The coronal magnetic field 1

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Number: 67
1st Author: Hugh Hudson
2nd Author:
Published: 15 January 2008
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Interpreting solar X-rays and gamma-rays ultimately requires that we understand the coronal magnetic field. The reason for this is that the particles that emit the radiation RHESSI detects are bound to the field lines. This is even true for the background coronal plasma, where the particles have much lower energies, as shown in Figure 1. The striations, enhanced in visibility by judicious radial filtering, have forms that strongly reflect the presence of a significant magnetic force in the solar corona. Eclipse photos such as this one have provided convincing qualitative evidence for solar magnetism long before Hale demonstrated it spectroscopically in sunspots.

	Figure 2: The solar corona, at solar maximum, seen in an eclipse picture.	 	

This is the first of a projected series of RHESSI science Nuggets giving short essays on the general subject of coronal magnetism, which is important for both organizing the source geometry and for providing the energy and the particle acceleration.

Solar field and terrestrial field

The Earth's magnetic field has the basic form of a dipole, and the regular pattern of field at the surface of the Earth is stable enough to guide mariners via use of a compass. This dipole is thought to be the result of dynamo. Currents flowing in the core generate magnetic fields which penetrate the nonconducting mantle of the earth and diminish rapidly with height. The solar field, on the other hand, is enormously complicated at the surface but approximately dipolar at large distances, because the solar wind flow enforces two sectors with inward and outward fields associated with their corresponding polar coronal holes. There is no true dipole magnet deep in the interior of the Sun. Density and |B|, and "beta"

We observe, from large-scale imaging in soft X-rays or the EUV, that the large-scale coronal structures changes only slowly, except during flares and CMEs. The forces acting on the coronal plasma in such a static condition come from gravity and from the Maxwell stress tensor. The former is easy - the hydrostatic law n = noe-h/H , where h is the height above the photosphere and H is the scale height, determined by gravity, composition, and temperature is applicable. A rough value for the scale height is 0.07 solar radii at the surface, and increases with height as gravity weakens. The Maxwell-stress term is also easily understood; the magnetic field can be described for these purposes as a bundle of magnetic field lines, each with a tension related to its curvature, plus an isotropic pressure proportional to B2. These properties of the magnetic field can be combined and simplified by calculating the "beta" parameter of plasma physics. This is the ratio of gas pressure to magnetic pressure, and a kind of upper limit to the coronal values is shown in Figure 2. This assumes the field to be strictly dipolar and static; the kink at 2.5 solar radii shows roughly what happens when the solar wind breaks these assumptions. In the solar wind, the plasma beta should increase approximately as the distance from the Sun. When the plasma beta is low, the magnetic forces dominates over gravity and inertia. This is true everywhere in the corona, except possibly for prominences.

Figure 2: The plasma "beta" - the ratio of gas to magnetic pressure - in a radial cut across the corona. The dotted lines show, left and right, the photosphere and the conventional "source surface."


Since the appearance of a new-cycle sunspot on New Year's (2008), we can expect new X-class flares and new views of particle acceleration. We therefore need to be as ready as possible with our understanding of the coronal magnetic field! See Figure 3 for a view of the new-cycle region and stay tuned for more information about the coronal magnetic field in future Nuggets.

Figure 3: The first reasonable sunspot group of Solar Cycle 24. It even flared! Note the reversal of polarity and the high latitude of the new region. Biographical note: Hugh Hudson is a RHESSI group member at Berkeley.

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