Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Strong tidal dissipation in Io and Jupiter from astrometric observations

Abstract

Io is the volcanically most active body in the Solar System and has a large surface heat flux1,2,3. The geological activity is thought to be the result of tides raised by Jupiter4, but it is not known whether the current tidal heat production is sufficiently high to generate the observed surface heat flow5,6. Io’s tidal heat comes from the orbital energy of the Io–Jupiter system (resulting in orbital acceleration), whereas dissipation of energy in Jupiter causes Io’s orbital motion to decelerate. Here we report a determination of the tidal dissipation in Io and Jupiter through its effect on the orbital motions of the Galilean moons. Our results show that the rate of internal energy dissipation in Io (k2/Q = 0.015 ± 0.003, where k2 is the Love number and Q is the quality factor) is in good agreement with the observed surface heat flow5,6, and suggest that Io is close to thermal equilibrium. Dissipation in Jupiter (k2/Q = (1.102 ± 0.203) × 10-5) is close to the upper bound of its average value expected from the long-term evolution of the system7, and dissipation in extrasolar planets may be higher than presently assumed8. The measured secular accelerations indicate that Io is evolving inwards, towards Jupiter, and that the three innermost Galilean moons (Io, Europa and Ganymede) are evolving out of the exact Laplace resonance.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Astrometric residuals.
Figure 2: Comparison of Io’s thermal emission with the global dissipation determined in the present study.

References

  1. 1

    Matson, D. L., Ransford, G. A. & Johnson, T. V. Heat flow from Io. J. Geophys. Res. 86, 1664–1672 (1981)

    ADS  Article  Google Scholar 

  2. 2

    Veeder, G., Matson, D., Johnson, T., Blaney, D. & Goguen, J. Io’s heat flow from infrared radiometry: 1983–1993. J. Geophys. Res. 99, 17095–17162 (1994)

    ADS  Article  Google Scholar 

  3. 3

    Spencer, J. R. et al. Io’s thermal emission from the Galileo photopolarimeter-radiometer. Science 288, 1198–1201 (2000)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Peale, S. J., Cassen, P. & Reynolds, R. T. Melting of Io by tidal dissipation. Science 203, 892–894 (1979)

    ADS  CAS  Article  Google Scholar 

  5. 5

    McEwen, A. S., Keszthelyi, P., Lopes, R., Schenk, P. M. & Spencer, J. R. in Jupiter: The Planet, Satellites and Magnetosphere (eds Bagenal, F., Dowling, T. E. & McKinnon, W. B.) 307–328 (Cambridge Univ. Press, 2004)

    Google Scholar 

  6. 6

    Moore, B., Schubert, G., Anderson, J. D. & Spencer, J. R. in Io After Galileo: A New View of Jupiter’s Volcanic Moon (eds Lopes, R. M. C. & Spencer, J. R.) 89–105 (Springer, 2007)

    Google Scholar 

  7. 7

    Yoder, C. F. & Peale, S. The tides of Io. Icarus 47, 1–35 (1981)

    ADS  Article  Google Scholar 

  8. 8

    Levrard, B. et al. Tidal dissipation within hot Jupiters: a new appraisal. Astron. Astrophys. 462, L5–L8 (2007)

    ADS  CAS  Article  Google Scholar 

  9. 9

    De Sitter, W. Orbital elements determining the longitudes of Jupiter's satellites, derived from observations. Leiden Ann. 16 (2), 1–92 (1928)

    Google Scholar 

  10. 10

    Lieske, J. H. Galilean satellite evolution - observational evidence for secular changes in mean motions. Astron. Astrophys. 176, 146–158 (1987)

    ADS  Google Scholar 

  11. 11

    Segatz, M., Spohn, T., Ross, M. N. & Schubert, G. Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io. Icarus 75, 187–206 (1988)

    ADS  Article  Google Scholar 

  12. 12

    Ojakangas, G. & Stevenson, D. Episodic volcanism of tidally heated satellites with application to Io. Icarus 66, 341–358 (1986)

    ADS  Article  Google Scholar 

  13. 13

    Greenberg, R. Galilean satellites - evolutionary paths in deep resonance. Icarus 70, 334–347 (1987)

    ADS  Article  Google Scholar 

  14. 14

    Fischer, H. J. & Spohn, T. Thermal-orbital histories of viscoelastic models of Io (J1). Icarus 83, 39–65 (1990)

    ADS  Article  Google Scholar 

  15. 15

    Hussmann, H. & Spohn, T. Thermal-orbital evolution of Io and Europa. Icarus 171, 391–410 (2004)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Moore, W. Tidal heating and convection in Io. J. Geophys. Res. 108 doi: 10.1029/2002JE001943 (2003)

  17. 17

    Keszthelyi, L. et al. New estimates for Io eruption temperatures: implications for the interior. Icarus 192, 491–502 (2007)

    ADS  Article  Google Scholar 

  18. 18

    Moore, W. The thermal state of Io. Icarus 154, 548–550 (2001)

    ADS  Article  Google Scholar 

  19. 19

    Anderson, J. D., Jacobson, R. A. & Lau, E. L. Io’s gravity field and interior structure. J. Geophys. Res. 106, 32963–32969 (2001)

    ADS  Article  Google Scholar 

  20. 20

    Gavrilov, S. V. & Zharkov, V. N. Love numbers of the giant planets. Icarus 32, 443–449 (1977)

    ADS  Article  Google Scholar 

  21. 21

    Ogilvie, G. I. & Lin, D. N. C. Tidal dissipation in rotating giant planets. Astrophys. J. 610, 477–509 (2004)

    ADS  Article  Google Scholar 

  22. 22

    Wu, Y. Origin of tidal dissipation in Jupiter. II. The value of Q. Astrophys. J. 635, 688–710 (2005)

    ADS  Article  Google Scholar 

  23. 23

    Yoder, C. F. How tidal heating in Io drives the Galilean orbital resonance locks. Nature 279, 747–770 (1979)

    ADS  Article  Google Scholar 

  24. 24

    Goldstein, S. J. & Jacobs, K. C. A recalculation of the secular acceleration of Io. Astron. J. 110, 3054–3057 (1995)

    ADS  Article  Google Scholar 

  25. 25

    Vasundhara, R., Arlot, J.-E. & Descamps, P. in Dynamics, Ephemerides and Astrometry of the Solar System (eds Ferraz-Mello, S., Morando, B. & Arlot, J.-E.) 145–149 (Proc. 172nd Symp. Int. Astron. Union, IAU, 1996)

    Google Scholar 

  26. 26

    Aksnes, K. & Franklin, F. A. Secular acceleration of Io derived from mutual satellite events. Astron. J. 122, 2734–2739 (2001)

    ADS  Article  Google Scholar 

  27. 27

    Stone, R. C. Positions for the outer planets and many of their satellites. V. FASTT observations taken in 2000–2001. Astron. J. 122, 2723–2733 (2001)

    ADS  Article  Google Scholar 

  28. 28

    Morrison, D. & Telesco, C. M. Io - observational constraints on internal energy and thermophysics of the surface. Icarus 44, 226–233 (1980)

    ADS  Article  Google Scholar 

  29. 29

    Sinton, W. M. The thermal emission spectrum of Io and a determination of the heat flux from its hot spots. J. Geophys. Res. 86, 3122–3128 (1981)

    ADS  Article  Google Scholar 

  30. 30

    Johnson, T. V. et al. Volcanic hotspots on Io - stability and longitudinal distribution. Science 226, 134–137 (1984)

    ADS  CAS  Article  Google Scholar 

  31. 31

    Veeder, G. J., Matson, D. L., Johnson, T. V., Davies, A. G. & Blaney, D. L. The polar contribution to the heat flow of Io. Icarus 169, 264–270 (2004)

    ADS  Article  Google Scholar 

  32. 32

    Rathbun, J. A. et al. Mapping of Io’s thermal radiation by the Galileo photopolarimeter-radiometer (PPR) instrument. Icarus 169, 127–139 (2004)

    ADS  CAS  Article  Google Scholar 

  33. 33

    Lay, T., Hernlund, J. & Bussett, B. A. Core–mantle boundary heat flow. Nature Geosci. 1, 25–32 (2008)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank D. Pascu for sharing his unpublished observations.

Author Contributions All authors contributed to the writing of the manuscript. V.L. developed and fitted to the observations the full numerical model presented in this work. J.-E.A. fitted to the observations the secular accelerations using L1 astrometric residuals (Supplementary Information). Theoretical calculations of the energy dissipation and Fig. 2 were made by Ö.K. T.V.H. and Ö.K. contributed to the geophysical interpretations of the secular accelerations.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Valéry Lainey.

Supplementary information

Supplementary Information

This file provides a detailed description of the dynamical model, a Supplementary Discussion, Supplementary Notes including references, Supplementary Tables 1-5 and Supplementary Figures 1-3 with Legends. (PDF 555 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lainey, V., Arlot, JE., Karatekin, Ö. et al. Strong tidal dissipation in Io and Jupiter from astrometric observations. Nature 459, 957–959 (2009). https://doi.org/10.1038/nature08108

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing