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

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Abstract

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.

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References

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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.

  • Christensen, U. (1984), Convection with pressure and temperature-dependent non-Newtonian rheology, Geophys. J. Roy. Astron. Soc. 77, 343–384.

    Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • de Pater, I., and J.J. Lissauer (2001), Planetary Sciences, Cambridge Univ. Press, Cambridge, 528 pp.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Hobbs, P.V. (1974), Ice Physics, Oxford Univ. Press, New York.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • Officer, C.B. (1974), Introduction to Theoretical Geophysics, Springer-Verlag, Berlin.

    Google Scholar 

  • Meyer, J., and J. Wisdom (2007), Tidal heating in Enceladus, Icarus 188, 2, 535–539, DOI: 10.1016/j.icarus.2007.03.001.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Peale, S.J. (2003), Tidally induced volcanism, Celest. Mech. and Dyn. Astr. 87, 1/2, 129–155, DOI: 10.1023/A:1026187917994.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Rothery, D.A. (1992), Satellites of the Outer Planets, Clarendon Press, Oxford.

    Google Scholar 

  • 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 

  • Schubert, G., D.L. Turcotte and P. Olson (2001), Mantle Convection in the Earth and Planets, Cambridge Univ. Press, Cambridge, 940 pp.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Solomatov, V.S. (1995), Scaling of temperature- and stress-dependent viscosity convection, Phys. Fluids 7, 2, 266–274, DOI: 10.1063/1.868624.

    Article  Google Scholar 

  • Turcotte, D.L., and G. Schubert (1982), Geodynamics, J. Wiley & Sons, New York, 450 pp.

    Google Scholar 

  • 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 

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Correspondence to Leszek Czechowski.

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Czechowski, L. Uniform parameterized theory of convection in medium sized icy satellites of Saturn. Acta Geophys. 57, 548–566 (2009). https://doi.org/10.2478/s11600-008-0084-0

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