A. The Magnetic Sun

We can "see" inside the Sun using helioseismology, allowing us to determine how the Sun rotates and how that rotation interacts with convection to give complicated motions.  The interior of the Sun is made of a highly conducting fluid of charged particles (a plasma), and these motions generate electrical currents.  Any electrical current has a magnetic field associated with it.  Since the material of the Sun is so highly conducting, the magnetic fields are "frozen in" to the fluid and cannot move independently.  The fluid will concentrate the magnetic field until the energy density in the magnetic field equals the energy density of the gas.  We have already seen what the gas energy density is (an energy density has units J / m³ = N / m² = F / A but force per unit area is pressure) P = nkT.  The energy density in the magnetic field (or the magnetic field pressure) is B²/2m₀. where B is in Tesla, and m₀ = 4p x 10^-7 W/A-m. is the permeability of free space.

• Gas pressure (or energy density) P_g = nkT
• Magnetic pressure (or energy density) P_mag = B²/2m₀
• Ratio is an important quantity called plasma beta: b = nkT / B²/2m₀


If the gas pressure is greater than the magnetic pressure (b > 1, a high-beta plasma), the gas will control the structure of the atmosphere.  If the magnetic pressure is greater than the gas pressure (b < 1, a low-beta plasma), the magnetic field will control the structure.  The study of the interplay between magnetic fields and fluids is called magnetohydrodynamics or MHD.

The interior (and surface, or photosphere) of the Sun is normally a high-beta plasma.  That means the magnetic field can be pushed around by the fluid.  However, magnetic fields are like unbreakable ropes, or rubber bands.  They get wound up tighter by the fluid until the magnetic field strength becomes so great locally that P_mag  ~ P_g, and after that they are not easily pushed around by the plasma. At the surface,this interplay between plasma motion and magnetic field is seen in sunspots, granulation, and supergranulation. Velocity images (dopplergrams) with solar rotation and supergranulation, with solar rotation removed, with both rotation and supergranulation removed .

Sunspots: Areas of high magnetic field strength where electric currents have been concentrated by fluid motions inside the Sun until the magnetic pressure equals the gas pressure.  The high field strength inhibits convection, and hence heat flow, into the spot, so the spot is much cooler (4500 K) than the surrounding photosphere (5770 K).  That is why spots appear much darker than the photosphere, but in fact they are not dark--they would glow quite brightly if seen against a dark background.

The corona of the Sun is a low-beta plasma.  That means the magnetic field is in control, which explains why the corona is full of magnetic loops.  The low density material in the corona has to follow the magnetic field lines.
 

Corona in X-rays: The solar corona has a low gas density, but relatively high magnetic field strength emanating from sunspots.  Here the magnetic pressure is greater than the gas pressure, so magnetic loops dominate the structure.  The magnetic fields are a source of stored energy, and the release of that energy makes the corona so hot that it shines brightly in X-rays, especially in regions of especially strong magnetic fields.

B. Solar Activity

The Sun goes through an 11-year activity cycle, where the number of sunspots becomes almost zero, then grows to a large number, then back to near zero over approximately 11 years.  Here is the changing sunspot number over the last 11 years.  In 2007 we were in sunspot minimum, when there were almost no sunspots, but for some reason the minimum continued for three years, only starting to rise in late 2009.  The dotted and dashed curves are two predictions of what the sunspot number may be next year. 

The plot below shows the previous sunspot cycle (#23) and the start of the current cycle (#24) in a somewhat different way.  The chart on the right is just the sunspot number as before, but the chart on the left shows the latitude dependence of the sunspot locations on the Sun.  Notice that early in the cycle, the sunspots generally start appearing near 30 degrees latitude on the Sun.  Over the cycle they occur at progressively lower latitudes. At the current time of the new solar cycle, they appear again at high latitudes, and late in the cycle they appear near the equator.  This is called a butterfly diagram.

The next plot shows the butterfly diagram for the last 140 years!  Notice that the sunspot cycle is very regular, but seems to have been growing stronger over the more recent cycles. However, there have been predictions that the solar cycle is declining again, and this seems to be borne out by the latest solar cycle.

This butterfly diagram and at least two other effects, Joy's Law, and Hale's Law, can be explained in a rough way by the operation of a solar dynamo.  A 2D movie shows the influence of "meridianal flow." With the addition of Hale's Law, the solar cycle is actually seen to be a 22-year cycle. Here is the "magnetic butterfly diagram."

Magnetic fields can be measured in the photosphere using the Zeeman Effect.  Below is an "image" of magnetic field strength showing not only the strength of the sunspot regions, but also their magnetic polarity.  White in the image represents fields coming out of the Sun (north magnetic polarity) while black represents fields going into the Sun (south polarity).
 

Magnetic Fields: The sunspots in the image at right are revealed to be areas of strong, opposite polarity magnetic fields, which extend to even larger areas than the spots themselves.

Notice the lighter areas, called faculae, which are found near sunspots and are also areas of strong magnetic field.

Sunspots and their surrounding magnetic field areas are called active regions.  Active regions are the site of solar flares, vast explosions of energy that send high-energy particles (electrons and protons mostly, but some helium atoms and a very few heavier elements) into space.  They are also involved in a phenomenon called coronal mass ejections (CMEs), which are spectacular "bubbles" of magnetic field and plasma that lift off from the Sun and expand quickly into interplanetary space.  Sometimes these CMEs are directed toward Earth, and when they run into the Earth's magnetosphere they can cause magnetic storms. Here is a Sun to Earth movie using actual data. See the SDO daily data page. Here is a link to a recent solar flare seen with NJIT's Expanded Owens Valley Solar Array.