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A Millennium of Geomagnetism

5.   Sunspot Magnetism and the Terrestrial Dynamo

Reviews of Geophysics, 40(3), p.1-1 to 1-30, Sept 2002
David P. Stern, Laboratory for Extraterrestrial Physics
Goddard Space Flight Center, Greenbelt, MD 20771

Table of Contents

Clicking on any marked section on the list below brings up a file containing it and all unmarked sections immediately following it on the list. This list is repeated at the beginning of each file.

  1. Introduction
  2. Early discoveries
  3. William Gilbert
  4. Halley
  5. Coulomb
  6. Oersted and Ampere
  7. The Lodestone
  8. Gauss and Humboldt
  9. Explorations and Surveys
  10. Faraday's Lines of Force (field lines)
  11. Faraday's Disk Dynamo
  12. Sunspots
  13. The Dynamo Process on the Sun
  14. The Earth's Dynamo
  15. Dipole Reversals and Plate Tectonics
  16. Magnetic Storms and Ring Currents
  17. The Magnetosphere
  18. Magnetic Reconnection
  19. Planetary Magnetospheres
  20. Assessment

Chronology of Geomagnetism

References: A-G
References: H-P
References: Q-Z

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12. Sunspots
Group of sunspots

    The story of the Earth's magnetism is strongly tied to that of solar research, in several ways. Large magnetic storms, and observations of "northern lights" far south from their usual locations (i.e. of the "aurora borealis," now commonly known as "polar aurora"), were found to be associated with solar phenomena. And not only did the Sun have a magnetic field, but concentrated sources of that field--dark sunspots--were visible on its surface, quite unlike the sources of the Earth's field which are buried deep in the Earth's core. This led to valuable insights into how the geomagnetic field might be generated.

    Sunspots were first reported in 1609, independently by Galileo, Scheiner and Fabricius [Newton, 1958; Phillips, 1992], all of whom used the newly invented telescope. Sporadic reports of earlier observations also exist, because the unaided eye can see large sunspots when thick haze dims the Sun near the horizon. Unfortunately, sunspots practically disappeared for a 70-year period starting around 1645 ("the Maunder minimum"). During those years the interest of astronomers wandered elsewhere, and when spots again became frequent, they were not investigated systematically.

    The 11-year sunspot cycle was discovered accidentally by Heinrich Schwabe (1789-1875), a German pharmacist and amateur astronomer living in the town of Dessau [Meadows, 1970; Newton, 1958]. Schwabe was looking for a yet-unknown planet of the Sun, moving inside the orbit of Mercury. Such a planet (given by other searchers the tentative name of Vulcan) would be hard to spot (except during a total solar eclipse) because its position in the sky would always be close to that of the Sun, where daylight would obscure it. Schwabe hoped to observe it as a dark spot moving across the face of the Sun, and day after day, year after year, whenever the sky was clear, he observed the Sun and looked for it.

    To properly conduct such a search, Schwabe also had to identify and track sunspots, to make sure none was mistaken for a new planet. He did so from 1826 onwards, and by 1843 he noted a cyclical rise and fall in their number, as well as in the number of days when no spots were observed. He then published a table of his yearly totals, but until 1851 it attracted little notice, except from Rudolf Wolf, noted below. Then Alexander von Humboldt republished it (extended to 1850) in the third volume of his "Kosmos," and suddenly sunspots and their cyclic behavior became a hot scientific topic.

    Rudolf Wolf (1816-93) of Berne (later of Zürich) collected earlier observations, tracing sunspot cycles before Schwabe's time. He introduced the "Zürich sunspot number," an empirical criterion for the number of spots, taking into account the fact they usually occurred in tight groups. The length of the sunspot cycle turned out to vary, but the average value was near 11 years. Sir Edward Sabine (1852) found an association between the sunspot cycle and the occurrence of large magnetic storms, and Richard Carrington (1826-75), also in England, studied the rotation of sunspots around the Sun, noting that their period and other properties depended on latitude.

    In September 1859 Carrington (as well as R. Hodgson, another British observer) saw by chance a bright outburst of light in a group of large sunspots, lasting about five minutes [Meadows, 1970; Newton, 1958]. This was followed 17 hours later by a very powerful magnetic storm, strongly suggesting a connection, although Carrington cautiously commented "One swallow does not make a summer."

    But what were the sunspots themselves? We now believe that they appear darker because they are slightly cooler than the regions that surround them. Galileo speculated that they might be clouds floating in the Sun's atmosphere, blocking some of its light. Their most significant feature, however, was discovered only in 1908, by George Ellery Hale (1868-1938), leader among US astronomers, founder of great observatories and designer of novel instruments [Wright, 1966]. One of his inventions (in 1892) was the spectroheliograph, also devised independently in France by Deslandres (1853-1948), a spectrograph adapted to scan the Sun in a single spectral color, producing a photographic image. Whereas in white light the Sun presented (apart from its spots) a bland appearance, the spectroheliograph (e.g. tuned to the red H_ line of hydrogen) isolated light from higher layers in the Sun's atmosphere and revealed many new features. These included mottling of the surfaces, prominences arching high above the Sun (turning to dark linear features when passing in front of the Sun) and bright areas near sunspots. Hale also found that "solar flares," such as the one observed by Carrington and Hodgson, were much more frequently seen in H__light, and big ones indeed often preceded magnetic storms.

    In 1896 Pieter Zeeman discovered the "Zeeman effect" by which the characteristic colors ("spectral lines") of elements, when emitted by a gas located in a strong magnetic field, often split into two or more components of slightly different wavelength, with their separation depending on the intensity of the field. Using the Zeeman effect, Hale in 1908 showed that sunspots were in fact strongly magnetic, with a typical field intensity of 1500 gauss (0.15 Tesla). The spots generally appeared in pairs of opposite polarity, suggesting that field lines emerged from the Sun at one of the pair and re-entered at the other. One spot was usually ahead of the other in the direction in which the Sun rotated, and the magnetic polarity of the "leading" spot north of the equator, in any solar cycle, was always the same, and was opposite to the "leading" polarity south of the equator. In the following solar cycle both these polarities were always reversed, suggesting that the sunspot cycle was a magnetic phenomenon, with an average period near 22 years.

    Hale's method was greatly refined by Horace Babcock [Babcock, 1960, 1963; Phillips, 1992; Eddy, 1978], Robert Leighton and others. Using the polarization of Zeeman lines to construct a "solar magnetograph," they greatly increased the sensitivity of Hale's method, to the point where not only sunspot fields could be observed, but also a general dipole field of the Sun, of the order of 5 gauss. The existence of such a field had been suspected from a feature of the solar corona, the Sun's outer atmosphere, previously seen only during total eclipses of the Sun. At the poles the corona displayed rays or "plumes" in a pattern which reminded observers of magnetic field lines of a dipole, like the ones above the poles in Figure 6. The magnetograph also showed that this field reversed each 11-year solar cycle, typically 3 years after sunspot minimum.

13. The Dynamo Process on the Sun

    The Sun is a giant ball of gas, hot enough to conduct electricity (i.e. a plasma), much hotter than anything that exhibits permanent magnetism. Sunspot magnetism therefore had to come from electric currents, and in 1919 Sir Joseph Larmor proposed that such currents could be produced by a self-sustaining fluid dynamo [Larmor, 1919]. A Faraday disk can serve as a model of such a dynamo, if its magnetic field is created by an electromagnet, powered by the output current of the same disk (other types of generator also can be so designed). Energy must be supplied by the outside force which rotates the disk., and the presence of iron is not essential: if the "electromagnet" has an iron-free core, the magnetic field produced in it may be much weaker, but it would still exist.

    But what comes first in a dynamo, the magnetic field needed for producing the current, or the electric current needed to produce the field? This sounds a bit like asking, what came first, chicken or egg? Actually, if conditions are appropriate, even a very weak initial field is amplified exponentially, rising until (neglecting friction, viscosity, acceleration etc.) the opposing magnetic force on the current creates a torque matching the applied one.

    Larmor suggested that a similar situation may arise in an electrically conducting fluid, in which suitable flows are produced, e.g. circulation of the fluid due to heat convection, that can play the role of a rotating disk. He was quite tentative about it--just one brief paragraph, followed by two alternative suggestions (and his follow-up note of 1927 did not get any closer). The idea survived in part because nothing else seemed to lead anywhere, but implementing it--finding such flows in a conducting medium--proved quite difficult. In a conventional dynamo, the electric current is channeled by wires wrapped in insulators, in a way forcing it to generate the required magnetic field. In a continuous conducting fluid, no such channeling exists.

    Attempts to model fluid dynamos were further discouraged by the "anti-dynamo" theorem of Thomas G. Cowling (1906-1990), who proved that the fluid dynamo problem had no axially symmetric solutions [Cowling, 1933, 1985]. That eliminated easy and simple solutions, and some researchers began to wonder whether solutions existed at all.

    A useful concept in the theory of plasmas and of conducting fluids is the "freezing" of magnetic field lines, developed by Walén [1946] and by Alfvén [1950; Alfvén and Fälthammar, 1963] , although the idea itself may be older. It can be shown that in a fluid with extremely high electrical conductivity, such field lines are "frozen" into the plasma, in the sense that two particles which share the same field line at any time, usually continue doing so later on, even when the flow has separated them and has deformed their magnetic field. In fluids whose conductivity is merely large, not infinite, Cowling showed that field lines slowly slipped from their "frozen" positions. The criterion for "extremely high" also involved the dimensions of the flow, and was therefore more likely to be fulfilled by large-scale flows, on the Sun and in the Earth's core, rather than in the laboratory.

    For instance, the "solar wind" which flows more-or-less radially outwards from the Sun is a hot plasma and may be viewed as such a conductor. The region at which this wind originates is permeated by magnetic fields, originating in the global solar dipole and in sunspot regions. As some solar wind ions move out radially to the Earth's orbit and beyond, others on the same field lines but deeper in the Sun's atmosphere stay behind. By the "field line preservation" theorem, however, they continue to share the same field line.

    Out near Earth, the field carried by the first group forms the local interplanetary magnetic field (IMF). The particles left behind on the Sun, on the other hand, have meanwhile rotated with the Sun to other meridians. Solar wind particles on the same field line will therefore be on different meridians than the "roots" of that line on the Sun. The longer these particles have traveled through space, the more have their "roots" rotated and therefore the greater the difference in solar longitude from those roots, suggesting that the magnetic field lines curve to form a spiral, which ultimately becomes wrapped tighter and tighter. This curvature has indeed been observed by spacecraft, at the Earth's orbit and throughout the solar system, suggesting that the solar wind "remembers" its solar roots for days and even months after leaving the Sun.

    The stretching of magnetic field lines in general implies an amplification of the magnetic field. The intensity of the IMF, for instance, decreases with distance R from the Sun like R-1 (for the azimuthal component, in the direction of the rotation) or like R-2 (for the other components), whereas that of the undistorted dipole decreases much faster, like R-3 . If the Sun's field were a pure dipole, its intensity at the Earth's orbit would be much weaker than what is actually observed.

    On the Sun, such stretching may be expected from the observed uneven ("differential") rotation of the photosphere, the visible surface layer of the Sun. The rotation period, as seen from Earth (whose motion around the Sun adds to it about 2 days) can be measured from the apparent motion of sunspots, and its value in days, as function of the latitude in degrees, is shown in Table 1 [Newton, 1958]      

    Latitude          Period     
    (degrees)            (days)      
        0            26.7     
        10           27.1    
        20            27.6    
        30            28.4     
        40            29.6     

Table 1   Rotation period of the Sun as function of latitude
The difference in periods presumably reflects heat-driven flows in the Sun. If the Sun had started off with a dipole field, the differential rotation would have gradually wrapped field lines around it (Figure 9), in opposite directions north and south of the equator.
Fig. 9   Schematic view of the way the faster rotation of the Sun's equator might wrap magnetic field lines around the Sun.

    The original idea was that this happened not too far below the visible surface (today we are less sure [Parker, 2000]) . As field lines become draped around the Sun, they become denser, meaning the intensity B of the wrapped field would grow, and theory predicted that a growing "magnetic pressure" (proportional to B2) would develop in the tube-like region those lines occupy. That pressure pushes plasma out of the tube, reducing its density and causing parts of the tube to float up and break the surface, becoming visible as sunspot pairs. Note that since the field's direction is reversed in opposite hemispheres, the spots leading the pair in the direction of the rotation have opposite polarities north and south of the equator.

    A subtle problem needs to be addressed, however [Elsasser 1955, 1956a,b] . In a spherical geometry, like that of the Sun, magnetic fields can be divided into two classes, toroidal and poloidal fields. If the field is axially symmetric, poloidal field lines lie in meridional planes (like those of the dipole field) while toroidal field lines form circles around the axis of symmetry. However, non-symmetric modes also exist in each class--for instance the main field due to the Earth's core and observed near its surface is poloidal. In principle, every magnetic field can be resolved into toroidal and poloidal parts. If for some reason the dynamo process creating the field stopped, electric resistance would cause a gradual decay of the field, and it can be shown that each class decays independently of the other.

    The scenario envisioned above began with a dipole field, which is purely poloidal. The stretching of the field line due to uneven rotation adds and amplifies a toroidal field, proportionally to the "seed" poloidal field. However, unless that "seed field" itself gets reinforced, one can foresee that after some time, electrical resistance will cause the currents that produce it to decay, and without the "seed" the entire dynamo process comes to a halt.

    Resistive decay might take many millions of years, but what is actually observed is different and much faster--the reversal of the poloidal field (and hence also of the toroidal field it produces) every 11-year solar cycle. This suggests some sort of This suggests some sort of feedback, and Eugene Parker suggested [Parker, 1955, 1979, 2000] that it arose from cyclonic motion, like the one seen in hurricanes. Namely, the interaction between the rising motion of plasma above sunspots and the Sun's rotation caused the plasma to rotate around a vertical axis as it rose. Field lines embedded in the plasma were also twisted, from the toroidal wrap-around direction to the meridional direction, which returned part of their field back to the poloidal component.

    The above ideas of the solar cycle were developed by the Babcock [1961] in the 1960s. More recent work [Parker, 2000] suggests that the Sun's magnetism may extend to a substantial depth, but many unsolved questions remain, including the causes of the uneven rotation.

14. The Earth's Dynamo

    If a fluid dynamo exists inside the Earth, it has to be in its core, with about half the radius of the Earth. The reason is that the process requires a conducting fluid, and the propagation of earthquake waves has suggested the core is liquid, with a solid inner core in its middle [Brush, 1980]. Its high density fits a liquid metal, generally believed to be iron (possibly, with other elements dissolved in it), a relatively abundant element. The iron has sunk to the center of the Earth because it is heavy, the same reason that molten iron sinks to the bottom of a blast furnace.

    For a while, around 1950, another idea was proposed, namely that every spinning massive object developed an intrinsic magnetic field, proportional to its angular momentum. According to that view, the field asymmetries observed on the Earth's surface were due to secondary processes, such as the circulation of liquid iron in the core. While Gilbert suggested that the Earth rotated because it was magnetic, this explanation argued the opposite--the Earth was magnetic because it rotated. Arthur Schuster (1851-1934) was the first to propose the idea [Schuster, 1912; Warwick, 1971], and its main supporter in the 20th century was Patrick M. Blackett (1897-1974), a British physicist who was awarded the 1948 Nobel prize for his work on cosmic rays [Blackett, 1947]. By then it was known that in electrons and protons, spin and magnetic moment were related: couldn't the same hold for matter at large? However, the observation that the field did not weaken in deep mines [Runcorn, 1948; includes appendix by Sydney Chapman] was evidence against the idea, and Blackett finally ruled it out by an experiment with a spinning gold sphere [Blackett, 1952].

    Meanwhile other physicists--initially, Walter Elsasser at Columbia U.-- tried to find mathematical solutions to the dynamo problem [Elsasser, 1946, 1947, 1956b]. The method devised by Gauss to represent the Earth's internal field outside the region of electrical currents can be generalized to describe any toroidal and poloidal fields, and this generalization should in principle be applicable to represent the flows and fields in the Earth's core. Unfortunately, because of Cowling's "anti-dynamo" theorem, no axially symmetric solutions were expected, leading researchers to assume a most general class of fields and motions. This produced complicated relations, which led to even more complicated ones, with no closure in sight.

    For a while some scientists wondered whether any solutions existed at all. Then in 1964 Stanislaw Braginsky [1964a, b] in Russia surprised the world by producing an entire class of solutions which were almost symmetric--a symmetric field, plus a small addition. Because the addition was small, the procedure converged.

    All these were solutions of the "kinematic dynamo problem," in which the flow pattern of the conducting fluid could be freely specified. A realistic model of the dynamo also requires a mechanism and a source of energy driving the flow. Bullard [1949] pointed out that a modest amount of heat generation by radioactivity would suffice. Braginsky suggested that the solidification of molten iron and its deposition on the inner core could also supply the heat which produced the flows and thus drive the dynamo effect.

    Considerable progress has taken place since then [Levy, 1976, Inglis, 1981, Jacobs, 1987 (vol. 2), Buffett, 2000, Roberts and Glatzmaier, 2000]. The problem of feedback from toroidal to poloidal modes was addressed by the "alpha-mode" dynamo of Steenbeck, Krause and Rädler[1966] of the Institute of Astrophysics in Potsdam, Germany. They showed that fluid turbulence whose statistical properties had no mirror symmetry could lead to a mean electromotive force, driving electric currents whose magnitude was α times the magnetic intensity, in the direction of the underlying average field. This may be viewed as a generalization of Parker's idea for explaining the solar cycle. An interesting "dynamo experiment" in the laboratory was reported by Lowes and Wilkinson [1963], who spun two iron cylinders (each representing an eddy) inside a container of mercury, at right angles to each other. When the angular velocity exceeded a certain value, the magnetic field jumped to a new higher plateau, and that was viewed as the initiation of dynamo action.

    One interesting development has been the mathematical simulation of the dynamo process, using high-speed computers [Glatzmaier and Roberts, 1997; Glatzmaier et al., 1999; Coe et al, 2000]. The simulation assumes a heat source in the core and heat loss through the core-mantle interface. Dynamo action is generally obtained, but the complexity of the field and the frequency of main field reversals (discussed in the next section) depend greatly on the distribution of the heat loss--whether it was uniform across the interface, highest at the pole, equator or in between, etc. The simulations also found occasional "excursions" in which the field seemed to head towards a reversal but then reasserted its original polarity, a class of events also deduced from the paleomagnetic record. Interestingly, a simulation run with a much smaller inner core produced no reversals at all.

  Next Stop:   Magnetic Reversals and Plate Tectonics

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Author and Curator:   Dr. David P. Stern
     Mail to Dr.Stern:   earthmag("at" symbol)phy6.org

Last updated 31 January 2003