Analytical estimation of the scale of Earth-like planetary magnetic fields. (English) Zbl 1327.85002
Summary: In this paper, we analytically estimate the magnetic field scale of planets with physical core conditions similar to that of Earth from a statistical physics point of view. We evaluate the magnetic field on the basis of the physical parameters of the center of the planet, such as density, temperature, and core size. We look at the contribution of the Seebeck effect on the magnetic field, showing that a thermally induced electrical current can exist in a rotating fluid sphere. We apply our calculations to Earth, where the currents would be driven by the temperature difference at the outer-inner core boundary, Jupiter and the Jupiter’s satellite Ganymede. In each case, we show that the thermal generation of currents leads to a magnetic field scale comparable to the observed fields of the considered celestial bodies.
MSC:
| 85A05 | Galactic and stellar dynamics |
| 78A25 | Electromagnetic theory (general) |
| 62P35 | Applications of statistics to physics |
| 83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |
Keywords:
planetology of solid surface planets: magnetic field and magnetism; planetology of fluid planets: magnetic field and magnetism; Earth’s interior structure and propertiesReferences:
| [1] | D. Alfè, M. Gillan, G.D. Price, Composition and temperature of the Earth’s core constrained by combining ab initio calculations and seismic data. EPSL 195, 91 (2002) · doi:10.1016/S0012-821X(01)00568-4 |
| [2] | J. Ashok, R. Evans, Calculation of the electrical resistivity of liquid iron in the Earth’s core. Nature 235, 165 (1972) · doi:10.1038/235165a0 |
| [3] | M. Berhanu, R. Monchaux, S. Fauve, N. Mordant, F. Pétrélis, A. Chiffaudel, F. Daviaud, B. Dubrulle, L. Marié, F. Ravelet, M. Bourgoin, Ph Odier, J.-F. Pinton, R. Volk, Magnetic field reversals in an experimental turbulent dynamo. Europhys. Lett. 77, 59001 (2007) · doi:10.1209/0295-5075/77/59001 |
| [4] | M.T. Bland, A.P. Showman, G. Tobie, The production of Ganymedes magnetic field. Icarus 198, 384 (2008) · doi:10.1016/j.icarus.2008.07.011 |
| [5] | M. Bologna, B. Tellini, Generating a magnetic field by a rotating plasma. Europhys. Lett. 91, 45002 (2010) · doi:10.1209/0295-5075/91/45002 |
| [6] | B.A. Buffett, The thermal state of Earth’s core. Science 299, 1675 (2003) · Zbl 1364.93146 · doi:10.1126/science.1081518 |
| [7] | B.A. Buffett, Tidal dissipation and the strength of the Earths internal magnetic field. Nature 468, 952 (2010) · doi:10.1038/nature09643 |
| [8] | F.H. Busse, Homogeneous dynamos in planetary cores and in the laboratory. Annu. Rev. Fluid Mech. 32, 383 (2000) · Zbl 0988.76097 · doi:10.1146/annurev.fluid.32.1.383 |
| [9] | A. de Wijs Gilles, G. Kresse, L. Vočadlo, D. Dobson, D. Alfè, J. Gillan Michael, D. Price Geoffrey, The viscosity of liquid iron at the physical conditions of the Earths core. Nature 392, 805 (1988) |
| [10] | J.J. Fortney, N. Nettelmann, The interior structure, composition, and evolution of giant planets. Space Sci. Rev. 152, 423 (2010) · doi:10.1007/s11214-009-9582-x |
| [11] | M. French, A. Becker, W. Lorenzen, N. Nettelmann, M. Bethkenhagen, J. Wicht, R. Redmer, Ab initio simulations for material properties along the Jupiter adiabat. ApJSS 202, 5 (2012) · doi:10.1088/0067-0049/202/1/5 |
| [12] | G. Giampieri, A. Balogh, Mercurys thermoelectric dynamo model revisited. Planet. Space Sci. 50, 757 (2002) · doi:10.1016/S0032-0633(02)00020-X |
| [13] | G. Glatzmaier, P. Roberts, A three-dimensional self-consistent computer simulation of a geomagnetic field reversal. Nature 377, 203 (1995) · doi:10.1038/377203a0 |
| [14] | W.B. Hubbard, Thermal models of Jupiter and Saturn. Astrophys. J. 155, 333 (1969) · doi:10.1086/149868 |
| [15] | J.D. Jackson, Classical Electrodynamics (Wiley, New York, 1998) · Zbl 0913.00013 |
| [16] | J.A. Jacobs, The earth’s inner core. Nature 172, 297 (1953) · doi:10.1038/172297a0 |
| [17] | R.A. Kerr, Earth’s inner core is running a tad faster than the rest of the planet. Science 309, 1313 (2005) · doi:10.1126/science.309.5739.1313a |
| [18] | M. Kono, P. Roberts, Recent geodynamo simulations and observations of the geomagnetic field. Rev. Geophys. 40, 1013 (2002) · doi:10.1029/2000RG000102 |
| [19] | W. Kuang, J. Bloxham, An Earth-like numerical dynamo model. Nature 389, 371 (1997) · doi:10.1038/38712 |
| [20] | L. Landau, E. Lifshitz, Physical Kinetics (Pergamon Press, Oxford, 1981), pp. 329-332 |
| [21] | L. Landau, E. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, Oxford, 1981) · Zbl 0122.45002 |
| [22] | L. Landau, E. Lifshitz, Fluid Mechanics (Pergamon Press, Oxford, 1987) · Zbl 0655.76001 |
| [23] | H.K. Lee, International Handbook of Earthquake and Engineering Seismology (Academic Press, Waltham, 2002) |
| [24] | M.H. Manghnani, T. Yagi, Properties of Earth and Planetary Materials at High Pressure and Temperature (AGU books board, USA, 1998) · doi:10.1029/GM101 |
| [25] | W.J. Nellis, S.T. Weir, A.C. Mitchell, Minimum metallic conductivity of fluid hydrogen at 140 GPa (1.4 Mbar). Phys. Rev. B 59, 3434 (1999) · doi:10.1103/PhysRevB.59.3434 |
| [26] | N.F. Ness, Magnetic fields of mars and venus: Solar wind interactions. Earth, Moon, and Planets 9, 43 (1974) |
| [27] | I. Orgzall, S. Franck, Mars and its magnetic field Some new aspects. Earth, Moon, and Planets 43, 201 (1988) · doi:10.1007/BF00117092 |
| [28] | J.P. Poirier, Introduction to the Physics of the Earths Interior (Cambridge University Press, Cambridge, 1991) |
| [29] | M. Pozzo, C. Davies, D. Gubbins, D. Alfè, Thermal and electrical conductivity of iron at Earths core conditions. Nature 485, 355 (2012) · doi:10.1038/nature11031 |
| [30] | P. Roberts, G.A. Glatzmaier, Geodynamo theory and simulations. Rev. Modern Phys. 72, 1081 (2000) · doi:10.1103/RevModPhys.72.1081 |
| [31] | A.P. Showman, R. Malhotra, The Galilean satellites. Science 286, 77 (1999) · doi:10.1126/science.286.5437.77 |
| [32] | E.J. Smith, L. Jr. Davis, D.E. Jones, P.J. Jr. Coleman, D.S. Colburn, P. Dyal, C.P. Sonett, Jupiter’s magnetic field. Magnetosphere, and interaction with the solar wind: Pioneer 11. Science 188, 451 (1975) · doi:10.1126/science.188.4187.451 |
| [33] | F.D. Stacey, Electrical resistivity of the earth’s core. EPSL 3, 204 (1967) · doi:10.1016/0012-821X(67)90037-4 |
| [34] | D.J. Stevenson, Planetary magnetic fields. Rep. Prog. Phys. 46, 555 (1983) · doi:10.1088/0034-4885/46/5/001 |
| [35] | D.J. Stevenson, Mercurys magnetic field: a thermoelectric dynamo? Earth Planet. Sci. Lett. 82, 114 (1987) · doi:10.1016/0012-821X(87)90111-7 |
| [36] | D.J. Stevenson, Planetary magnetic fields: achievements and prospects. Space Sci. Rev. 152, 651 (2010) · doi:10.1007/s11214-009-9572-z |
| [37] | G.W. Sutton, A. Sherman, Engineering magnetohydrodynamics (Dover Publications, New York, 2006) |
| [38] | J.A. Tarduno, R.D. Cottrell, M.K. Watkeys, A. Hofmann, P.V. Doubrovine, E.E. Mamajek, D. Liu, D.G. Sibeck, L.P. Neukirch, Y. Usui, Geodynamo, solar wind, and magnetopause 3.4 to 3.45 billion years ago. Science 327, 1238 (2010) · doi:10.1126/science.1183445 |
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