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Celestial Mechanics and Dynamical Astronomy

, Volume 126, Issue 1–3, pp 131–144 | Cite as

Constraints on dissipation in the deep interiors of Ganymede and Europa from tidal phase-lags

  • Hauke Hussmann
  • Daigo Shoji
  • Gregor Steinbrügge
  • Alexander Stark
  • Frank Sohl
Original Article

Abstract

Jupiter’s satellites are subject to strong tidal forces which result in variations of the gravitational potential and deformations of the satellites’ surfaces on the diurnal tidal cycle. Such variations are described by the Love numbers \(k_2\) and \(h_2\) for the tide-induced potential variation due to internal mass redistribution and the radial surface displacement, respectively. The phase-lags \( \phi _{k_2}\) and \( \phi _{h_2}\) of these complex numbers contain information about the rheological and dissipative states of the satellites. Starting from interior structure models and assuming a Maxwell rheology to compute the tidal deformation, we calculate the phase-lags in application to Ganymede and Europa. For both satellites we assume a decoupling of the outer ice-shell from the deep interior by a liquid subsurface water ocean. We show that, in this case, the phase-lag difference \(\varDelta \phi = \phi _{k_2}- \phi _{h_2}\) can provide information on the rheological and thermal state of the deep interiors if the viscosities of the deeper layers are small. In case of Ganymede, phase-lag differences can reach values of a few degrees for high-pressure ice viscosities \({<}10^{14}\) Pa s and would indicate a highly dissipative state of the deep interior. In this case \(\varDelta \phi \) is dominated by dissipation in the high-pressure ice layer rather than dissipation within the ice-I shell. These phase lags would be detectable from spacecraft in orbit around the satellite. For Europa \(\varDelta \phi \) could reach values exceeding \(20^\circ \) and phase-lag measurements could help distinguish between (1) a hot dissipative silicate mantle which would in thermal equilibrium correspond to a very thin outer ice-I shell and (2) a cold deep interior implying that dissipation would mainly occur in a thick (several tens of km) outer ice-I shell. These measurements are highly relevant for ESA’s Jupiter Icy Moons Explorer (JUICE) and NASA’s Europa Multiple Flyby Mission, both targeted for the Jupiter system.

Keywords

Solar system Satellites of Jupiter Tides Interior Ganymede Europa Love numbers JUICE 

Notes

Acknowledgments

We thank V. Lainey and an anonymous reviewer for very helpful and constructive comments. DS would like to acknowledge support from a JSPS Research Fellowship.

References

  1. Bland, M.T., Showman, A.P., Tobie, G.: The orbital-thermal evolution and global expansion of Ganymede. Icarus 200(1), 207–221 (2009)ADSCrossRefGoogle Scholar
  2. Cameron, M.E., Smith-Konter, B.R., Pappalardo, R.T., Collins, G., Nimmo, F.: Tidally-driven strike-slip failure mechanics on Ganymede. In: Lunar and Planetary Science Conference, Lunar and Planetary Institute, Technical Report, vol. 44, p. 2711 (2013)Google Scholar
  3. Chen, E.M.A., Nimmo, F., Glatzmaier, G.A.: Tidal heating in icy satellite oceans. Icarus 229, 11–30 (2014)ADSCrossRefGoogle Scholar
  4. Durham, W.B., Stern, L.A., Kirby, S.H.: Rheology of water ices V and VI. J. Geophys. Res. 101, 2989–3002 (1996)ADSCrossRefGoogle Scholar
  5. Durham, W.B., Prieto-Ballesteros, O., Goldsby, D.L., Kargel, J.S.: Rheological and thermal properties of icy materials. Space Sci. Rev. 153, 273–298 (2010)ADSCrossRefGoogle Scholar
  6. Ferraz-Mello, S., Rodriguez, A., Hussmann, H.: Tidal friction in close-in satellites and exoplanets: the Darwin theory re-visited. Celest. Mech. Dyn. Astron. 101(1–2), 171–201 (2008). Errata: Celest. Mech. Dyn. Astron. 104(3), 319–320 (2009)Google Scholar
  7. Goldsby, D.L., Kohlstedt, D.L.: Superplastic deformation of ice: experimental observations. J. Geophys. Res. 106, 11 (2001)CrossRefGoogle Scholar
  8. Goodman, J.C., Lenferink, E.: Numerical simulations of marine hydrothermal plumes for Europa and other icy worlds. Icarus 221, 970–983 (2012)ADSCrossRefGoogle Scholar
  9. Grasset, O., Dougherty, M.K., Coustenis, A., Bunce, E.J., Erd, C., Titov, D., et al.: JUpiter ICy moons Explorer (JUICE): an ESA mission to orbit Ganymede and to characterise the Jupiter system. Planet. Space Sci. 78, 1–21 (2013)ADSCrossRefGoogle Scholar
  10. Hussmann, H., Spohn, T.: Thermal-orbital evolution of Io and Europa. Icarus 171(2), 391–410 (2004)ADSCrossRefGoogle Scholar
  11. Hussmann, H., Choblet, G., Lainey, V., Matson, D.L., Sotin, C., Tobie, G., et al.: Implications of rotation, orbital states, energy sources, and heat transport for internal processes in icy satellites. Space Sci. Rev. 153(1–4), 317–348 (2010)ADSCrossRefGoogle Scholar
  12. Hussmann, H., Sohl, F., Oberst, J.: Measuring tidal deformations at Europa’s surface. Adv. Space Res. 48(4), 718–724 (2011)ADSCrossRefGoogle Scholar
  13. Mazarico, E., Barker, M.K., Neumann, G.A., Zuber, M.T., Smith, D.E.: Detection of the lunar body tide by the Lunar Orbiter Laser Altimeter. Geophys. Res. Lett. 41(7), 2282–2288 (2014a)ADSCrossRefGoogle Scholar
  14. Mazarico, E., Genova, A., Goossens, S., Lemoine, F.G., Neumann, G.A., Zuber, M.T., et al.: The gravity field, orientation, and ephemeris of Mercury from MESSENGER observations after 3 years in orbit. J. Geophys. Res. Planets 119(12), 2417–2436 (2014b)ADSCrossRefGoogle Scholar
  15. McCarthy, C., Castillo-Rogez, J.C.: Planetary ices attenuation properties. In: Gudipati, S.M., Castillo-Rogez, J. (eds.) The Science of Solar System Ices, pp. 183–225. Springer, New York (2013)CrossRefGoogle Scholar
  16. Moore, W.B., Schubert, G.: The tidal response of Europa. Icarus 147(1), 317–319 (2000)ADSCrossRefGoogle Scholar
  17. Moore, W.B., Schubert, G.: The tidal response of Ganymede and Callisto with and without liquid water oceans. Icarus 166(1), 223–226 (2003)ADSCrossRefGoogle Scholar
  18. Murray, C.D., Dermott, S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  19. Parisi, M., Iess., L, Finocchiaro., S: The gravity fields of Ganymede, Callisto and Europa: how well can JUICE do? EGU General Assembly Conference Abstracts 16 (2014)Google Scholar
  20. Peale, S.J.: Origin and evolution of the natural satellites. Annu. Rev. Astron. Astrophys. 37(1), 533–602 (1999)ADSCrossRefGoogle Scholar
  21. Roberts, J.H., Nimmo, F.: Tidal heating and the long-term stability of a subsurface ocean on Enceladus. Icarus 194(2), 675–689 (2008)ADSCrossRefGoogle Scholar
  22. Schubert, G., Anderson, J.D., Spohn, T., McKinnon, W.B.: Interior composition, structure and dynamics of the galilean satellites. In: Bagenal, F., Dowling, T.E., McKinnon, W.B. (eds.) Jupiter: The Planet, Satellites and Magnetosphere, vol. 1, pp. 281–306. Cambridge University Press, Cambridge (2004)Google Scholar
  23. Schubert, G., Sohl, F., Hussmann, H.: Interior of Europa. In: Pappalardo, R.T., McKinnon, W.B., Khurana, K.K. (eds.) Europa, pp. 353–367. University of Arizona Press, Tucson (2009)Google Scholar
  24. Segatz, M., Spohn, T., Ross, M.N., Schubert, G.: Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io. Icarus 75(2), 187–206 (1988)ADSCrossRefGoogle Scholar
  25. Shoji, D., Hussmann, H., Kurita, K., Sohl, F.: Ice rheology and tidal heating of Enceladus. Icarus 226(1), 10–19 (2013)ADSCrossRefGoogle Scholar
  26. Showman, A.P., Malhotra, R.: Tidal evolution into the laplace resonance and the resurfacing of ganymede. Icarus 127(1), 93–111 (1997)ADSCrossRefGoogle Scholar
  27. Sohl, F., Spohn, T., Breuer, D., Nagel, K.: Implications from Galileo observations on the interior structure and chemistry of the Galilean satellites. Icarus 157(1), 104–119 (2002)ADSCrossRefGoogle Scholar
  28. Sotin, C., Poirier, J.P., Gillet, P.: Creep of high-pressure ice VI. In: Klinger J, Benest D, Dollfus A, Smoluchowski R (eds) NATO Advanced Science Institutes (ASI) Series C, NATO Advanced Science Institutes (ASI) Series C, vol. 156, pp. 109–118 (1985)Google Scholar
  29. Spohn, T., Schubert, G.: Oceans in the icy Galilean satellites of Jupiter? Icarus 161(2), 456–467 (2003)ADSCrossRefGoogle Scholar
  30. Steinbrügge, G., Stark, A., Hussmann, H., Sohl, F., Oberst, J.: Measuring tidal deformations by laser altimetry. A performance model for the Ganymede Laser Altimeter. Planet. Space Sci. 117, 184–191 (2015)ADSCrossRefGoogle Scholar
  31. Tobie, G., Choblet, G., Sotin, C.: Tidally heated convection: constraints on Europa’s ice shell thickness. J. Geophys. Res. Planets 108, E11 (2003)CrossRefGoogle Scholar
  32. Travis, B.J., Palguta, J., Schubert, G.: A whole-moon thermal history model of Europa: impact of hydrothermal circulation and salt transport. Icarus 218, 1006–1019 (2012)ADSCrossRefGoogle Scholar
  33. Tyler, R.: Comparative estimates of the heat generated by ocean tides on icy satellites in the outer solar system. Icarus 243, 358–385 (2014)ADSCrossRefGoogle Scholar
  34. Vance, S., Bouffard, M., Choukroun, M., Sotin, C.: Ganymede’s internal structure including thermodynamics of magnesium sulfate oceans in contact with ice. Planet. Space Sci. 96, 62–70 (2014)ADSCrossRefGoogle Scholar
  35. Wahr, J.M., Zuber, M.T., Smith, D.E., Lunine, J.I.: Tides on Europa, and the thickness of Europa’s icy shell. J. Geophys. Res. Planets 111(E12005), 10 (2006)Google Scholar
  36. Zschau, J.: Tidal friction in the solid earth: loading tides versus body tides. In: Brosche, P., Sündermann, J. (eds.) Tidal Friction and the Earth’s Rotation, pp. 62–94. Springer, Berlin (1978)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.DLR Institute of Planetary ResearchBerlinGermany

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