Acta Geophysica

, Volume 57, Issue 2, pp 548–566 | Cite as

Uniform parameterized theory of convection in medium sized icy satellites of Saturn

  • Leszek CzechowskiEmail author
Research Article


We develop a parameterized theory of convection driven by radiogenic and tidal heating. The tidal heating depends on eccentricity e of a satellite’s orbit. Using parameterized theory we determine the intensity of convection as a function of e and satellite’s properties. The theory is used for 6 medium sized satellites of Saturn. We find that endogenic activity on Tethys and Dione is possible if e exceeds some critical values e cr . For Enceladus, e was probably close to the present value for billions of years. We cannot find constrains for e of Mimas and Iapetus. The theory successfully predicts the possibility of present endogenic activity in Dione and rules out such activity in Tethys. Both these facts were recently confirmed by Cassini mission.

Key words

medium-sized satellites thermal evolution tectonics orbit eccentricity 


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  1. Barr, A.C., and R.T. Pappalardo (2005), Onset of convection in the icy Galilean satellites: Influence of rheology, J. Geophys. Res. 110, E12005, DOI: 10.1029/2004JE002371.CrossRefGoogle Scholar
  2. Burch, J.L., J. Goldstein, W.S. Lewis, D.T. Young, A.J. Coates, M.K. Dougherty, and N. André (2007), Tethys and Dione as sources of outward-flowing plasma in Saturn’s magnetosphere, Nature 447, 833–835, DOI: 10.1038/nature05906.CrossRefGoogle Scholar
  3. Castillo, J.C., D.L. Matson, C. Sotin, T.V. Johnson, J.I. Lunine, and P.C. Thomas (2006), A new understanding of the internal evolution of Saturnian icy satellites from Cassini observations, 37th Annual Lunar and Planetary Science Conference, March 13-17, 2006, League City, TX, abstr. no. 2200.Google Scholar
  4. Chen, E.M.A., and F. Nimmo (2008), Thermal and orbital evolution of Tethys as constrained by surface observations, 39th Lunar and Planetary Science Conference, March 10–14, 2008, League City, TX, p. 1968.Google Scholar
  5. Christensen, U. (1984), Convection with pressure and temperature-dependent non-Newtonian rheology, Geophys. J. Roy. Astron. Soc. 77, 343–384.Google Scholar
  6. Czechowski, L. (1993), Theoretical approach to mantle convection. In: R. Teisseyre, L. Czechowski, and J. Leliwa-Kopystynski (eds.), Dynamics of the Earth’s Evolution, Elsevier, Amsterdam, 161–271.Google Scholar
  7. Czechowski, L. (2006)a, Parameterized model of convection driven by tidal and radiogenic heating, Adv. Space Res. 38, 4, 788–793, DOI: 10.1016/j.asr.2005.12.013, presented also in COSPAR 2004, Session B0.5/D3.7/C3.4.CrossRefGoogle Scholar
  8. Czechowski, L. (2006)b, Two models of parameterized convection for mediumsized icy satellites of Saturn, Acta Geophys. 54, 3, 280–302, DOI: 10.2478/s11600-006-0021-z.CrossRefGoogle Scholar
  9. Czechowski, L. (2006)c, Endogenic activity of medium size icy satellites of Saturn and eccentricities of their orbits, 36th COSPAR Scientific Assembly, 16–23 July, 2006, Beijing, China, Session B0.3-0035.Google Scholar
  10. Czechowski, L., and J. Leliwa-Kopystynski (2005), Convection driven by tidal and radiogenic heating in medium size icy satellites, Planet. Space Sci. 53, 7, 749–769, DOI: 10.1016/j.pss.2005.01.004.CrossRefGoogle Scholar
  11. Czechowski, L., and J. Leliwa-Kopystynski (2008), The Iapetus’s ridge: Possible explanations of its origin, J. Adv. Space Res. 42, 1, 61–69, DOI: 10.1016/j.asr.2007.08.008.CrossRefGoogle Scholar
  12. Davaille, A., and C. Jaupart (1993), Transient high-Rayleigh-number thermal convection with large viscosity variations, J. Fluid Mech. 253, 141–166, DOI: 10.1017/S0022112093001740.CrossRefGoogle Scholar
  13. de Pater, I., and J.J. Lissauer (2001), Planetary Sciences, Cambridge Univ. Press, Cambridge, 528 pp.Google Scholar
  14. Dumoulin, C., M.-P. Doin, and L. Fleitout (1999), Heat transport in stagnant lid convection with temperature- and pressure-dependent Newtonian or non-Newtonian rheology, J. Geophys. Res. 104, B6, 12759–12777, DOI: 10.1029/1999JB900110.CrossRefGoogle Scholar
  15. Durham, W.B., S.H. Kirby, and L.A. Stern (1993), Flow of ices in the ammoniawater system, J. Geophys. Res. 98, B10, 17667–17682, DOI: 10.1029/93JB01564.CrossRefGoogle Scholar
  16. Durham, W.B., S.H. Kirby, and L.A. Stern (1998), Rheology of planetary ices. In: B. Schmitt, C. de Bergh, and M. Festou (eds.), Solar System Ices, Kluwer Academic Publ., Dordrecht, 63–78.Google Scholar
  17. Fischer, H.-J., and T. Spohn (1990), Thermal-orbital histories of viscoelastic models of Io (J1), Icarus 83, 1, 39–65, DOI: 10.1016/0019-1035(90)90005-T.CrossRefGoogle Scholar
  18. Forni, O., A. Coradini, and C. Federico (1991), Convection and lithospheric strength in Dione, an icy satellite of Saturn, Icarus 94, 1, 232–245, DOI: 10.1016/0019-1035(91)90153-K.CrossRefGoogle Scholar
  19. Gavrilov, S.V., and V.N. Zharkov (1977), Love numbers of the giant planets, Icarus 32, 4, 443–449, DOI: 10.1016/0019-1035(77)90015-X.CrossRefGoogle Scholar
  20. Goldsby, D.L., and D.L. Kohlstedt (1997), Grain boundary sliding in fine-grained ice I, Scr. Mater. 37, 9, 1399–1406, DOI: 10.1016/S1359-6462(97)00246-7.CrossRefGoogle Scholar
  21. Goldsby, D.L., and D.L. Kohlstedt (2001), Superplastic deformation of ice: Experimental observations, J. Geophys. Res. 106, B6, 11017–11030, DOI: 10.1029/2000JB900336.CrossRefGoogle Scholar
  22. Hobbs, P.V. (1974), Ice Physics, Oxford Univ. Press, New York.Google Scholar
  23. Jacobson, R.A. (2004), The orbits of the major Saturnian satellites and the gravity field of Saturn from spacecraft and Earth-based observations, Astron. J. 128, 1, 492–501, DOI: 10.1086/421738.CrossRefGoogle Scholar
  24. Jurac, S., R.E. Johnson, J.D. Richardson, and C. Paranicas (2001), Satellite sputtering in Saturn’s magnetosphere, Planet. Space Sci. 49, 3-4, 319–326, DOI: 10.1016/S0032-0633(00)00153-7.CrossRefGoogle Scholar
  25. Kargel, J.S., and S. Pozio (1996), The volcanic and tectonic history of Enceladus, Icarus 119, 2, 385–404, DOI: 10.1006/icar.1996.0026.CrossRefGoogle Scholar
  26. Kossacki, K.J., and J. Leliwa-Kopystynski (1993), Medium-sized icy satellites: thermal and structural evolution during accretion, Planet. Space Sci. 41, 10, 729–741, DOI: 10.1016/0032-0633(93)90115-I.CrossRefGoogle Scholar
  27. Leisner, J.S., K.K. Khurana, C.T. Russell, M.K. Dougherty, A.M. Persoon, X. Blanco-Cano, and R.J. Strangeway (2007), Observations of Enceladus and Dione as sources for Saturn’s neutral cloud, 38th Lunar and Planetary Science Conference, 12–16 March, 2007, League City, TX, p. 1425.Google Scholar
  28. Officer, C.B. (1974), Introduction to Theoretical Geophysics, Springer-Verlag, Berlin.Google Scholar
  29. Meyer, J., and J. Wisdom (2007), Tidal heating in Enceladus, Icarus 188, 2, 535–539, DOI: 10.1016/j.icarus.2007.03.001.CrossRefGoogle Scholar
  30. Meyer, J., and J. Wisdom (2008), Tidal evolution of Mimas, Enceladus, and Dione, Icarus 193, 1, 213–223, DOI: 10.1016/j.icarus.2007.09.008.CrossRefGoogle Scholar
  31. Multhaup, K., and T. Spohn (2007), Stagnant lid convection in the mid-sized icy satellites of Saturn, Icarus 186, 2, 420–435, DOI: 10.1016/j.icarus.2006.09.001.CrossRefGoogle Scholar
  32. Peale, S.J., P. Cassen, and R.T. Reynolds (1979), Melting of Io by tidal dissipation, Science 203, 4383, 892–894, DOI: 10.1126/science.203.4383.892.CrossRefGoogle Scholar
  33. Peale, S.J. (2003), Tidally induced volcanism, Celest. Mech. and Dyn. Astr. 87, 1/2, 129–155, DOI: 10.1023/A:1026187917994.CrossRefGoogle Scholar
  34. Peltier, W.R., and G.T. Jarvis (1982), Whole mantle convection and the thermal evolution of the Earth, Phys. Earth Planet. Int. 29, 3-4, 281–304, DOI: 10.1016/0031-9201(82)90018-8.CrossRefGoogle Scholar
  35. Prentice, A.J.R. (2005), Saturn’s icy moons: a model for their origin and bulk chemical composition, 36th Lunar and Planetary Science Conference, 14–18 March, 2005, League City, TX, 2378.pdf.Google Scholar
  36. Poirier, J.P., L. Boloh, and P. Chambon (1983), Tidal dissipation in small viscoelastic ice moons: The case of Enceladus, Icarus 55, 2, 218–230, DOI: 10.1016/0019-1035(83)90076-3.CrossRefGoogle Scholar
  37. Porco, C.C., and 34 co-workers (2005), Cassini Imaging Science: Initial results on Phoebe and Iapetus, Science 307, 5713, 1237–1242, DOI: 10.1126/science.1107981.CrossRefGoogle Scholar
  38. Porco, C.C., and 24 co-workers (2006), Cassini observes the active south pole of Enceladus, Science 311, 5766, 1393–1401, DOI: 10.1126/science.1123013.CrossRefGoogle Scholar
  39. Roscoe, R. (1952), The viscosity of suspensions of rigid spheres, British J. Appl. Phys. 3, 8, 267–269, DOI: 10.1088/0508-3443/3/8/306.CrossRefGoogle Scholar
  40. Ross, M.N., and G. Schubert (1989), Viscoelastic models of tidal heating in Enceladus, Icarus 78, 1, 90–101, DOI: 10.1016/0019-1035(89)90071-7.CrossRefGoogle Scholar
  41. Rothery, D.A. (1992), Satellites of the Outer Planets, Clarendon Press, Oxford.Google Scholar
  42. Schubert, G., T. Spohn, and R.T. Reynolds (1986), Thermal histories, compositions and internal structures of the moons of the solar system. In: J.A. Burns and M.S. Matthews (eds.), Satellites, Univ. of Arizona Press, Tucson, 224–292.Google Scholar
  43. Schubert, G., D.L. Turcotte and P. Olson (2001), Mantle Convection in the Earth and Planets, Cambridge Univ. Press, Cambridge, 940 pp.Google Scholar
  44. Sohl, F., H. Hussman, B. Schwentker, T. Spohn, and R.D. Lorenz (2003), Interior structure models and tidal Love numbers of Titan, J. Geophys. Res. 108, E12, 5130, DOI: 10.1029/2003JE002044.CrossRefGoogle Scholar
  45. Solomatov, V.S. (1995), Scaling of temperature- and stress-dependent viscosity convection, Phys. Fluids 7, 2, 266–274, DOI: 10.1063/1.868624.CrossRefGoogle Scholar
  46. Turcotte, D.L., and G. Schubert (1982), Geodynamics, J. Wiley & Sons, New York, 450 pp.Google Scholar
  47. Wagner, R.J., G. Neukum, B. Giese, T. Roatsch, and U. Wolf (2007), Geomorphology of Saturn’s satellite Rhea: preliminary implicatons from the Cassini ISS data, Geophys. Res. Abstracts 9, 09505.Google Scholar

Copyright information

© © Versita Warsaw and Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Institute of GeophysicsWarsaw UniversityWarszawaPoland

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