Advertisement

Acta Geophysica

, Volume 63, Issue 3, pp 900–921 | Cite as

Comparison of Early Evolutions of Mimas and Enceladus

  • Leszek Czechowski
  • Piotr Witek
Open Access
Article

Abstract

Thermal history of Mimas and Enceladus is investigated from the beginning of accretion to 400 Myr. The numerical model of convection combined with the parameterized theory is used. The following heat sources are included: short lived and long lived radioactive isotopes, accretion, serpentinization, and phase changes. The heat transfer processes are: conduction, solid state convection, and liquid state convection. We find that temperature of Mimas’ interior was significantly lower than that of Enceladus. If Mimas accreted 1.8 Myr after CAI then the internal melting and differentiation did not occur at all. Comparison of thermal models of Mimas and Enceladus indicates that conditions favorable for the start of tidal heating lasted for a short time (~107 yr) in Mimas and for ~108 yr in Enceladus. This could explain the Mimas—Enceladus paradox. In fact, in view of the chronology based on cometary impact rate, one cannot discard a possibility that also Mimas was for some time active and it has the interior differentiated on porous core and icy mantle.

Key words

medium-sized satellites thermal evolution differentiation Mimas—Enceladus paradox 

References

  1. Abramov, O., and S.J. Mojzsis (2011), Abodes for life in carbonaceous asteroids? Icarus 213, 1, 273–279, DOI: 10.1016/j.icarus.2011.03.003.CrossRefGoogle Scholar
  2. Bobojć, A., and A. Drożyner (2011), GOCE satellite orbit in the aspect of selected gravitational perturbations, Acta Geophys. 59, 2, 428–452, DOI: 10.2478/s11600-010-0052-3.Google Scholar
  3. Charnoz, S., A. Morbidelli, L. Dones, and J. Salmon (2009), Did Saturn’s rings form during the Late Heavy Bombardment? Icarus 199, 2, 413–428, DOI: 10.1016/j.icarus.2008.10.019.CrossRefGoogle Scholar
  4. Christensen, U. (1984), Convection with pressure- and temperature-dependent non-Newtonian rheology, Geophys. J. Int. 77, 2, 343–384, DOI: 10.1111/j.1365-246X.1984.tb01939.x.CrossRefGoogle Scholar
  5. Czechowski, L. (1993), Theoretical approach to mantle convection. In: R. Teisseyre, L. Czechowski, and J. Leliwa-Kopystynski (eds.), Dynamics of the Earth’s Evolution, PWN — Polish Scientific Publ., Warszawa, Elsevier, Amsterdam, 161–271.Google Scholar
  6. Czechowski, L. (2006a), 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.CrossRefGoogle Scholar
  7. Czechowski, L. (2006b), 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
  8. Czechowski, L. (2009), Uniform parameterized theory of convection in medium sized icy satellites of Saturn, Acta Geophys. 57, 2, 548–566, DOI: 10.2478/s11600-008-0084-0.CrossRefGoogle Scholar
  9. Czechowski, L. (2012), Thermal history and large scale differentiation of the Saturn’s satellite Rhea, Acta Geophys. 60, 4, 1192–1212, DOI: 10.2478/s11600-012-0041-9.CrossRefGoogle Scholar
  10. Czechowski, L. (2014), Some remarks on the early evolution of Enceladus, Planet. Space Sci. 104, 185–199, DOI: 10.1016/j.pss.2014.09.010.CrossRefGoogle Scholar
  11. Czechowski, L., and K.J. Kossacki (2012), Thermal convection in the porous methane-soaked regolith in Titan: finite amplitude convection, Icarus 217, 1, 130–143, DOI: 10.1016/j.icarus.2011.10.006.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. 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
  14. 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, DOI: 10.1007/978-94-011-5252-5_3.Google Scholar
  15. Ellsworth, K., and G. Schubert (1983), Saturn’s icy satellites: Thermal and structural models, Icarus 54, 3, 490–510, DOI: 10.1016/0019-1035(83)90242-7.CrossRefGoogle Scholar
  16. Eluszkiewicz, J. (1990), Compaction and internal structure of Mimas, Icarus 84, 1, 215–225, DOI: 10.1016/0019-1035(90)90167-8.CrossRefGoogle Scholar
  17. Essa, K.S. (2007), A simple formula for shape and depth determination from residual gravity anomalies, Acta Geophys. 55, 2, 182–190, DOI: 10.2478/s11600-007-0003-9.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. Goldsby, D.L., and D.L. Kohlstedt (1997), Grain boundary sliding in fine-grained Ice — I, Scripta. Mater. 37, 9, 1399–1406, DOI: 10.1016/S1359-6462(97)00246-7.CrossRefGoogle Scholar
  20. Grasset, O., and E.M. Parmentier (1998), Thermal convection in a volumetrically heated, infinite Prandtl number fluid with strongly temperature-dependent viscosity: Implications for planetary evolution, J. Geophys. Res. 103, B8, 18171–18181, DOI: 10.1029/98JB01492.CrossRefGoogle Scholar
  21. Jaumann, R., R.N. Clark, F. Nimmo, A.R. Hendrix, B.J. Buratti, T. Denk, J.M. Moore, P.M. Schenk, S.J. Ostro, and R. Srama (2009), Icy satellites: Geological evolution and surface processes. In: M.K. Dougherty L.W. Esposito, and S.M. Krimigis (eds.), Saturn from Cassini-Huygens, Springer Science+Business Media, Dordrecht, 637–681, DOI: 10.1007/978-1-4020-9217-6_20.CrossRefGoogle Scholar
  22. Kriegel, H., S. Simon, J. Müller, U. Motschmann, J. Saur, K.-H. Glassmeier, and M.K. Dougherty (2009), The plasma interaction of Enceladus: 3D hybrid simulations and comparison with Cassini MAG data, Planet. Space Sci. 57, 14–15, 2113–2122, DOI: 10.1016/j.pss.2009.09.025.CrossRefGoogle Scholar
  23. Leliwa-Kopystynski, J., and K.J. Kossacki (2000), Evolution of porosity in small icy bodies, Planet. Space Sci. 48, 7–8, 727–745, DOI: 10.1016/S0032-0633(00)00038-6.CrossRefGoogle Scholar
  24. Malamud, U., and D. Prialnik (2013), Modeling serpentinization: Applied to the early evolution of Enceladus and Mimas, Icarus 225, 1, 763–774, DOI:10.1016/j.icarus.2013.04.024.CrossRefGoogle Scholar
  25. Matson, D.L., J.C. Castillo-Rogez, G. Schubert, C. Sotin, and W.B. McKinnon (2009), The thermal evolution and internal structure of Saturn’s mid-sized icy satellites. In: M.K. Dougherty, L.W. Esposito, and S.M. Krimigis (eds.), Saturn from Cassini-Huygens, Springer Science+Business Media, Dordrecht, 577–612, DOI: 10.1007/978-1-4020-9217-6_18.CrossRefGoogle Scholar
  26. McKinnon, W.B. (1998), Geodynamics of icy satellites. In: B. Schmitt, C. de Bergh, and M. Festou (eds.), Solar System Ices, Kluwer Academic Publ., Dordrecht, 525–550, DOI: 10.1007/978-94-011-5252-5_22.Google Scholar
  27. McKinnon, W.B., and A.C. Barr (2007), The Mimas paradox revisited plus crustal spreading on Enceladus? LPI Contrib. 1357, 91–92.Google Scholar
  28. Merk, R., D. Breuer, and T. Spohn (2002), Numerical modeling of 26Al-induced radioactive melting of asteroids concerning accretion, Icarus 159, 1, 183–191, DOI: 10.1006/icar.2002.6872.CrossRefGoogle Scholar
  29. 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
  30. Multhaup, K., and T. Spohn (2007), Stagnant lid convection in the mid-sized icy satellite of Saturn, Icarus 186, 2, 420–435, DOI: 10.1016/j.icarus.2006.09.001.CrossRefGoogle Scholar
  31. Muro, G.D., and F. Nimmo (2011), Modeling the coupled thermal and orbital evolution of Mimas, LPI Contrib. 1608, 1560.Google Scholar
  32. Peale, S.J. (2003), Tidally induced volcanism, Celest. Mech. Dyn. Astr. 87, 1–2, 129–155, DOI: 10.1023/A:1026187917994.CrossRefGoogle Scholar
  33. 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
  34. Peltier, W.R., and G.T. Jarvis (1982), Whole mantle convection and the thermal evolution of the Earth, Phys. Earth Planet. In. 29, 3–4, 281–304, DOI: 10.1016/0031-9201(82)90018-8.CrossRefGoogle Scholar
  35. 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
  36. Robuchon, G., G. Choblet, G. Tobie, O. Čadek, C. Sotin, and O. Grasset (2010), Coupling of thermal evolution and despinning of early Iapetus, Icarus 207, 2, 959–971, DOI: 10.1016/j.icarus.2009.12.002.CrossRefGoogle Scholar
  37. 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
  38. Rothery, D.A. (1992), Satellites of the Outer Planets: Worlds in Their Own Right, Clarendon Press, Oxford, 208 pp.Google Scholar
  39. 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, University of Arizona Press, Tucson, 224–292.Google Scholar
  40. Schubert, G., D.L. Turcotte, and P. Olson (2001), Mantle Convection in the Earth and Planets, Cambridge Univ. Press, Cambridge, 956 pp.CrossRefGoogle Scholar
  41. Schubert, G., J.D. Anderson, B.J. Travis, and J. Palguta (2007), Enceladus: Present internal structure and differentiation by early and long-term radiogenic heating, Icarus 188, 2, 345–355, DOI: 10.1016/j.icarus.2006.12.012.CrossRefGoogle Scholar
  42. Sharpe, H.N., and W.R. Peltier (1978), Parameterized mantle convection and the Earth’s thermal history, Geophys. Res. Lett. 5, 9, 737–740, DOI: 10.1029/GL005i009p00737.CrossRefGoogle Scholar
  43. Spencer, J.R., A.C. Barr, L.W. Esposito, P. Helfenstein, A.P. Ingersoll, R. Jaumann, C.P. McKay, F. Nimmo, and J.H. Waite (2009), Enceladus: An active cryovolcanic satellite. In: M.K. Dougherty, L.W. Esposito, and S.M. Krimigis (eds.), Saturn from Cassini-Huygens, Springer Science+Business Media, Dordrecht, 683–724, DOI: 10.1007/978-1-4020-9217-6_21.CrossRefGoogle Scholar
  44. Taubner, R.S., J.J. Leitner, M.G. Firneis, and R. Hirzenberger (2014), Including Cassini’s gravity measurements from the flybys E9, E12, E19 into interior structure models of Enceladus. In: Proc. European Planetary Science Congress, 7–12 September 2014, Cascais, Portugal, EPSC Abstracts, 2014-Google Scholar
  45. Thomas, P.C. (2010), Sizes, shapes, and derived properties of the Saturnian satellites after the Cassini nominal mission, Icarus 208, 61, 395–401, DOI: 10.1016/j.icarus.2010.01.025.CrossRefGoogle Scholar
  46. Turcotte, D.L., and G. Schubert (2002), Geodynamics, 2nd ed., Cambridge University Press, Cambridge, 465 pp.CrossRefGoogle Scholar
  47. Zahnle, K., P. Schenk, H. Levison, and L. Dones (2003), Cratering rates in the outer Solar System, Icarus 163, 2, 263–289, DOI: 10.1016/S0019-1035(03)00048-4.CrossRefGoogle Scholar

Copyright information

© Czechowski and Witek 2015

Authors and Affiliations

  1. 1.Institute of GeophysicsUniversity of WarsawWarszawaPoland

Personalised recommendations