Magnetic fields in active regions

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Number: 59
1st Author: Hugh Hudson
2nd Author: Lyndsay Fletcher
Published: 4 January 2007
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In this Nugget we discuss some of the basic properties of the solar corona as background information. "Solar corona" means different things to different people, not surprising since its physical properties span at least six decades in density and three or four in temperature and in B, the intensity of the all-important magnetic field. For high-energy observations such those by RHESSI, we need to know about the corona in active regions, close to the photosphere. Here we find intense fields, a range of densities, and other properties that make it possible for this tenuous medium to produce RHESSI's gamma-ray flares. What produces these magnetic fields, and how do theorists make use of them? Publisher's note: this Nugget is sort of a theoretical backgrounder, not directly related to RHESSI as such, but that's OK.

Magnetic field: photospheric and coronal

To a first approximation a sunspot is a large region of intense unipolar magnetism in the solar photosphere. The field can be deduced from the Zeeman splitting it produces in the line spectrum, and with full polarization measurements (the Stokes parameters) one can deduce the vector field. Figure 1 below shows the results of such Stokes measurements on a large sunspot. Typically the large sunspots, the ones which lie below the active regions that produce gamma-ray flares, have dimensions on the order of 30,000 km and central magnetic intensities of up to a few thousand Gauss.

Figure 1: Vector field measurements of a large sunspot. From left to right, the azimuth angle of the field, its horizontal component, and its vertical component. The field of view is 35 Mm (about 45 arc sec) across. But what is the field in the corona, where we believe the flare action to occur? Roughly speaking, the photospheric field should extend into the corona as high as a unipolar region (e.g., a spot) is wide. But this is just an order-of-magnitude statement, and for theoretical purposes we would like to have better knowledge. We cannot observe the coronal field directly by Zeeman spectroscopy, so there is an active community struggling to make model (MHD-based or otherwise) extrapolations from the field observed in the photosphere from data like that shown in Figure 1. With STEREO data now becoming available, this is an exciting time for this activity since we can see the coronal magnetic structures in full 3D.

But there is a direct measurement technique based upon microwave spectroscopy, taking advantage of the gyroresonance resulting from the Larmor motion of the electrons. This confirms directly that the scale height of strong fields in active regions is of the order of 104, as expected from the basic geometry:

Figure 2: Illustrating the gyroresonance technique in a model sunspot field seen in cross-section. The "x mode" and "o mode" follow the birefringence of the medium due to the presence of the magnetic field, so that its polarization provides a signature of the field sharply localized in the shells seen in the upper panel. This is all very complicated, so here is a reference for those interested in the gory details. In summary, both theory and observation agree that fields comparable to sunspot fields exist in the low corona, at altitudes comparable to sunspot dimensions. Since powerful solar flares - the gamma-ray events in particular - happen in these regions, these fields should be used by theorists working on particle acceleration theory to explain the RHESSI observations. A previous Nugget shows a nice example of flare effects in a sunspot umbra (see Figure 4 of that Nugget).

Coronal Alfven speed

The strong fields in the active-region corona imply large Alfvenspeeds. Briefly, waves analogous to sound waves exist in a magnetized plasma, and the Alfven speed is the analog of the sound speed. These waves are crucial to understanding the plasma dynamics, and hence to figuring out the RHESSI hard X-ray and gamma-ray observations. The restoring force in these wave motions is not just gas pressure, but a combination of gas pressure and magnetic forces, including the magnetic pressure. The Alfven speed is given by

where B is in Gauss, ne is the electron density in cm-3, and the Alfven speed vA is in cm/sec. We (the Nugget authors) were somewhat surprised to put this information together: B of 1,000 G at a density of 109 cm-3, reasonable for an altitude of 10,000 km near a large sunspot, results in vA = 60,000 km/s, or 0.2 times the speed of light!


We have discussed the basic parameters B and vA in magnetic active regions in the corona. Most textbooks will not mention such large fields as "coronal", mostly they will also assert that the "coronal" Alfven speed is less than 10% of the estimate above. This is the danger of trying to characterize a complex medium such as the solar corona with typical values. It is extremely important to recognize these more correct estimates, which incidentally also imply a remarkably low plasma beta of 2 x 10-5, because of their strong influence on theoretical considerations. We'll defer discussing plasma beta to some future Nugget. Our new values of B and vA are entirely reasonable but very different from the values normally assumed by theorists, so we think that adjustments to some of their theories may be necessary.

Biographical note: Hugh Hudson and Lyndsay Fletcher are RHESSI team members at UC Berkeley and at Glasgow University, respectively. We borrowed the figures from papers by S. Mathew and S. White.

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