Magnetoconvection dynamos and the magnetic fields of Io and Ganymede

Science

Volumn 276, Issue 5315, 1997, Pages 1106-1108

  Sarson, G R ^a   Jones, C A ^a   Zhang, K ^a   Schubert, G ^b  

^a UNIVERSITY OF EXETER   (United Kingdom)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ASTRONOMY; DATA ANALYSIS; ENVIRONMENTAL TEMPERATURE; HYDRODYNAMICS; MAGNETIC FIELD; PRIORITY JOURNAL;

EID: 0030989199     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.276.5315.1106     Document Type: Article

References (23)

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3. M. G. Kivelson et al., Nature 384, 537 (1996).
4. G. Schubert, K. Zhang, M. G. Kivelson, J. D. Anderson, ibid., p. 544. (This paper evaluates alternative possibilities for the generation of the internal fields; we refer to it for such discussion and henceforth assume that the fields of lo and Ganymede are generated by MHD processes in a molten Fe-rich core.)
5. J. D. Anderson, W. L. Sjogren, G. Schubert, Science 272, 709 (1996).
6. J. D. Anderson, E. L. Lau, W. L. Sjogren, G. Schubert, W. B. Moore, Nature 384, 541 (1996).
7. 0) x B to Eq. 2. These additional terms destroy the reflectional symmetry B → -B, under which the original equations are invariant. [See, for example, D. Gubbins and K. Zhang, Phys. Earth Planet. Inter. 75, 225 (1993).] The additional (Lorentz) terms in Eq. 2 also provide the system with new possibilities for balancing the Coriolis force (on the left side), which otherwise dominates and inhibits convection.
8. c, leads directly to convection with an associated magnetic field. See, for example, M. R. E. Proctor and A. D. Gilbert, Eds., Lectures on Solar and Planetary Dynamos (Cambridge Univ. Press, Cambridge, 1994), for discussions of both these problems of relevance to the present context.
9. K. K. Khurana, J. Geophys. Res., in press.
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11. In earlier work [for example, R. Hollerbach and C. A. Jones, ibid. 87, 171 (1995)], it was noted that the relatively stable fields that can develop in a substantial inner core can stabilize otherwise oscillatory or chaotic solutions. In the present problem, the imposed ambient field may play a similar role.
12. S. J. Peale, P. Cassen, R. T. Reynolds, Science 203, 892 (1979).
13. G. Schubert, T. Spohn, R. T. Reynolds, in Satellites, J. A. Burns and M. S. Matthews, Eds. (Univ. of Arizona Press, Tucson, 1986), pp. 224-292.
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15. The model used is described in more detail in G. R. Sarson, C. A. Jones, K. Zhang, in preparation.
16. -1 for Ganymede, values that are orders of magnitude greater than even turbulent estimates of these parameters. We have used q = 2 for lo and q = 10 for Ganymede, these being the smallest values allowing convincing numerical resolution in each case. A more reasonable turbulent value for both models would be q = 1. The solutions detailed below were then obtained at Ra = 170 for lo and Ra = 60 for Ganymede, corresponding to "magnetic Rayleigh" numbers Ra* = qRa - a more useful measure of the vigor of the buoyancy force in this context - of 340 and 600 for lo and Ganymede, respectively.
17. 0(2Ωρμη), which we model, high wave numbers might be expected to dominate the nonaxisymmetric field. On the other hand, the relatively large magnetic fields internally produced, particularly in the case of Ganymede, result in much larger effective Λ and should lead to smaller preferred m. Here we adopt m = 4 as a compromise. Other calculations we performed suggest, however, that the results are not qualitatively changed for different wave numbers.
18. The distinction between toroidal and poloidal fields, and their generation by the ω and a effects, is somewhat more subtle than presented here. See H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge Univ. Press, Cambridge, 1978), for a more detailed discussion. It is worth explicitly noting that the presence of the poloidal ambient field, which allows Cowling's theorem to be bypassed (17), would allow us to adopt a purely axisymmetric system for our magnetoconvection-type models. Such a system has not yet been considered, however; in the model for lo presented here, the nonaxisymmetric field remains important. The importance of an ambient field in the traditional mean-field context was considered by E. H. Levy [Proc. Lunar Planet. Sci. Conf. 10, 2335 (1979)].
19. The distinction between toroidal and poloidal fields, and their generation by the ω and a effects, is somewhat more subtle than presented here. See H. K. Moffatt, Magnetic Field Generation in Electrically Conducting Fluids (Cambridge Univ. Press, Cambridge, 1978), for a more detailed discussion. It is worth explicitly noting that the presence of the poloidal ambient field, which allows Cowling's theorem to be bypassed (17), would allow us to adopt a purely axisymmetric system for our magnetoconvection-type models. Such a system has not yet been considered, however; in the model for lo presented here, the nonaxisymmetric field remains important. The importance of an ambient field in the traditional mean-field context was considered by E. H. Levy [Proc. Lunar Planet. Sci. Conf. 10, 2335 (1979)].
20. L. A. Morabito, S. P. Synnott, P. M. Kupferman, S. A. Collins, Science 204, 972 (1979).
21. V. Wienbruch and T. Spohn, Planet. Space Sci. 43, 1045 (1995).
22. D. Gubbins and P. H. Roberts, in Geomagnetism, J. A. Jacobs, Ed. (Academic Press, London, 1987), pp. 1-183.
23. G.R.S., C.A.J., and K.Z. are supported by the U.K. Particle Physics and Astronomy Research Council grants GR/K06495 and GR/L22973.