Abstract
As the giant planets of our Solar System continue to cool and contract, they radiate more energy than they receive from the Sun. A giant planet’s cooling rate, luminosity and temperature at a given age can be determined using the first and second principles of thermodynamics. Measurements of Saturn’s infrared luminosity, however, reveal that Saturn is significantly brighter than predicted for its age1,2. This excess luminosity has been attributed to the immiscibility of helium in Saturn’s hydrogen-rich envelope, which leads to rains of helium-rich droplets3,4,5,6,7,8. Existing calculations of Saturn’s evolution, however, suggest that the energy released by helium rains might be insufficient to resolve the luminosity puzzle9. Here we demonstrate, using semi-analytical models of planetary thermal evolution, that the cooling of Saturn’s interior is significantly slower in the presence of layered convection generated—like in Earth’s oceans—by a compositional gradient. We find that layered convection can explain Saturn’s present luminosity for a wide range of initial energy configurations without invoking any additional energy source. Our findings suggest that the interior structure, composition and thermal evolution of giant planets in our Solar System and beyond may be more complex than the conventional approximation of giant planets as homogeneous adiabatic bodies.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Pollack, J. et al. A calculation of Saturn’s gravitational contraction history. Icarus 30, 111–128 (1977).
Fortney, J. J., Ikoma, M., Nettelmann, N., Guillot, T. & Marley, M. S. Self-consistent model atmospheres and the cooling of the solar system’s giant planets. Astrophys. J. 729, 32 (2011).
Salpeter, E. E. On convection and gravitational layering in Jupiter and in stars of low mass. Astrophys. J. 181, L83–L86 (1973).
Stevenson, D. J. & Salpeter, E. E. The dynamics and helium distribution in hydrogen-helium fluid planets. Astrophys. J. Suppl. Ser. 35, 239–261 (1977).
Hubbard, W. B. & DeWitt, H. E. Statistical mechanics of light elements at high pressure. VII—A perturbative free energy for arbitrary mixtures of H and He. Astrophys. J. 290, 388–393 (1985).
Pfaffenzeller, O., Hohl, D. & Ballone, P. Miscibility of Hydrogen and Helium under astrophysical conditions. Phys. Rev. Lett. 74, 2599–2602 (1995).
Lorenzen, W., Holst, B. & Redmer, R. Demixing of hydrogen and helium at megabar pressures. Phys. Rev. Lett. 102, 115701 (2009).
Morales, M. A. et al. Phase separation in hydrogen-helium mixtures at Mbar pressures. Proc. Natl Acad. Sci. USA 106, 1324 (2009).
Fortney, J. J. & Hubbard, W. B. Phase separation in giant planets: inhomogeneous evolution of Saturn. Icarus 35, 228–243 (2003).
Stevenson, D. J. Cosmochemistry and structure of the giant planets and their satellites. Icarus 62, 4–15 (1985).
Podolak, M., Hubbard, W. B. & Stevenson, D. J. Model of Uranus’ interior and magnetic field. Uranus 29–61 (Univ. Arizona Press, 1991).
Chabrier, G. & Baraffe, I. Heat transport in giant (Exo)planets: A new perspective. Astrophys. J. Lett. 667, L81–L84 (2007).
Leconte, J. & Chabrier, G. A new vision of giant planet interiors: Impact of double diffusive convection. Astron. Astrophys. 540, A20 (2012).
Stern, M. E. The salt-fountain and thermohaline convection. Tellus 12, 172 (1960).
Radko, T. What determines the thickness of layers in a thermohaline staircase? J. Fluid Mech. 523, 79–98 (2005).
Rosenblum, E. P., Garaud, P., Traxler, A. & Stellmach, S. Turbulent mixing and layer formation in double-diffusive convection: Three-dimensional numerical simulations and theory. Astrophys. J. 731, 66 (2011).
Mirouh, G. M., Garaud, P., Stellmach, S., Traxler, A. L. & Wood, T. S. A new model for mixing by double-diffusive convection (semi-convection). I. The conditions for layer formation. Astrophys. J. 750, 61 (2012).
Hansen, C. J. & Kawaler, S. D. Stellar Interiors. Physical Principles, Structure, and Evolution (Springer, 1994).
Pollack, J. B. et al. Formation of the giant planets by concurrent accretion of solids and gas. Icarus 124, 62–85 (1996).
Marley, M. S., Fortney, J. J., Hubickyj, O., Bodenheimer, P. & Lissauer, J. J. On the luminosity of young Jupiters. Astrophys. J. 655, 541–549 (2007).
Bagenal, F., Dowling, T. E. & McKinnon, W. B. (eds) in Jupiter. The Planet, Satellites and Magnetosphere 35–57 (Cambridge Planetary Science, Vol. 1, Cambridge Univ. Press, 2004).
Wilson, H. F. & Militzer, B. Solubility of water ice in metallic hydrogen: Consequences for core erosion in gas giant planets. Astrophys. J. 745, 54 (2012).
Wilson, H. F. & Militzer, B. Rocky core solubility in Jupiter and giant exoplanets. Phys. Rev. Lett. 108, 111101 (2012).
Stevenson, D. J. Formation of the giant planets. Planet. Space Sci. 30, 755–764 (1982).
Saumon, D. & Guillot, T. Shock compression of deuterium and the interiors of Jupiter and Saturn. Astrophys. J. 609, 1170–1180 (2004).
Stevenson, D. J. & Salpeter, E. E. The phase diagram and transport properties for hydrogen-helium fluid planets. Astrophys. J. Suppl. Ser. 35, 221–237 (1977).
Miller, N. & Fortney, J. J. The heavy-element masses of extrasolar giant planets, Revealed. Astrophys. J. Lett. 736, L29 (2011).
Laughlin, G., Crismani, M. & Adams, F. C. On the anomalous radii of the transiting extrasolar planets. Astrophys. J. Lett. 729, L7 (2011).
Leconte, J., Chabrier, G., Baraffe, I. & Levrard, B. Is tidal heating sufficient to explain bloated exoplanets? Consistent calculations accounting for finite initial eccentricity. Astron. Astroph. 516, A64 (2010).
Acknowledgements
J.L. thanks J. Fortney for making his atmospheric grids available to us in electronic format. The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013 Grant Agreement no. 247060). J.L. acknowledges financial support from the DIM ACAV.
Author information
Authors and Affiliations
Contributions
J.L. carried out analytical calculations, developed the model and performed the numerical simulations. G.C. suggested the idea and carried out analytical calculations. J.L and G.C. wrote the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
Supplementary Information (PDF 515 kb)
Rights and permissions
About this article
Cite this article
Leconte, J., Chabrier, G. Layered convection as the origin of Saturn’s luminosity anomaly. Nature Geosci 6, 347–350 (2013). https://doi.org/10.1038/ngeo1791
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/ngeo1791
This article is cited by
-
In Situ exploration of the giant planets
Experimental Astronomy (2022)
-
A diffuse core in Saturn revealed by ring seismology
Nature Astronomy (2021)
-
Understanding dense hydrogen at planetary conditions
Nature Reviews Physics (2020)
-
Uranus and Neptune: Origin, Evolution and Internal Structure
Space Science Reviews (2020)
-
Layer formation in double-diffusive convection over resting and moving heated plates
Theoretical and Computational Fluid Dynamics (2019)