Shock Compression of Deuterium and the Interiors of Jupiter and Saturn

Recently, deuterium has been the focus of a high level of experimental and theoretical activity, sparked by a disagreement on the experimental value of the maximum compression along the principal Hugoniot. The behavior of deuterium at megabar pressures is not well understood. It is of great interest to understand how the current uncertainty on the hydrogen/deuterium equation of state (EOS) affects the inferred structures of Jupiter and Saturn. In particular, the mass of a core of heavy elements (other than H and He) and the total mass of those heavy elements in these two planets are quite sensitive to the EOS of hydrogen and constitute important clues to their formation process. We present a study of the range of structures allowed for Jupiter and Saturn by the current uncertainty in the hydrogen EOS and astrophysical observations of the two planets. An improved experimental understanding of hydrogen at megabar pressures and better determinations of the gravitational moments of both planets are necessary to put tight bounds on their internal structure.

[1]  D. Hunten,et al.  Helium in Jupiter's atmosphere: Results from the Galileo probe Helium Interferometer Experiment , 1998 .

[2]  T. Guillot,et al.  New Constraints on the Composition of Jupiter from Galileo Measurements and Interior Models , 1997, astro-ph/9707210.

[3]  Gilles Chabrier,et al.  An Equation of State for Low-Mass Stars and Giant Planets , 1995 .

[4]  M. Ross.  Erratum: Linear-mixing model for shock-compressed liquid deuterium [Phys. Rev. B 58, 669 (1998)] , 1999 .

[5]  W. Nellis,et al.  Temperature measurements of shock-compressed liquid hydrogen: implications for the interior of Jupiter , 1995, Science.

[6]  William J. Nellis,et al.  Shock Compression of Liquid Helium to 56 GPa (560 kbar) , 1984 .

[7]  S. Synnott,et al.  Gravity field of the Saturnian system from Pioneer and Voyager tracking data , 1985 .

[8]  M. S. Matthews,et al.  Planetary Science. (Book Reviews: Origin and Evolution of Planetary and Satellite Atmospheres) , 1989 .

[9]  Phase separation in giant planets: inhomogeneous evolution of Saturn , 2003, astro-ph/0305031.

[10]  M. Desjarlais.  Density-functional calculations of the liquid deuterium Hugoniot, reshock, and reverberation timing , 2003 .

[11]  D. Saumon,et al.  The Molecular-Metallic Transition of Hydrogen and the Structure of Jupiter and Saturn , 1992 .

[12]  J. Kress,et al.  Density-functional calculation of the Hugoniot of shocked liquid deuterium , 2000 .

[13]  M. Knudson,et al.  Use of a wave reverberation technique to infer the density compression of shocked liquid deuterium to 75 GPa. , 2003, Physical review letters.

[14]  M. Ross.  Linear-mixing model for shock-compressed liquid deuterium , 1998 .

[15]  G. V. Simakov,et al.  Shock compression of solid deuterium , 2002 .

[16]  A. Boss,et al.  Possible Rapid Gas Giant Planet Formation in the Solar Nebula and Other Protoplanetary Disks , 2000, The Astrophysical journal.

[17]  Mao,et al.  Equation of state and phase diagram of solid 4He from single-crystal x-ray diffraction over a large P-T domain. , 1993, Physical review letters.

[18]  D. Gautier,et al.  Saturn Helium Abundance: A Reanalysis of Voyager Measurements , 2000 .

[19]  J. Kress,et al.  Molecular-dynamics modeling of the Hugoniot of shocked liquid deuterium , 1997 .

[20]  Ross,et al.  Temperature measurements and dissociation of shock-compressed liquid deuterium and hydrogen. , 1995, Physical review. B, Condensed matter.

[21]  Francois Gygi,et al.  Ab initio simulations of compressed liquid deuterium , 2000 .

[22]  B. Barrett,et al.  Shock compression of deuterium to 900 Kbar , 1974 .

[23]  T. Guillot.  A COMPARISON OF THE INTERIORS OF JUPITER AND SATURN , 1999, astro-ph/9907402.

[24]  W. Nellis,et al.  Equation‐of‐state data for molecular hydrogen and deuterium at shock pressures in the range 2–76 GPa (20–760 kbar)a) , 1983 .

[25]  T. Guillot,et al.  Effect of Radiative Transport on the Evolution of Jupiter and Saturn , 1995 .

[26]  Paul Loubeyre,et al.  Optical studies of solid hydrogen to 320 GPa and evidence for black hydrogen , 2002, Nature.

[27]  John N. Bahcall,et al.  Solar models with helium and heavy-element diffusion , 1995 .

[28]  D. Young,et al.  The equation of state of molecular hydrogen at very high densitya) , 1983 .

[29]  W. Hubbard.  Effects of differential rotation on the gravitational figures of Jupiter and Saturn , 1982 .

[30]  Ceperley,et al.  Path integral monte carlo calculation of the deuterium hugoniot , 2000, Physical review letters.

[31]  Gilbert W. Collins,et al.  Temperature measurements of shock compressed liquid deuterium up to 230 GPa. , 2001, Physical review letters.

[32]  Gilbert W. Collins,et al.  Absolute equation of state measurements of shocked liquid deuterium up to 200 GPa (2 Mbar) , 1997 .

[33]  G. V. Simakov,et al.  Shock-wave compression of solid deuterium at a pressure of 120 GPa , 2003 .

[34]  W. J. Nellis,et al.  Metallization of fluid molecular hydrogen at 140 GPa (1.4 Mbar) , 1996 .

[35]  D. Stevenson.  Thermodynamics and phase separation of dense fully ionized hydrogen-helium fluid mixtures , 1975 .

[36]  T. Guillot,et al.  Nonadiabatic Models of Jupiter and Saturn , 1994 .

[37]  B. Dorizzi,et al.  Solvable Integrodifferential Equations and Their Relation to the Painlevé Conjecture , 1984 .

[38]  G. Chabrier,et al.  Equation of state of fully ionized electron-ion plasmas. II. Extension To relativistic densities and to the solid phase , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[39]  M. Knudson,et al.  Equation of state measurements in liquid deuterium to 70 GPa. , 2001, Physical review letters.

[40]  N. Ashcroft.  Hydrogen at high density , 2003 .

[41]  T. Gudkova,et al.  Models of Jupiter and Saturn after Galileo mission , 1999 .

[42]  Russell J. Hemley,et al.  Ultrahigh-pressure transitions in solid hydrogen , 1994 .

[43]  Weber,et al.  Measurements of the equation of state of deuterium at the fluid insulator-metal transition , 1998, Science.

[44]  Jack J. Lissauer,et al.  Formation of the Giant Planets by Concurrent Accretion of Solids and Gas , 1995 .

[45]  G. Chabrier.  An equation of state for fully ionized hydrogen , 1990 .

[46]  E. Salpeter,et al.  The dynamics and helium distribution in hydrogen-helium fluid planets , 1977 .