Planetary magnetic fields

Planet. Space Sci.

1966. Vol. 14. pp. 579 to 586.

Pergamon Press Ltd.

PLANETARY

Printed in Northern Ireland

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FIELDS*

R. HIDE Department of Geology and Geophysics and Department of Physics, Massachusetts Institute of Technology, Cambridge, Mass. 02139 U.S.A. (Received 5 February 1966) Abstract-Present knowledge and modern theories of the Earth’s main magnetic field are outlined and the state of knowledge of the magnetic fields of the other planets is sketched. 1. INTRODUCTION

The evidence for significant magnetic fields of internal origin is compelling for only two objects in the planetary system-the Earth and Jupiter. Although the first attempts to explain the Earth’s main magnetic field go back a century or more, only in the past 20 years have important theoretical advances been made. It is now generally accepted that hydromagnetic (magneto-hydrodynamic) processes in the Earth’s liquid, metallic core are responsible for the Earth’s magnetism, although a detailed description of these processes is still lacking. That no completely acceptable theory of the Earth’s magnetism has been proposed is a direct consequence of the incompleteness of our knowledge of the Earth’s deep interior and of the Earth’s magnetic field in the past, and also of the mathematical difficulties that arise in all realistic studies in hydrodynamics and hydromagnetics. Hence, although the above-mentioned theoretical advances have led to insight into hydromagnetic processes in the core, the subject is still mainly qualitative. This paper will sketch our present knowledge of the Earth’s main magnetic field, outline modern theories of the origin of the Earth’s field and discuss briefly the circumstantial evidence suggesting that some of the other planets possess magnetic fields of their own. 2. THE EARTH’S

MAIN

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FIELD

Description

The magnetic field at the surface of the Earth may be separated into two parts: the “main field”, of internal origin, and the small (less than 1 per cent of the total field) remaining part, of external origin. The external part, which is subject to changes on timescales ranging from fractions of seconds (sub-acoustic oscillations) to several days (magnetic storms), is due to electric currents flowing in regions well above the Earth’s surface, in the ionosphere and beyond. This part will not be considered further here. The main field, as we shall see, is probably due to electric currents flowing at great depths within the Earth, in the liquid metallic core, which lies between 1400 km and 3470 km from the Earth’s center (the radius of the Earth is 6370 km). Variations in the main field occur on time-scales ranging from a few years upwards. Observatory data, on which most of our knowledge of the main field is based, go back * Paper No. 15, Geophysical Fluid Dynamics Laboratory, Department of Geology and Geophysics, M.I.T.; presented at the 1965 Woods Hole Summer Study held by the Space Science Board of the National Academy of Sciences. 519

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only a few hundred years (i.e., IO-’ of the accepted age of the Earth). These data suggest the following:(1-6) (1) The main field is predominantly that of a hypothetical axial (i.e., parallel to the rotation axis of the Earth), centered magnetic dipole with a moment of 8 x 1O25e.m.u., giving a surface field of about O-5 G. (2) It also possesses small but significant equatorial dipole and non-dipole components. (3) The main field undergoes secular changes with the following properties: (a) the non-dipole field undergoes the most rapid changes; (b) the r.m.s. amplitude of the secular changes is 5 x 1O-4G/year, and the maximum amplitude about l-5 x low3 G/year (the corresponding dipole changes being of the order of 3.5 x 10” G/year); (c) on typical magnetic maps lines of equal annual change of any element (isopors) form a series of sets of oval curves surrounding points at which the changes are most rapid; (d) at any epoch, the sets of isopors cover areas of continental size, and are separated by regions over which changes are small; (e) isoporic foci migrate westward (as does the field itself) at a fraction of a degree of longitude per year;(5*7-9) (f) in addition to the westward drift (e), the pattern of the secular variation field may alter significantly in a few decades; (g) compared with the world-wide average, the secular changes are systematically low in the Pacific hemisphere and high in the Antarctic. Palaeomagnetic studies based on measurements of the magnetic properties of igneous and sedimentary rocks and of human artifacts (10-21)have extended our knowledge of the main field as far back into the geological past as the Pre-Cambrian ( log years ago). According to these studies: (4) The main field has probably been largely that of an axial centered dipole for the past 5 x 10’ years (during the Quaternary and Tertiary periods). (5) If the field was that of a centered dipole prior to the Tertiary, the angle between the dipole axis and the present geographic axis may have varied more or less systematically by large amounts (up to 90’). (6) The polarity of the (assumed) dipole may have reversed several hundred times since the Pre-Cambrian.(12*15*16*19J (7) The intensity of the dipole has not changed much in the past 5000 years. (8) 10,000 years ago, the time-scales associated with the secular variation (see property (3) above) were similar to those revealed by observatory data. (9) The secular changes over the Pacific hemisphere may have been weaker than the world-wide average for the past lo6 yearsc21) (cJ property (3g) above). The magnetic$eld

within the Earth

The poloidal field within the Earth cannot be determined uniquely from the field at the

surface without making further physical hypotheses. Moreover, lines of force of any toroidal magnetic field inside the Earth cannot, by definition, penetrate to the surface. Modern theories of the main geomagnetic field invoke toroidal fields of at least a hundred G within the Earth’s liquid core (see below). Theories

The main geomagnetic field could in principle be due to: (a) permanent magnetism;

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(b) the rotation of an electrostatically charged Earth; (c) ordinary electric currents flowing within the Earth; (d) some new physical property of gravitating bodies. Theories under categories (a) and (b) are mainly of historical interest only.c2) In addition to the qualitative difficulties of accounting solely in terms of these processes for a surface magnetic field with the spatial and temporal variations observed, there are serious quantitative difficulties. Our knowledge of the properties of materials at very high pressures is still, however, very poor; we cannot, for example, be sure that the temperature of the central body of the Earth everywhere exceeds its Curie point.(22) Theories under category (d) are hard to discuss briefly, for obvious reasons. Attempts to account for cosmical phenomena in terms of new effects that would be very difficult, or even impossible, to measure in the laboratory are not uncommon. The most recent suggestion of this kind to account for the Earth’s magnetism is that by Blackett,(*) which was subsequently disproved by delicate laboratory experiments carried out by Blackett himself@) and by a geophysical test involving the determination of the radial variation of the Earth’s magnetic field from measurements made in deep coal mines.(24) Nowadays, most geophysicists believe that ordinary electric currents inside the Earth (category (c)) are largely responsible for the main geomagnetic field and its secular variation. That these currents flow mainly in the liquid metallic core is evinced by the short (geologically speaking) time-scale of the secular variation and the high electrical conductivity (IO5 Q-l m-l) of the liquid core as compared with that of the surrounding “solid” mantle (less than 103 Q-l m-1).(25-2s) Because the time of free decay of currents in the core is less than 105 years, electromotive forces must exist there which are capable of sustaining against ohmic losses the electric currents responsible for the geomagnetic field. These electromotive forces could be due to : (a) thermoelectric effects; (b) chemical effects; (c) motional induction. Lack of sufficiently detailed knowledge of the Earth’s deep interior precludes serious consideration of possibilities (a) and (b). However, it may be shown that fluid motions in the Earth’s core of the magnitude suggested by the secular variation could, by motional induction, interact with the magnetic fields there to produce electric currents of the strength This is the rough quantitative basis of the required to sustain the magnetic fields present. so-called “homogeneous dynamo theories”, first introduced by Bullard and Elsasser (following an earlier suggestion due to Larmor), on which there is now an extensive literature (5,6*2Os25-27s30-37) If a self-maintaining dynamo is to occur in the core, the system of fluid motions there must be quite complicated and highly asymmetric. The interaction of horizontal motions with a dipole magnetic field leads to a toroidal magnetic field. Interaction of vertical motions with these toroidal and poloidal fields then leads to the regeneration of the original dipole field. With such a system either direction of dipole field could be maintained. For a given toroidal magnetic field the sign of the dipole field depends mainly on the particular form of the velocity field; reversal of the external dipole field may involve comparatively minor changes in the magnetic field and the field of fluid motion in the core. A quantitive requirement for “dynamo action” is that a magnetic Reynolds number,(36*37) R = ,uLaU,

(1)

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should exceed about 10, where ,u and (Tdenote, respectively, the magnetic permeability and the electrical conductivity of the core, and L is a length scale associated with the fluid motions, typical speeds of which (relative to the rotating Earth) are of order U. Taking (,~a)-’ = 3m2/sec, L = 3 x IO6m and U = lo”1 m/set for the core, then R = 1000, which should suffice for dynamo action. The geomagnetic secular variation is due, presumably, to fluctuations in the hydromagnetic flow in the core. The extent to which the secular variation involves the re-arrangement-as opposed to the creation and destruction-of lines of magnetic force has not yet been fully investigated .@s*3s)Neither has the contribution made by hydromagnetic oscillations to flow fluctuations in the core been fully assessed. Most theoretical work has ignored such oscillations.(s*7*27*m,41) A ccording to one recent study, however, if the strength of the toroidal magnetic field in the core is about 100 G, the re-arrangement of lines of force of the poloidal field by free hydromagnetic oscillations of the core might account for the observed geomagnetic secular variation .(3s*42)On the “free oscillations” theory, the westward drift of the magnetic field at the Earth’s surface is due to a slow westward-propagating wave in the core. Associated with this wave would be an eastward-propagating wave moving so rapidly that the electrical conductivity of the Earth’s mantle, though weak, is sufficient to suppress from the magnetic record any direct manifestation of its presence. The same theory also predicts that in a sufficiently thin fluid layer, the slow wave would probably move eastwards, a result which may be of interest in the study of the magnetic fields of other planets. Hydromagnetics of the Earth’s core

The magnetic energy of the Earth far exceeds the kinetic energy of core motions. The source of energy responsible for these motions must be capable of overcoming dissipative agencies, the most important of which is ohmic heating, amounting to lOlo W for the whole core. The nature of the energy source has not yet been established. According to several recent discussions of the problem, radioactive heating within the Earth, the Earth’s precessional motion (which is due largely to the action of the Moon upon the equatorial bulge), and gravitational energy released if the Earth is still condensing, may contribute significantly to the stirring of the core.(2s-27*30*43-47) The transmission of magnetic energy between different parts of the core is due mainly to hydromagnetic waves, diffusive processes being entirely negligible. The Earth’s rotation renders these waves highly dispersive.(3s,42,4s) Owing to their low speed, hydrodynamical motions in the core are very strongly influenced by the Earth’s rotation, the axial nature of the dipole field being almost certainly a direct consequence of the action of Coriolis forces on core motions.(20*2s*27*3s*42--44) The most obvious role of Coriolis forces is the alignment of core eddies by gyroscopic action, giving the magnetic field rough symmetry about the axis of rotation of the planet. Less obvious but probably at least equally important is the role that Coriolis forces play in ensuring that, irrespective of the size of the energy-producing eddies in the core, the system can produce the large eddies required to give the low degree of symmetry necessary for efficient dynamo action to occur. These large eddies gain kinetic energy by non-linear interactions with smaller eddies, a process which, though impossible in isotropic homogeneous turbulence (where energy cascades in the opposite direction, from large to small eddies), is probably quite common in more realistic systems, where isotropy is the exception rather than the rule.‘3s*4s)

PLANETARY 3. MAGNETIC

MAGNETIC

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OF

FIJZLDS

OTHER

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PLANETS

Three kinds of observational evidence from which the existence of a planetary magnetic field may be inferred are: (a) space-probe magnetometer measurements, (b) non-thermal electromagnetic radiation from the planet with appropriate frequency, polarization and intensity characteristics, and (c) evidence that in modulating the “solar wind” the effective planetary cross-section greatly exceeds the cross-section of the visible planet. This evidence has not yet been sought for most planets; planets in this category will simply be designated “unknown” in the summary to follow. (Kern and Vestine,(50) who have recently written a useful review of certain aspects of planetary magnetic fields, present a table containing estimates of the surface magnetic fields of all the planets and several satellites. In preparing the present paper, however, it seemed preferable to avoid making estimates that are speculative, since one of the purposes of this paper is to expose areas of ignorance.) Mercury. Unknown. P’eVenus.Magnetometer data, obtained as Mariner II flew past the planet at a distance from its center of about 7 planetary radii, gave no evidence of a Venusian magnetic field at any point on the trajectory. (51*52)The upper limit thus set on the (hypothetical) magnetic dipole moment is less than 8 x 1O24e.m.u., only 10 per cent that of the Earth. The field may, of course, be highly non-dipolar in character. There is no evidence for electromagnetic radiation of non-thermal origin, observations having been made at wavelengths up to 11 m.(53) Earth. See Section 2 above. Mars. Magnetometer data, obtained as Mariner IV flew past Mars at a distance from its center of about 2 planetary radii, gave no evidence of a Martian magnetic field at any point on the trajectory. The details of this work are expected to be published shortly (see “note added in proof” at the end of this paper). There is no evidence of non-thermal radiation from Mars.(53s54) Jupiter. Non-thermal electromagnetic radiation from Jupiter on decimeter and decameter wavelengths is so strong that this planet is one of the brighest radio-sources in the sky. Since this radiation was first discovered 10 years ago by Burke and Franklin, numerous papers, both observational and theoretical, have appeared on the subject.‘5542) Spectrum and polarization studies indicate that electrons in the radiation belts of Jupiter may be 103 times more energetic than those in the Earth’s radiation belts, and that Jupiter’s magnetic moment is about 8 x 103Oe.m.u., 105 times that of the Earth, and inclined about 1 lo from the rotation axis. Asymmetries in the total radiation, together with “dynamic spectra” of radiation bursts on decameter wavelengths, suggest that the magnetic field is much more complicated than that of a centered dipole.(6044) Radio-astronomical observations indicate a definite rotation period for the magnetic field. (This discovery has led to the introduction of System III, with a period of 9h 55m 29s. 37, for convenience in measuring the longitude of radio-sources on Jupiter.) The motion of the magnetic field corresponds, presumably, to the motion of material within the planet at the lowest depth at which the magnetic Reynolds number (see equation (1) above) exceeds about 10.(65) Though the radio-period was apparently constant when first determined, changes have now been detected .(57*66)The reconciliation of these changes with the motion

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of other internal parts of the planet, as evinced by the excursions in longitude of the Great Red Spot, is a fascinating problem. (62*65*67,6a) As one writer has remarked, “. . . this is the first instance in astronomy when the distribution of angular momentum within a rotating cosmic body (perhaps even including the Earth) manifests itself in observational effects measurable within a short time-scale.” The theoretical exploitation of these observations will bear both on the internal structure of Jupiter and on the origin of his magnetic field.(65*68) The possibility that a homogeneous dynamo mechanism is operating in the lower reaches of Jupiter’s atmosphere is not inconsistent with the (admittedly limited) theoretical and observational evidence.(65,70) If this is indeed the case, variations in the motions of the Red Spot and of the radio-sources could be manifestations of hydromagnetic torsional oscillations of the planet. (66) Moreover, the “topographical feature” to which the Red Spot may be due might be magnetic in nature.(65*67-70) Saturn. There have been several recent reports of weak and fluctuating radio-bursts on decameter wavelengths from Saturn. If these bursts are real, they are far less frequent and much less intense than those from Jupiter. (53) The equivalent black-body temperatures of Saturn at wavelengths of 9.4 cm and 21.2 cm are 180°K and about 300°K respectively,(“*‘l) suggesting that weak non-thermal emission may occur at larger wavelengths. Uranus. Unknown. Neptune. Unknown. Pluto. Unknown. Satellites. The Lunik II magnetometer showed that the surface field of the Moon may be less than 1O-3G, the corresponding magnetic moment being 2 x 1021 e.m.u., some 2 x 1O-s that of the Earth.‘51*72) Recently Bigg(73)reported strong modulation of Jupiter’s decametric emission by the innermost Galilean satellite, 10, suggesting that IO affects Jupiter’s radiation belts.(74) (A similar claim has subsequently been made on behalf of Ganymede.(75)) Whether or not the quantitative interpretation of these discoveries will require 10 to possess a magnetic field of its own has not yet been ascertained. 4. SOME

ADDITIONAL

REMARKS

When the solar wind encounters a magnetic body in the solar system, a bow wave and a stand-off shock wave are formed at distances which depend on the momentum of the solar wind and the strength of the magnetic field with which it interacts. These distances may be many times the dimensions of the body itself. On the other hand, if the body has no magnetic field of internal origin (e.g. the Moon and possibly Mars), as Gold(7s) has pointed out, the solar wind, together with its associated magnetic field, would reach the surface of the body. Any magnetic properties of the body would be due to induced eddy currents resulting from this interaction. The investigation of these properties might elucidate the history of the solar wind and the electrical conductivity distribution within the planet. Acknowledgements-The research reported in this paper has been supported by the Atmospheric Program, National Science Foundation, under Grant Number N.S.F. G22390.

Sciences

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4. E. H. VESTME, L. LAPORTE,I. LANGE and W. E. SCOTT, Carnegie Institute Publication No. 580 (1947). 5. R. HIDE and P. H. ROBERTS,Physics and Chemistry of the Earth 4 (Ed. L. H. Ahrens et al.), p. 25. Pergamon Press, London (1961). 6. J. A. JACOBS,The Earth’s Core and Geomagnetism. Pergamon Press, London (1963). 7. E. C. BULLARD, C. FREEDMAN,H. GELLMANand J. NIXON, Phil. Trans. R. Sot. A243,67 (1950). 8. T. NAGATA, in: Proceedings of the Benedum Earth Magnetism Symposium, p. 39. University of Pittsburgh Press, Pittsburgh (1962). 9. T. YUKUTAKE,Bull. Earthquake Res. Inst. 40, 1 (1962). 10. T. NAGATA, Rock Magnetism. Maruzen, Tokyo (1953). 11. P. M. S. BLACKETT,Lectures on Rock Magnetism. Weizmann Science Press of Israel, Jerusalem (1956). 12. S. K. RUNCORN, Hundbuch der Physik XLVII (Ed. J. Bartels), p. 469 (1956). 13. A. Cox and R. R. DOELL, Bull. Geol. Sot. America 71. 645 (1960). . ’ 14. J. M. ADE-HALL, Geophys. J. R. astr. Sot. 8,403 (1964). 15. A. Cox and R. R. DOELL, Bull. seism. Sot. Am. 54,2243 (1964). 16. A. Cox, R. R. DOELL, and G. B. DALRYMPLE,Science, N. Y. 144, 1537 (1964). 17. A. Cox, R. R. DOELL, and G. B. DALRYMPLE,Science, N. Y. 143,351 (1964). Wiley, New York (1964). 18. E. IRVING, Paleomagnetism. 19. P. M. S. BLACKET~,in: Magnetism and the Cosmos (Ed. S. K. Runcorn). Oliver & Boyd, Edinburgh (In press). * 20. S. K. RUNCORN, Hundbuch der Physik XLVII (Ed. J. Bartels), p. 498 (1956). 21. R. R. DOELL and A. Cox, J. Geophys. Res. 70,3377 (1965). 22. R. J. WEISS, Nature, Lond. 197, 1289 (1963). 23. P. M. S. BLACKET~,Phil. Trans. R. Sot. A245, 309 (1952). 24. S. K. RUNCORN,A. C. BENSON,A. F. Moonz and D. H. GRIFFITHS,Phil. Trans. R. Sot. A244,113 (1951). 25. E. C. BULLARD, Proc. R. Sot. Lond. A197,433 (1949). 26. W. M. ELSASSER,Rev. Mod. Phys. 22, 1 (1950). (1954). 27. E. C. BULLARD and H. GELLMAN,Phil. Trans. R. Sot. A247,213 28. D. C. TOZER, Physics and Chemistry of the Earth 3 (Ed. L. H. Ahrens et rd.), p. 414. Pergamon Press, London, (1959). 29. R. HIDE, Dictionary of Geophysics (Ed. S. K. Runcorn). Pergamon Press, London (In press). 30. D. R. INGLIS,Rev. Mod. Phys. 27,212 (1955). 31. E. N. PARKER, Astrophys. J. 122, 293 (1955). Proc. natn. Acad. Set’. U.S.A. 42, 105 (1956). 32. G. E. BACKUS and S. CHANDRASEKHAR, 33. G. E. BACKUS, Ann. Phys. 4,372 (1958). (1958). 34. A. IIERZENBERG,Phil. Trans. R. Sot. A250,543 35. T. G. COWLING, Mon. Not. R. Astr. Sot. 94,39 (1934). Interscience, New York (1957). 36. T. G. COWLING, Magnetohydrodynamics. 37. T. G. COWLING, Rep. Progr. Phvs. XXV, 244 (1962). XVII, 137 (1965). 38. P. H. ROBERTSand-S. SC&T, J..Geomag. Geoelect.Kyoto 39. R. HIDE, Phil. Truns. R. Sot. A259. 615 (1966). 40. J. COULOMB,Ann. Geophys. 11,80 {1955i 41. D. W. ALLAN and E. C. BULLARD, Rev. Mod. Phys. 30,1087 (1958). 42. R. HIDE, in: Magnetism and the Cosmos (Ed. S. K. Runcorn). Oliver & Boyd, Edinburgh (In press).* 43. W. M. ELSASSER,Trans. Am. geophys. Un. 31,454 (1950). 44. R. HIDE, Physics and Chemistry of the Earth 1 (Ed. L. H. Ahrens et al.) p. 94. Pergamon Press, London (1956). 45. J. VERHOOGEN,Geophys. J. R. astr. Sot. 4, 276 (1961). (1963). 46. W. V. R. MALKUS, J. geophys. Res. 68,287l Conference on the Earth-Moon System (Ed. B. G. Marsden 47. A. TOOMRE,in: Transactions of the N.A.S.A. and A. G. W. Cameron). Plenum Press, New York (1966). 48. R. HYDEand P. H. ROBERTS,Advanc. appl. Mech. 7, 215. Academic Press, New York. 49. W. M. ELSASSER,Rev. Mod. Phys. 28, 135 (1956). 50. J. W. KERN and E. H. VESTINE,Space Science Reviews (Ed. C. de Jager), p. 136. Reidel, Utrecht (1963). 51. E. J. Sr,rrrrr,L. DAVIS, JR., P. J. COLEMANand C. P. SONETT,Science, N. Y. 139, 909 (1963). 52. E. J. SMITH, L. DAVIS, JR., P. J. COLEMANand C. P. SONETT,J. geopkys. Res. 70,157l (1965). Van Nostrand, Princeton 53. A. G. SMITH and T. D. CARR, Radio Exploration of the Planetary System. (1964). Oliver and 54. R. D. DAVIES and D. WILLIAMS, in: Magnetism and the Cosmos (Ed. S. K. Runcorn). Boyd, Edinburgh (In press).* 55. G. B. FIELD, J.geophys. Res. 65, 1661 (1960). 56. B. F. BURKE,in: Planets and SateBites (Ed. G. P. Kuiper and B. M. Middlehurst), p. 473. University of Chicago Press, Chicago (1961).

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(In press). * R. Hme, Magnetism and the Cosmos (Ed. S. K. Runcorn). Oliver and Boyd, Edinburgh (In press).* J. N. DOUGLASand H. J. SMITH,Nature, Lond. 199. 1808 (1963). _ R. HIDE, Nature, Lond. 190, 89j (1961). R. HIDE, Les CongrPs et Collogues de I’UniversitC de Lit?ge 24, “La Physique des PlanBtes” (also Mim. Sot. r. Sci. Lit’ge V, 7,481) (1962). R. H. DICKE, Unpublished remark. R. HJ.~E,Planet. Space Sci. (In press). W. K. ROSE, in: Magnetism and the Cosmos (Ed. S. K. Runcorn). Oliver and Boyd, Edinburgh (In press). * SH. SH. DOLGINOV,YE. G. YEROSHENKO, L. N. ZHUZG~V and N. V. PUSHKOV,Geomagn. Aeron. 1, 18

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(1965).

* Proceedings of the N.A.T.O. Advanced Study Institute on Planetary and Stellar Magnetism held at the University of Newcastle upon Tyne, April 1965. Note added in proof. The magnetic results of Marino IV (see Section 3 above) have now been reported by E. J. Smith, L. Davis, P. J. Coleman and D. E. Jones (see Science, N.Y. 149, 1240, (1965) also R. K. Sloan, Sci. Ann. 214 NO. 5, 62 (1966)). PesxoM~B

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