Tuesday, March 4, 2008

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.

1. How close does the sun's dynamo model work in analyzing the core of the earth I mean, there is hot plasma inside the earth which effects magnetic fields right? (If not this shows I didn't take geology.) How closely are these processes like those in the sun?

If they are similar, do you get "sunspot" type structures in the earth's core?

If these questions sound like I am completely uninformed it is because I am.

I guess the larger question I am getting at is: Do all plasmas in magnetic fields generate sunspot type structures? If so, might these be in things like the Earth's core assuming the earth's core has plasmas somewhere.

2. The Earth's dynamo follows the same general dynamo model as the sun's, however there are some differences that change the results of the geodynamo as compared to the solar dynamo.

The first has to do with that "frozen in" condition that I referenced. In a superconductor, the fluid is truely forced to flow along field lines. However, in the solar convection zone, there is some resistivity which means that the magnetic field is not completely frozen in place - it can and does slowly diffuse outward. In a sun spot, this diffusion is unimportant because sun spots only last on the order of weeks while the magnetic diffusion times are on the order of hundreds of years. The earth's core, however, has much higher resistivity than the solar interior or surface, so it allows magnetic fields to diffuse on much shorter time scales.

Also, the flows that power the dynamo in the earth's core are extremely slow (~100 meters per year) compared to flows in the solar interior (~1 kilometer per second). This leads to much weaker fields (~0.5 Gauss) in the Earth's magnetic field than the sun's (up to 1 kiloGauss). This makes the non-linear terms much more important in the sun than the earth.

Interestingly, the code we use to model the sun's interior was originally designed by Gary Glatzmaier to work on the Earth's dynamo. Gary Glatzmaier is widely credited with proving the mechanism for generating the Earth's magnetic field.