IOP PUBLISHING REPORTS ON PROGRESS IN PHYSICS Rep. Prog. Phys. 76 (2013) 096801 (55pp) doi:10.1088/0034-4885/76/9/096801 On the genesis of the Earth’s magnetism Paul H Roberts1,3 and Eric M King2 1 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095, USA 2 Earth and Planetary Science, University of California, Berkeley, CA 94720, USA E-mail: [email protected] Received 23 January 2011, in final form 26 June 2013 Published 4 September 2013 Online at stacks.iop.org/RoPP/76/096801 Abstract Few areas of geophysics are today progressing as rapidly as basic geomagnetism, which seeks to understand the origin of the Earth’s magnetism. Data about the present geomagnetic field pours in from orbiting satellites, and supplements the ever growing body of information about the field in the remote past, derived from the magnetism of rocks. The first of the three parts of this review summarizes the available geomagnetic data and makes significant inferences about the large scale structure of the geomagnetic field at the surface of the Earth’s electrically conducting fluid core, within which the field originates. In it, we recognize the first major obstacle to progress: because of the Earth’s mantle, only the broad, slowly varying features of the magnetic field within the core can be directly observed. The second (and main) part of the review commences with the geodynamo hypothesis: the geomagnetic field is induced by core flow as a self-excited dynamo. Its electrodynamics define ‘kinematic dynamo theory’. Key processes involving the motion of magnetic field lines, their diffusion through the conducting fluid, and their reconnection are described in detail. Four kinematic models are presented that are basic to a later section on successful dynamo experiments. The fluid dynamics of the core is considered next, the fluid being driven into motion by buoyancy created by the cooling of the Earth from its primordial state. The resulting flow is strongly affected by the rotation of the Earth and by the Lorentz force, which alters fluid motion by the interaction of the electric current and magnetic field. A section on ‘magnetohydrodynamic (MHD) dynamo theory’ is devoted to this rotating magnetoconvection. Theoretical treatment of the MHD responsible for geomagnetism culminates with numerical solutions of its governing equations. These simulations help overcome the first major obstacle to progress, but quickly meet the second: the dynamics of Earth’s core are too complex, and operate across time and length scales too broad to be captured by any single laboratory experiment, or resolved on present-day computers. The geophysical relevance of the experiments and simulations is therefore called into question. Speculation about what may happen when computational power is eventually able to resolve core dynamics is given considerable attention. The final part of the review is a postscript to the earlier sections. It reflects on the problems that geodynamo theory will have to solve in the future, particularly those that core turbulence presents. (Some figures may appear in colour only in the online journal) Contents 1. Introduction 2 3.2. Archaeo- and paleomagnetism; 2. Description of the Earth’s magnetic field 4 paleomagnetic secular variation 8 2.1. Gauss decisively identifies an internal 4. The geodynamo hypothesis 10 5. Kinematic geodynamo theory 10 magnetic origin 4 5.1. Pre-Maxwell electrodynamics 10 2.2. The power spectrum; the magnetic curtain 5 5.2. Extremes of Rm and finite Rm 13 3. Time dependence 6 5.3. Four successful kinematic models 15 3.1. Historical secular variation 6 5.4. Mean field electrodynamics 16 3 Author to whom any correspondence should be addressed. 0034-4885/13/096801+55$88.00 1 © 2013 IOP Publishing Ltd Printed in the UK & the USA Rep. Prog. Phys. 76 (2013) 096801 P H Roberts and E M King 6. MHD geodynamo theory 18 7.6. Scaling 38 6.1. The cooling Earth model 18 7.7. Taylorization and hints of magnetostrophy 41 6.2. A simplified cooling Earth model 22 8. Laboratory experiments 41 6.3. Rotational dominance; Proudman–Taylor 8.1. Dynamo experiments 42 theorem; CMHD 25 8.2. Core flow experiments 44 6.4. Convection of small and finite amplitude 28 9. The future 45 7. Numerical simulations 33 7.1. Numerical methods 33 9.1. Computational progress and limitations 45 7.2. Dynamo mechanisms 33 9.2. Turbulence 47 7.3. Dynamo regimes 35 10. Overview 50 7.4. Reversals; boundary conditions 36 Acknowledgments 51 7.5. Inner core rotation 37 References 51 1. Introduction had previously, in a letter written in 1269, partially anticipated Gilbert. He had constructed his own terrella and, by laying a In his encyclopedia, Pliny the elder told a story about a needle on its surface, had mapped out the lines of magnetic shepherd in northern Greece who was astonished to find that longitude, finding them to be approximately great circles his iron-tipped staff and the nails in his shoes were strongly converging at two antipodal points which, in analogy with the attracted to a rock, now called lodestone. His name, Magnes, Earth, he called poles. With the help of other magnets, he possibly led to the phenomenon he experienced being called established that like poles repel and unlike poles attract. ‘magnetism’. Gilbert believed that the Earth is magnetically modeled The directional property of the magnetic compass needle so well by his terrella that its magnetism is time independent was apparently discovered, perhaps thousands of years ago, too, but in 1635 Henry Gellibrand produced convincing in China. It is certain that, from about the third century AD observational evidence that contradicted this. Time 83 onwards, Chinese geomancers knew that a spoon, made of dependence is the very significant topic of section 3. Since lodestone spun on a smooth horizontal surface, would come permanent magnets creating constant magnetic fields were to rest pointing in a unique southerly direction, which was not the only sources of magnetism that were known at that time, precisely south. The deviation is today called declination and it was natural to suppose that the Earth’s magnetic field is is denoted by D. produced by moving magnetic poles within the Earth. Halley, That magnetism can be acquired by iron by stroking it of comet fame, who in 1701 had produced a famous map of with lodestone was an important though undated discovery D in the Atlantic, visualized four magnetic poles moving in a that led to the magnetic compass, first mentioned by Shen hollow Earth, but that did not explain the observational facts Kua in 1088, a century before the first European reference well. The situation was, from 1635 until almost a century ago, by Alexander Neckham of St Albans England in 1190. By frustratingly mysterious. As Christopher Hansteen eloquently the fourteenth century the nautical compass was in regular use complained in 1819, ‘The mathematicians of Europe since the by the British navy. Christopher Columbus carried one on his times of Kepler and Newton have all turned their eyes to the epic voyage of 1492. By this time, a portable sundial could heavens, to follow the planets in their finest motions and mutual be easily purchased whose gnomen could be orientated by a perturbations: it is now to be wished that for a time they would magnetic compass needle beneath a window in its base. In turn their gaze downwards towards the earth’s center, where 1581 Robert Norman, an instrument maker in London, reported also there are marvels to be seen; the earth speaks of its internal that a magnetized needle that was freely suspended, instead of movements through the silent voice of the magnetic needle’ being pivoted about a vertical axis, orientates itself at a steep (Chapman and Bartels 1940). In defense of mathematicians, angle to the horizontal plane. This angle is called inclination it must be admitted that what they could do in 1819 was very and denoted by I. limited; the Earth’s core was not discovered until 1906 by At first many thought the magnetism of the Earth was Richard Dixon Oldham. That it was fluid was not known for created externally, by attraction to the pole star. The discovery certain until two decades later. that it originates mainly inside the Earth is often attributed The first mathematician to take up Hansteen’s challenge to William Gilbert, court physician of Queen Elizabeth 1st was Karl Friedrich Gauss who, in 1838 in an analysis of England, who in 1600 published De Magnete, a book that described in section 2, gave Gilbert’s idea mathematical soon became famous and is often called ‘the first scientific teeth. But it still left geomagnetism without an adequate textbook’. He there describes his ‘terrella’, or little Earth, physical explanation. This came only after the birth of experiment, in which he placed the points of iron pins on electromagnetism. Allessandro Volta discovered in 1800 the surface of a spherical block of lodestone (or magnetic how to construct what became known as a voltaic pile, from rock), and found that they became orientated at different points which electric current could be carried along an electrically on the surface in ways similar to the directions in which a conducting wire. In 1820, Hans Christian Oersted showed that freely suspended magnetic compass needle points at different the needle of a compass placed near a wire carrying an electric locations on the Earth’s surface; see figure 1. ‘The Earth is a current was deflected. News quickly reached Paris where, in great magnet’, he announced. Petrus Peregrinus de Maricourt the same year, Franc¸ois Arago demonstrated that the magnetic 2 Rep.