloidal magnetic potential and the toroidal magnetic vector component were extracted for each time step of the model. The radial and latitudinal magnetic vectors are computed from the poloidal magnetic potential. These data are then color-mapped to create the slices visible as the model opens. The magnetic field lines are propagated from fixed locations (near the surface at the north and south poles of the Sun, and in the interior at mid-latitude regions) for each time step. The field lines are not moving but being regenerated at each time step of the model. The model was processed from the FITS data file using python, numpy and scipy.  These components were then assembled into a complete model and rendered using Maya(TM) and RenderMan(TM).

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