Advertisement

Tides of io

  • Tilman Spohn
Tides In Outer Space
Part of the Lecture Notes in Earth Sciences book series (LNEARTH, volume 66)

Abstract

Jupiter's satellite Io is the most active earth-like planetary body in the solar system with a surface heat flow of, at least, 2.5 W m−2, a resurfacing rate of 1.3 cm a−1, and, possibly, a self-sustained magnetic field. It is universally accepted that the activity is driven by tidal energy dissipated in Io's mantle. Tides with amplitudes two orders of magnitude larger than the lunar tides on Earth are raised on Io by Jupiter. Since Io rotates synchronously with its orbital revolution, substantial tidal deformation requires an eccentric orbit. The orbital eccentricity is maintained by the Laplace resonance between the inner Jovian satellites against the damping induced by tidal dissipation in Io's interior. Models of tidal dissipation assume a visco-elastic mantle rheology and require a fluid (outer) core to allow sufficiently strong tidal deformation. The mantle most likely is partially molten and there may be an asthenosphere or magmasphere underneath the lithosphere. The energy that is dissipated in Io is drawn from Jupiter's rotational energy and is transferred to Io's orbital energy before part of it is dissipated in the satellite. Tidal dissipation thus is a sink in the orbital energy balance and a source in the energy balance of the interior. The energy balances are coupled through the temperature dependent rheology parameters. Models of the thermal-orbital evolution indicate that a quasi-stationary high dissipation state is possible as well as oscillations of the thermal and orbital parameters. A magnetic field is unlikely in a quasi-stationary state. The time rate of change of orbit parameters such as the mean motion are constrained by astrometrical observation over the past 300 years. These data can be used to constrain the present tidal dissipation rate. These constraints indicate that the present heat flow is an order of magnitude larger than the present dissipation rate. A model of time dependent heat transfer with local hot spots in the mantle where melt is generated by viscous dissipation is proposed. This model may explain the gap between the present heat flow and the tidal dissipation rate.

Keywords

Heat Flow Rayleigh Number Dissipation Rate Dynamo Action Galilean Satellite 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alterman, Z., H. Jarosch, C. L. Pekeris. 1959. Oscillations of the Earth. Proc. R. Soc. London A 252: 80–95.Google Scholar
  2. Anderson, J. D., W. L. Sjogren, and G. Schubert. 1996. Galileo gravity results and the internal structure of Io. Science 272: 709–712.Google Scholar
  3. Balachandar, S., D. A. Yuen, and D. Reuteler. 1993. Viscous and adiabatic heating effects in three-dimensional compressible convection at infinite Prandtl number. Phys. Fluids A 5: 2938–2945.Google Scholar
  4. Balachandar, S., D. A. Yuen, D. Reuteler, and G. Lauer. 1995. Viscous dissipation in three dimensional convection with temperature-dependent viscosity. Science 267: 1150–1153.Google Scholar
  5. Boehler, R. 1986. The phase diagram of iron to 430 kbar. Geophys. Res. Lett. 13: 1153–1156.Google Scholar
  6. Boehler, R. 1992. Melting of the Fe-FeO and the Fe-FeS systems at high pressure: Constraints on core temperature. Earth Planet. Sci. Lett. 111: 217–227.Google Scholar
  7. Burns, J. A. 1986. Some background about satellites. In: Satellites. pp. 1–38. J. A. Burns and M. S. Matthews (eds.). Univ. Arizona Press, Tucson.Google Scholar
  8. Busse, F. H. 1976. Generation of planetary magnetism by convection. Phys. Earth Planet. Int. 12: 350–358.Google Scholar
  9. Castaing, B., G. Gunaratne, F. Heslot, L. Kadanoff, S. Libchaber, S. Thomae, X.-Z. Wu, S. Zaleski, and G. Zanetti. 1982. Scaling of hard thermal turbulence in Rayleigh-Bénard convection. J. Fluid. Mech. 204: 1–30.Google Scholar
  10. Christensen, U. R. 1985. Thermal evolution models for the earth. J. geophys. Res. 90: 2995–3007.Google Scholar
  11. Consolmagno G. J. 1981. Io: Thermal models and chemical evolution. Icarus 47: 36–45.Google Scholar
  12. Fischer H. J., and T. Spohn. 1990. Thermal-orbital histories of viscoelastic models of Io (J1). Icarus 83: 39–65.Google Scholar
  13. Frank, L. A., W. R. Paterson, K. L. Ackerson, V. M. Vasyliunas, F. V. Coroniti, and S. J. Bolton. 1996. Plasma observations of Io with the Galileo spacecraft. Science 274: 394–395.Google Scholar
  14. Gaskell, R. W. and S. T. Synott. 1988. Large-scale topography of Io: Implications for internal structure and heat transfer. Geophys. Res. Lett. 15: 581–584.Google Scholar
  15. Hansen, U. and D. A. Yuen. 1990. Heat transport in strongly chaotic thermal convection. In: HTD-Vol 149, Heat Transfer in Earth Science Studies. pp. 43–46. C. Carrigan and T. Y. Chu (eds.) American Society of Mechanical Engineers, Book No. G00543.Google Scholar
  16. Johnson, T. V., D. L. Matson, D. L. Blaney, G. J. Veeder, and A. Davies.1995. Stealth plumes on Io. Geophys. Res. Lett. 22: 3293–3296.Google Scholar
  17. Kaula, W. M. 1964. Tidal dissipation by solid friction and the resulting orbital evolution. Rev. Geophys. 2: 661–685.Google Scholar
  18. Kivelson, M. G., K. K. Khurana, R. J. Walker, C. T. Russell, J. A. Linker, D. J. Southwood, and C. Polanskey. 1996. A magnetic signature on Io: Initial report from the Galileo magnetometer. Science 273: 337–340.Google Scholar
  19. Lewis J. S. 1982. Io: Geochemistry of sulfur. Icarus 50: 103–114.Google Scholar
  20. Lieske J. H. 1987. Galilean satellite evolution: Observational evidence for secular changes in mean motions. Astron. Astrophys. 176: 146–158.Google Scholar
  21. Love, A. E. H. 1927. A treatise on the mathematical theory of elasticity. 4th Ed., Dover, New York. 643 pp.Google Scholar
  22. Malevsky, A. V. and D. A. Yuen. 1992. Strongly chaotic non-Newtonian mantle convection. Geophys. Astrophys. Fluid Dyn. 65: 149–171.Google Scholar
  23. Malhotra, R. 1991. Tidal Origin of the Laplace resonance and the resurfacing of Ganymede. Icarus 94: 399–412.Google Scholar
  24. McEwen, A. S., J. I. Lunine, and H. C. Carr. 1989. Dynamic geophysics on Io. 11-46. In: Time variable phenomena in the Jovian system. M. J. S. Belton, R. A. West, and J. Rahe (eds.) NASA SP-494.Google Scholar
  25. Neubauer, F. M. 1978. Possible strengths of dynamo magnetic fields of the Galilean satellites and of Titan. Geophys. Res. Lett. 5: 905–908.Google Scholar
  26. Peale S. J., P. Cassen, and R. T. Reynolds. 1979. Melting of Io by tidal dissipation. Science 203: 892–894.Google Scholar
  27. Platzman, G. W. 1984. Planetary energy balance for tidal dissipation. Rev. Geophys. Space Phys. 22: 73–84.Google Scholar
  28. Ross M. N., G. Schubert, T. Spohn, and R. W. Gaskell. 1990. Internal Structure of Io and the global distribution of its topography. Icarus 85: 309–325.Google Scholar
  29. Schubert, G., T. Spohn, and R. T. Reynolds. 1986. Thermal histories, compositions and internal structures of the moons of the solar system. 224–292. In: Satellites. J. A. Burns and M. S. Matthews (eds.). Univ. Arizona Press, Tucson.Google Scholar
  30. Schubert, G., M. N. Ross, D. J. Stevenson, and T. Spohn. 1988. Mercury's thermal history and the generation of its magnetic field. 429–460. In: Mercury. F. Vilas, C. R. Chapman, and M. S. Matthews (eds.). Univ. Arizona Press, Tucson.Google Scholar
  31. Segatz M., T. Spohn, M. N. Ross, and G. Schubert. 1988. Tidal Dissipation, surface heat flow, and figure of viscoelastic models of Io. Icarus 75: 187–206.Google Scholar
  32. Spohn T., Schubert G. 1982. Modes of mantle convection and the removal of heat from the Earth's interior. J. geophys. Res. 87: 4682–4686.Google Scholar
  33. Stacey, F. D. 1977. Physics of the Earth. 2ed. Wiley, New York. 414 pp.Google Scholar
  34. Stevenson D. J., T. Spohn, and G. Schubert. 1983. Magnetism and thermal evolution of the terrestrial planets. Icarus 54: 466–489.Google Scholar
  35. Takahashi, E. 1986. Melting of a dry peridotite KLB-1 up to 14 GPa: Implications on the origin of peridotitic upper mantle. J. geophys. Res. 91: 9367–9382.Google Scholar
  36. Takahashi, E. 1990. Speculations on the Archean mantle: Missing link between komatiite and depleted garnet peridotite. J. geophys. Res. 95: 15941–15954.Google Scholar
  37. Takeuchi, H., M. Saito, and N. Kobayashi. 1962. Statical deformations and free oscillations of a model Earth. J. geophys. Res. 67: 1141–1154.Google Scholar
  38. Tozer, D. 1965. Heat transfer and convection currents. Phil. Trans. R. Soc. London A 258: 252–271.Google Scholar
  39. Turcotte, D. L. 1982. Magma migration. Ann. Rev. Earth Planet. Sci. 10: 397–408.Google Scholar
  40. Usselman, T. M. 1975a. Experimental approach to the state of the core: Part 1. The liquidus relations of the Fe-Ni-S system from 30 to 100 kb. Am. J. Sci. 275: 278–290.Google Scholar
  41. Usselman, T. M. 1975b. Experimental approach to the state of the core: Part 2. Composition and thermal regime. Am. J. Sci. 275: 291–303.Google Scholar
  42. Veeder G. J., D. L. Matson, T. V. Johnson, D. L. Blaney, and J. D. Goguen.1994. Io's heat flow from infrared radiometry: 1983–1993. J. geophys. Res. 99: 17095–17162.Google Scholar
  43. Verhoogen, J. 1980. Energetics of the Earth. National Academy Press, Washington. 139 pp.Google Scholar
  44. Vincent, A. P., U. Hansen, D. A. Yuen, A. V. Malevsky, and S. E. Kroening. 1991. The origin of a characteristic frequency in hard thermal turbulence. Phys. Fluids. A 3: 2003–2006.Google Scholar
  45. Webb, E. K. and D. J. Stevenson. 1987. Subsidence of topography on Io. Icarus 70: 348–353.Google Scholar
  46. Wieczerkowski, K. and D. Wolf. 1996. Viscoelastic tidal perturbations: Effects due to density contrasts. Annal. Geophys. 14, Suppl. I: 102.Google Scholar
  47. Wienbruch, U. and T. Spohn. 1995. A self sustained magnetic field on Io? Planet Space. Sci. 43: 1045–1057.Google Scholar
  48. Wyllie, P. J. 1988. Magma genesis, plate tectonics, and chemical differentiation of the Earth. Rev. Geophys. 26: 370–404.Google Scholar
  49. Yoder C.F. 1979. How tidal heating in Io drives the Galilean orbital resonance locks. Nature 279: 767–770.Google Scholar
  50. Yoder, C. F. and S. J. Peale. 1981. The tides of Io. Icarus 47: 1–5.Google Scholar
  51. Yuen, D. A., U. Hansen, W. Zhao, A. P. Vincent, and A. V. Malevsky. 1993. Hard turbulent thermal convection and thermal evolution of the mantle. J. geophys. Res. 98: 5355–5373.Google Scholar
  52. Zschau, J. 1978. Tidal friction in the solid Earth: Loading tides versus body tides. In: Tidal Friction and the Earth's Rotation. 62–94. P. Brosche and J. Sündermann (eds.). Springer Verlag, Berlin.Google Scholar

Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Tilman Spohn
    • 1
  1. 1.Institut für PlanetologieWestfälische Wilhelms-UniversitätMünsterGermany

Personalised recommendations