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A common mass scaling for satellite systems of gaseous planets

Nature volume 441, pages 834–839 (2006)Cite this article

Abstract

The Solar System's outer planets that contain hydrogen gas all host systems of multiple moons, which notably each contain a similar fraction of their respective planet's mass (∼10-4). This mass fraction is two to three orders of magnitude smaller than that of the largest satellites of the solid planets (such as the Earth's Moon), and its common value for gas planets has been puzzling. Here we model satellite growth and loss as a forming giant planet accumulates gas and rock-ice solids from solar orbit. We find that the mass fraction of its satellite system is regulated to ∼10-4 by a balance of two competing processes: the supply of inflowing material to the satellites, and satellite loss through orbital decay driven by the gas. We show that the overall properties of the satellite systems of Jupiter, Saturn and Uranus arise naturally, and suggest that similar processes could limit the largest moons of extrasolar Jupiter-mass planets to Moon-to-Mars size.

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Figure 1: An inflow-supplied circumplanetary disk.
Figure 2: Results of satellite accretion simulations with time-constant inflows.
Figure 3: Properties of observed satellites compared to simulations.
Figure 4: Results of accretion simulations with time-dependent inflows.

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References

  1. Jewitt, D. & Sheppard, S. Irregular satellites in the context of planet formation. Space Sci. Rev. 116, 441–455 (2005)

    Article  ADS  Google Scholar 

  2. Stevenson, D. J., Harris, A. W. & Lunine, J. I. in Satellites (eds Burns, J. A. & Matthews, M. S.) 39–88 (University of Arizona Press, Tucson, 1986)

    Google Scholar 

  3. Pollack, J. B., Lunine, J. I. & Tittemore, W. C. in Uranus (eds Bergstralh, J. T., Miner, E. D. & Matthews, M. S.) 469–512 (University of Arizona Press, Tucson, 1991)

    Google Scholar 

  4. Lunine, J. I., Coradini, A., Gautier, D., Owen, T. C. & Wuchterl, G. in Jupiter: The Planet, Satellites and Magnetosphere (eds Bagenal, F., Dowling, T. E. & McKinnon, W. B.) 19–34 (Cambridge University Press, Cambridge, UK, 2004)

    Google Scholar 

  5. Calvet, N., Hartmann, L. & Strom, S. E. in Protostars and Planets IV (eds Mannings, V., Boss, A. P. & Russell, S. S.) 377–399 (University of Arizona Press, Tucson, 2000)

    Google Scholar 

  6. Lubow, S. H., Seibert, M. & Artymowicz, P. Disk accretion onto high-mass planets. Astrophys. J. 526, 1001–1012 (1999)

    Article  ADS  Google Scholar 

  7. Bate, M. R., Lubow, S. H., Ogilvie, G. I. & Miller, K. A. Three-dimensional calculations of high- and low-mass planets embedded in protoplanetary discs. Mon. Not. R. Astron. Soc. 341, 213–229 (2003)

    Article  ADS  Google Scholar 

  8. Papaloizou, J. C. B. & Nelson, R. P. Models of accreting gas giant protoplanets in protostellar disks. Astron. Astrophys. 433, 247–265 (2005)

    Article  ADS  Google Scholar 

  9. Canup, R. M. & Ward, W. R. Formation of the Galilean satellites: Conditions of accretion. Astron. J. 124, 3404–3423 (2002)

    Article  ADS  Google Scholar 

  10. Ward, W. R. On disk-planet interactions and orbital eccentricities. Icarus 73, 330–348 (1998)

    Article  ADS  Google Scholar 

  11. Artymowicz, P. Disk-satellite interaction via density waves and the eccentricity evolution of bodies embedded in disks. Astrophys. J. 419, 166–180 (1993)

    Article  ADS  Google Scholar 

  12. Papaloizou, J. C. B. & Larwood, J. D. On the orbital evolution and growth of protoplanets embedded in a gaseous disc. Mon. Not. R. Astron. Soc. 315, 823–833 (2000)

    Article  ADS  Google Scholar 

  13. Ward, W. R. Density waves in the solar nebula—Differential Lindblad torque. Icarus 67, 164–180 (1986)

    Article  ADS  Google Scholar 

  14. Ward, W. R. Protoplanet migration by nebula tides. Icarus 126, 261–281 (1997)

    Article  ADS  CAS  Google Scholar 

  15. Tanaka, H. & Ward, W. R. Three-dimensional interaction between a planet and an isothermal gaseous disk. II. Eccentricity waves and bending waves. Astrophys. J. 602, 388–395 (2004)

    Article  ADS  Google Scholar 

  16. Tanaka, H., Takeuchi, T. & Ward, W. R. Three-dimensional interaction between a planet and an isothermal gaseous disk. I. Corotation and Lindblad torques and planet migration. Astrophys. J. 565, 1257–1274 (2002)

    Article  ADS  Google Scholar 

  17. Ward, W. R. Density waves in the solar nebula—Planetesimal velocities. Icarus 106, 274–287 (1993)

    Article  ADS  Google Scholar 

  18. Shakura, N. I. & Sunyaev, R. A. Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973)

    ADS  Google Scholar 

  19. Duncan, M. J., Levison, H. F. & Lee, M. H. A multiple timestep symplectic algorithm for integrating close encounters. Astron. J. 116, 2067–2077 (1998)

    Article  ADS  Google Scholar 

  20. Chambers, J. E., Wetherill, G. W. & Boss, A. P. The stability of multi-planet systems. Icarus 119, 261–268 (1996)

    Article  ADS  Google Scholar 

  21. Lissauer, J. J. Urey Prize Lecture: On the diversity of plausible planetary systems. Icarus 114, 217–236 (1995)

    Article  ADS  Google Scholar 

  22. Mosqueira, I. & Estrada, P. R. Formation of regular satellites of giant planets in an extended gaseous nebula I: Subnebula model and accretion of satellites. Icarus 163, 198–231 (2003)

    Article  ADS  CAS  Google Scholar 

  23. Alibert, Y., Mousis, O. & Benz, W. Modeling the Jovian subnebula. I. Thermodynamic conditions and migration of proto-satellites. Astron. Astrophys. 439, 1205–1213 (2005)

    Article  ADS  Google Scholar 

  24. Hubickyj, O., Bodenheimer, P. & Lissauer, J. J. Accretion of the gaseous envelope of Jupiter around a 5 to 10 Earth-mass core. Icarus 179, 415–431 (2005)

    Article  ADS  CAS  Google Scholar 

  25. Slattery, W. L., Benz, W. & Cameron, A. G. W. Giant impacts on a primitive Uranus. Icarus 99, 167–174 (1992)

    Article  ADS  Google Scholar 

  26. D'Angelo, G., Henning, T. & Kley, W. Thermodynamics of circumstellar disks with high-mass planets. Astrophys. J. 599, 548–576 (2003)

    Article  ADS  CAS  Google Scholar 

  27. Ward, W. R. & Hamilton, D. P. Tilting Saturn. I. Analytic model. Astron. J. 128, 2501–2519 (2004)

    Article  ADS  Google Scholar 

  28. Hamilton, D. P. & Ward, W. R. Tilting Saturn II. Numerical model. Astron. J. 128, 2510–2517 (2004)

    Article  ADS  Google Scholar 

  29. Goldreich, P. Inclination of satellite orbits about an oblate precessing planet. Astron. J. 70, 5–9 (1965)

    Article  ADS  Google Scholar 

  30. Brunini, A. Origin of the obliquities of the giant planets in mutual interactions in the early Solar System. Nature 440, 1163–1165 (2006)

    Article  ADS  CAS  Google Scholar 

  31. Canup, R. M. & Ward, W. R. A possible impact origin of the Uranian satellite system. Bull. Am. Astron. Soc. 32, 1105 (2000)

    ADS  Google Scholar 

  32. Ward, W. R. & Canup, R. M. Viscous evolution of an impact generated disk around Uranus. Bull. Am. Astron. Soc. 35, 1046 (2003)

    ADS  Google Scholar 

  33. Goldreich, P., Murray, N., Longaretti, P. Y. & Banfield, D. Neptune's story. Science 245, 500–504 (1989)

    Article  ADS  CAS  Google Scholar 

  34. McKinnon, W. B., Lunine, J. I. & Banfield, D. in Neptune and Triton (ed. Cruikshank, D. P.) 807–877 (University of Arizona Press, Tucson, 1995)

    Google Scholar 

  35. Agnor, C. B. & Hamilton, D. P. Neptune's capture of its moon Triton in a binary–planet gravitational encounter. Nature 441, 192–194 (2006)

    Article  ADS  CAS  Google Scholar 

  36. Cuk, M. & Gladman, B. J. Constraints on the orbital evolution of Triton. Astrophys. J. 626, L113–L116 (2005)

    Article  ADS  Google Scholar 

  37. Stevenson, D. J. Jupiter and its moons. Science 294, 71–72 (2001)

    Article  CAS  Google Scholar 

  38. Williams, D. M. & Kasting, J. F. Habitable moons around extrasolar giant planets. Nature 385, 234–236 (1997)

    Article  ADS  CAS  Google Scholar 

  39. Barnes, J. W. & O'Brien, D. P. Stability of satellites around close-in extrasolar giant planets. Astrophys. J. 575, 1087–1093 (2002)

    Article  ADS  Google Scholar 

  40. Burrows, A., Hubbard, W. B. & Lunine, J. K. The theory of brown dwarfs and extrasolar giant planets. Rev. Mod. Phys. 73, 719–765 (2001)

    Article  ADS  CAS  Google Scholar 

  41. Saumon, D. & Guillot, T. Shock compression of deuterium and the interiors of Jupiter and Saturn. Astrophys. J. 609, 1170–1180 (2004)

    Article  ADS  CAS  Google Scholar 

  42. Anderson, J. D. et al. Shape, mean radius, gravity field, and interior structure of Callisto. Icarus 153, 157–161 (2001)

    Article  ADS  Google Scholar 

  43. Johnson, T. V. & Lunine, J. I. Saturn's moon Phoebe as a captured body from the outer Solar System. Nature 435, 69–71 (2005)

    Article  ADS  CAS  Google Scholar 

  44. Cassen, P. & Moosman, A. On the formation of protostellar disks. Icarus 48, 353–376 (1981)

    Article  ADS  Google Scholar 

  45. Klahr, H. H. & Bodenheimer, P. Turbulence in accretion disks: vorticity generation and angular momentum transport via the global baroclinic instability. Astrophys. J. 582, 869–892 (2003)

    Article  ADS  Google Scholar 

  46. Goodman, J. & Rafikov, R. R. Planetary torques as the viscosity of protoplanetary disks. Astrophys. J. 552, 793–802 (2001)

    Article  ADS  Google Scholar 

  47. Lin, D. N. C. & Papaloizou, J. C. B. in Protostars and Planets III (eds Levy, E. H. & Lunine, J. I.) 749–835 (University of Arizona Press, Tucson, 1993)

    Google Scholar 

  48. Ward, W. R. & Hahn, J. in Protostars and Planets IV (eds Mannings, V., Boss, A. P. & Russell, S. S.) 1135–1155 (University of Arizona Press, Tucson, 2000)

    Google Scholar 

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Acknowledgements

This research was supported by NASA's Planetary Geology and Geophysics and Outer Planets Research programmes. Computer resources and support were provided by SwRI. We thank L. Dones, R. Mihran and S. Peale for comments.

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  1. Space Studies Department, Southwest Research Institute, Boulder, Colorado, 80302, USA

    Robin M. Canup & William R. Ward

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  1. Robin M. Canup
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Correspondence to Robin M. Canup.

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Canup, R., Ward, W. A common mass scaling for satellite systems of gaseous planets. Nature 441, 834–839 (2006). https://doi.org/10.1038/nature04860

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