Dynamos in Physics Today

One of the standard jokes in astrophysical modeling is that if there is ever a discrepancy between your model and observations you simply attribute it to some combination magnetic fields and turbulence.  Let's say your model of star formation fails miserably to reproduce the observed initial mass function in our galaxy.  What do you do?  Blame turbulence and magnetic fields, present some overly simplistic explanation of why turbulence and magnetic fields would give you the right answer if you could just capture them properly, and then promise to include them in some ill-defined future simulation.

These two phenomena have a fundamental link  - dynamo action.  In the words of a very well-written article by two of the top researchers in the field of laboratory dynamos, Cary Forest and Daniel Lathrop, "[a]ll astrophysical plasmas are, as far as we know, magnetized and turbulent" and thus ripe for dynamo action.  The problem is that we are orders of magnitude removed in both simulations and experiments from some of the physical regimes where dynamo action takes place, even within our own solar system (see the graph on the right).

Check out the article over at Physics Today for a great explanation of why dynamos are so ubiquitous, why they are so hard to predict, and what is being done with theory, modeling, and laboratory experiments to unravel the mystery.

The Solar Dynamo

This is part two of my series of posts on the exciting field of solar physics. For part one, click here.

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Despite centuries of study, we fundamentally don't understand how the sun generates its magnetic field and magnetic cycles of activity, but we do have some ideas. Here's what we know about the way the sun (and by extension other stars) produces and varies its magnetic field.

The source of the sun's magnetism is some kind of dynamo process. Dynamos occur when a highly conducting material shears against itself in the presence of a magnetic field. There are several requirements for this to occur. First, the material must be a very good conductor, such as the ionized plasma in the solar interior or the liquid iron in the earth's core. A good conductor means that charge carrying particles are essentially free to move through the material. When a free, charged particle encounters a magnetic field line, it will begin to move along that field line in a helix pattern. The magnetic field forces the fluid to move along it, while the fluid circling the field line creates a current that reinforces the magnetic field. This is referred to as the frozen in condition because the fluid can only flow along magnetic field lines and the magnetic field lines are continually regenerated by the motion of the fluid. In non-superconducting materials, like the solar interior, this is an imperfect process and it is not strictly true, howeverthe frozen in condition is still a good approximation.

In the solar convection zone, magnetic fields exist in the middle of extremely turbulent convection. When the convective motions cause motion of the fluid along a magnetic field line, they stretch the field line, much like taffy stretches when you pull it. This stretching puts energy into the magnetic field, causing it to grow stronger. The solar interior is therefore one gigantic, fusion-powered taffy pull which constantly regenerates the sun's magnetic field.

I should also mention that dynamo processes are inherently non-linear. The "taffy pull" effect requires advection, which mathematically comes in the form of the gradient of the velocity squared. That term (and a couple other non-linearities) cause me to periodically wake up at night in a cold sweat. Because of the non-linear properties, dynamos are both generally chaotic and almost impossible to work with analytically (although some brave people like Matthias Rempel at the National Center for Atmospheric Research try anyway). This means that almost all theoretical work must be done numerically.

So a dynamo seems like a nice theoretical construct for the source of the sun's magnetic field, but is that actually what is going on? And what about those cycles of magnetic activity? Can a dynamo explain that butterfly diagram from the last post? Tune in to my next post and we'll talk about how we investigate what is actually happening inside the sun.