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.
Preview
Unable to display preview. Download preview PDF.
References
Alterman, Z., H. Jarosch, C. L. Pekeris. 1959. Oscillations of the Earth. Proc. R. Soc. London A 252: 80–95.
Anderson, J. D., W. L. Sjogren, and G. Schubert. 1996. Galileo gravity results and the internal structure of Io. Science 272: 709–712.
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.
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.
Boehler, R. 1986. The phase diagram of iron to 430 kbar. Geophys. Res. Lett. 13: 1153–1156.
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.
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.
Busse, F. H. 1976. Generation of planetary magnetism by convection. Phys. Earth Planet. Int. 12: 350–358.
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.
Christensen, U. R. 1985. Thermal evolution models for the earth. J. geophys. Res. 90: 2995–3007.
Consolmagno G. J. 1981. Io: Thermal models and chemical evolution. Icarus 47: 36–45.
Fischer H. J., and T. Spohn. 1990. Thermal-orbital histories of viscoelastic models of Io (J1). Icarus 83: 39–65.
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.
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.
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.
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.
Kaula, W. M. 1964. Tidal dissipation by solid friction and the resulting orbital evolution. Rev. Geophys. 2: 661–685.
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.
Lewis J. S. 1982. Io: Geochemistry of sulfur. Icarus 50: 103–114.
Lieske J. H. 1987. Galilean satellite evolution: Observational evidence for secular changes in mean motions. Astron. Astrophys. 176: 146–158.
Love, A. E. H. 1927. A treatise on the mathematical theory of elasticity. 4th Ed., Dover, New York. 643 pp.
Malevsky, A. V. and D. A. Yuen. 1992. Strongly chaotic non-Newtonian mantle convection. Geophys. Astrophys. Fluid Dyn. 65: 149–171.
Malhotra, R. 1991. Tidal Origin of the Laplace resonance and the resurfacing of Ganymede. Icarus 94: 399–412.
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.
Neubauer, F. M. 1978. Possible strengths of dynamo magnetic fields of the Galilean satellites and of Titan. Geophys. Res. Lett. 5: 905–908.
Peale S. J., P. Cassen, and R. T. Reynolds. 1979. Melting of Io by tidal dissipation. Science 203: 892–894.
Platzman, G. W. 1984. Planetary energy balance for tidal dissipation. Rev. Geophys. Space Phys. 22: 73–84.
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.
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.
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.
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.
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.
Stacey, F. D. 1977. Physics of the Earth. 2ed. Wiley, New York. 414 pp.
Stevenson D. J., T. Spohn, and G. Schubert. 1983. Magnetism and thermal evolution of the terrestrial planets. Icarus 54: 466–489.
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.
Takahashi, E. 1990. Speculations on the Archean mantle: Missing link between komatiite and depleted garnet peridotite. J. geophys. Res. 95: 15941–15954.
Takeuchi, H., M. Saito, and N. Kobayashi. 1962. Statical deformations and free oscillations of a model Earth. J. geophys. Res. 67: 1141–1154.
Tozer, D. 1965. Heat transfer and convection currents. Phil. Trans. R. Soc. London A 258: 252–271.
Turcotte, D. L. 1982. Magma migration. Ann. Rev. Earth Planet. Sci. 10: 397–408.
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.
Usselman, T. M. 1975b. Experimental approach to the state of the core: Part 2. Composition and thermal regime. Am. J. Sci. 275: 291–303.
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.
Verhoogen, J. 1980. Energetics of the Earth. National Academy Press, Washington. 139 pp.
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.
Webb, E. K. and D. J. Stevenson. 1987. Subsidence of topography on Io. Icarus 70: 348–353.
Wieczerkowski, K. and D. Wolf. 1996. Viscoelastic tidal perturbations: Effects due to density contrasts. Annal. Geophys. 14, Suppl. I: 102.
Wienbruch, U. and T. Spohn. 1995. A self sustained magnetic field on Io? Planet Space. Sci. 43: 1045–1057.
Wyllie, P. J. 1988. Magma genesis, plate tectonics, and chemical differentiation of the Earth. Rev. Geophys. 26: 370–404.
Yoder C.F. 1979. How tidal heating in Io drives the Galilean orbital resonance locks. Nature 279: 767–770.
Yoder, C. F. and S. J. Peale. 1981. The tides of Io. Icarus 47: 1–5.
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.
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.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag
About this chapter
Cite this chapter
Spohn, T. (1997). Tides of io. In: Wilhelm, H., Zürn, W., Wenzel, HG. (eds) Tidal Phenomena. Lecture Notes in Earth Sciences, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0011471
Download citation
DOI: https://doi.org/10.1007/BFb0011471
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62833-0
Online ISBN: 978-3-540-68700-9
eBook Packages: Springer Book Archive