Planetary Magnetic Fields

Rep. Prog. Phys., Vol. 46, pp 555-620, 1983. Printed in Great Britain Planetary magnetic fields D J Stevenson Division of Geological and Planetary Science, California Institute of Technology, Pasadena, California 91125, USA Abstract As a consequence of the smallness of the electronic fine structure constant, the characteristic time scale for the free diffusive decay of a magnetic field in a planetary core is much less than the age of the Solar System, but the characteristic time scale for thermal diffusion is greater than the age of the Solar System. Consequently, primordial fields and permanent magnetism are small a;d the only means of providing a substantial planetary magnetic field is the dynamo process. This requires a large region which is fluid, electrically conducting and maintained in a non-uniform motion that includes a substantial RMS vertical component. The attributes of fluidity and conductivity are readily provided in the deep interiors of all planets and most satellites, either in the form of an Fe alloy with a low eutectic temperature (e.g. Fe-S-0 in terrestrial bodies and satellites) or by the occupation of conduction states in fluid hydrogen or ‘ice’ (H20-NH3-CH4) in giant planets. It is argued that planetary dynamos are almost certainly maintained by convection (compositional and/or thermal). If alternative mechanisms such as precessional torques work at all, they only work when they are not needed (i.e. when the core is neutrally or unstably stratified because of other larger energy sources). For any plausible convective vigour, it is possible to satisfy the sufficient conditions of dynamo onset (large magnetic Reynolds number, small Rossby number) for every planet and satellite. Estimates of convective vigour are obtained from estimates of likely energy fluxes and a consideration of the form of convective motions in a rotating fluid sphere. The reason that some planets and probably all satellites do not have dynamos is because the fluid regions of their cores are stably stratified and do not convect. Thermal evolution models indicate that any terrestrial body with an entirely fluid (iron alloy) core becomes stably stratified over geologic time and loses heat by conduction only at the present time. The core energy flux is then totally unavailable for dynamo generation. However, terrestrial bodies that nucleate an inner solid core (e.g. Earth) can usually continue to sustain a dynamo because of the resulting gravitational energy release and compositional buoyancy of convective motions. In contrast, giant planets can easily sustain a dynamo by gradual cooling alone. The field amplitudes of planetary dynamos are poorly understood. Existing attempts at ‘scaling laws’ are naive because they deny the diversity of planets, and @ 1983 The Institute of Physics 555 556 D J Stevenson poorly constrained because several ‘laws’ perform equally well. Nevertheless, it is possible to assess the likely presence or absence of a dynamo in each planet and satellite, primarily by an analysis of energetic considerations. An interpretation of each Solar-System body is offered and some testable predictions are given. This review was received in September 1982. Planetary magnetic fields 557 Contents Page 1. Introduction 559 2. The observations 561 2.1. Basic principles 561 2.2. Earth 563 2.3. Jupiter 564 2.4. Saturn 565 2.5. Mercury 566 2.6. Venus 566 2.7. Moon 567 2.8. Mars 567 2.9. Uranus, Neptune and outer Solar-System satellites 567 2.10. Small bodies and meteorites 568 3. Composition and evolution of planets 568 3.1. Basic principles 568 3.2. Evolution and structure of terrestrial planets 570 3.3. Evolution and structure of Jupiter and Saturn 581 3.4. Evolution and structure of Uranus and Neptune 583 4. The sources of planetary magnetism 5 84 4.1. Non-dynamo sources 5 84 4.2. The dynamo problem: kinematic preliminaries 587 4.3. Fluid motions in planets (H 0) 593 4.4. The onset of a convective dynamo (!ow-field limit) 598 4.5. Finite-field dynamos and scaling laws 601 4.6. Multipolarity and symmetry 605 4.7. Time variability and reversals 607 5. The synthesis 608 5.1. Mercury 608 5.2. Venus 609 5.3. Earth 61 1 5.4. Moon 612 5.5. Mars 613 5.6. Jupiter 613 5.7. Saturn 614 5.8. Uranus and Neptune 615 5.9. Pluto and giant planet satellites 616 6. The future 616 Acknowledgments 617 References 617 Planetary magnetic fields 559 1. Introduction Magnetic fields are ubiquitous in the Universe because of the abundance of free electric charges and the absence or relative scarcity of free magnetic monopoles. On the astrophysical scale, magnetic fields are a consequence of large-scale currents and the cause of complex motions of plasma. We are also familiar with magnetic fields on the human length scale, often associated with permanent magnetism and caused by microscopic currents. In view of the existence of magnetic fields on length scales as diverse as centimetres and light years, one’s first inclination is to be unsurprised by the existence of substantial magnetic fields associated with planets, which have a size halfway between centimetres and light years on a logarithmic scale. In fact, the persistence of large planetary magnetic fields is far from obvious and their explanation provides insights into the structure and dynamics of a planetary interior. The existence of large planetary magnetic fields is not immediately obvious because planets are too large (and hence too warm internally) to preserve much of the microscopic magnetism of permanently magnetised material, yet too small to sustain primordial magnetic fields in the non-magnetic conducting materials for the age of the Solar System. A non-magnetic m’aterial is one in which there is no possibility of spontaneous magnetisation and the magnetic field is equal to the magnetic induction (except for a constant dependent on the choice of units). Ohm’s law, Ampbre’s circuit law and Faraday’s law of induction are then respectively j=ai E+-xH P> 41r VxH=-j C 1 aH VxE+--=0 (1.3) c at (Gaussian units) where j is the current density, CT is the electrical conductivity, E is the electric field, H is the magnetic field, V is the velocity field of the conductor relative to the frame in which the fields are measured, and c is the velocity of light. Displacement currents are neglected because we are interested in phenomena with characteristic time scales much longer than the light travel time. Deviations from Ohm’s law are potentially significant but are neglected for the moment. Elimination of E and j yields aH -= AV~H+V x (V x H) (1.4) at where A = c2/41ra (assumed constant) is called the magnetic diffusivity and V H = 0 has been assumed (i.e. no magnetic monopoles. If the recent tentative detection of a monopole by Cabrera (1982) is correct then the equations require modification.) Suppose that one formed an electrically conducting planet at time t = 0 with an initial permeating field -Ho, this field being derived from some ‘external’ source such 560 D J Stevenson as the interstellar medium or the primordial solar nebula. If the external source is removed and the body is subsequently internally inactive (V= 0) then equation (1.4) predicts a diffusive decay of the field H - Hoexp (-f/7), where T = R2/r2A and R is the planetary radius (also the characteristic length scale of the field: IV2H(- H/R2). The characteristic atomic unit of electrical conductivity is e2/aoh (e is the electron charge, a. is the first Bohr radius, h is Planck's constant divided by 27r) so that A - cuG2(h/m)- lo4 cm2 s-', where afs is the fine structure constant and m is the electron mass. It follows that the magnetic diffusion time 7mag- (3000 yr)(R/103 km)2, much less than 4.5 x lo9yr, the age of the Solar System. Even in the case of Jupiter, where A is somewhat smaller and R is large, T,,~ is at most a few hundred million years. Primordial fields are thus almost certainly unimportant in the non-magnetic constituents of planets. In contrast, the thermal diffusion time is long. Application of the Wiedemann- Franz relationship (discussed in any elementary solid-state physics text, e.g. Ashcroft and Mermin (1976)) leads to the estimate K - 10(aokBT/e2)(h/m)-0.1 cm2 s-' for the thermal diffusivity of a metal, where T is the temperature and kB is Roltzmann's constant. Notice that K<<A,primarily because the fine structure constant is small (but also because thermal energies are much less than atomic energies). The thermal diffusion equation aT/Jt = KV2T has an associated characteristic decay time 7th = R2/r2K- (3 x 10' yr)(R/103 km)2. The time scale is even longer if the thermal diffusivity of an insulator cm2 s-') is used. Since planets possess large internal heat sources (radiogenic in the terrestrial planets, gravitational in the giant planets), high internal temperatures are unavoidable. The temperature is stabilised by convection (which occurs almost everywhere within most planets) but this stabilised value far exceeds the Curie point of ferromagnetic materials. Only the near-surface (crustal) materials of terrestrial planets possess permanent magnetism; the resulting magnetic field is orders of magnitude smaller than the 0.5 G surface field characterising the Earth but is important for bodies where the field is much smaller than the terrestrial field. However, equation (1.4) admits the possibility of sustaining a field indefinitely by virtue of the induction term V x (VX H). The ratio of this term to the diffusion term hV2H is of the order of the magnetic Reynolds number defined as RM= VL/A where V and L are characteristic magnitudes for the velocity field and the length scales of the magnetic-field variation, respectively.

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