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Comparison of Early Evolutions of Mimas and Enceladus

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.

References

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  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, PWN — Polish Scientific Publ., Warszawa, Elsevier, Amsterdam, 161–271.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    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 

  • 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 (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.

  • 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.

    Article  Google Scholar 

  • Eluszkiewicz, J. (1990), Compaction and internal structure of Mimas, Icarus 84, 1, 215–225, DOI: 10.1016/0019-1035(90)90167-8.

    Article  Google Scholar 

  • 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.

    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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

  • McKinnon, W.B., and A.C. Barr (2007), The Mimas paradox revisited plus crustal spreading on Enceladus? LPI Contrib. 1357, 91–92.

    Google Scholar 

  • 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.

    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 satellite of Saturn, Icarus 186, 2, 420–435, DOI: 10.1016/j.icarus.2006.09.001.

    Article  Google Scholar 

  • Muro, G.D., and F. Nimmo (2011), Modeling the coupled thermal and orbital evolution of Mimas, LPI Contrib. 1608, 1560.

    Google Scholar 

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

    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 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    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 

  • Rothery, D.A. (1992), Satellites of the Outer Planets: Worlds in Their Own Right, Clarendon Press, Oxford, 208 pp.

    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, University 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, 956 pp.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Turcotte, D.L., and G. Schubert (2002), Geodynamics, 2nd ed., Cambridge University Press, Cambridge, 465 pp.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

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Correspondence to Leszek Czechowski.

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Czechowski, L., Witek, P. Comparison of Early Evolutions of Mimas and Enceladus. Acta Geophys. 63, 900–921 (2015). https://doi.org/10.1515/acgeo-2015-0024

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Key words

  • medium-sized satellites
  • thermal evolution
  • differentiation
  • Mimas—Enceladus paradox