Advanced Search



ISSN  2096-3955

CN  10-1502/P

Citation: Ni, D. D. (2020). Signature of helium rain and dilute cores in Jupiter's interior from empirical equations of state. Earth Planet. Phys., 4(2), 111–119doi: 10.26464/epp2020017

2020, 4(2): 111-119. doi: 10.26464/epp2020017


Signature of helium rain and dilute cores in Jupiter's interior from empirical equations of state


State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau 999078, China


Institute for Planets and Exoplanets, University of California, Los Angeles, CA 90095-1567, USA

Corresponding author: DongDong Ni,

Received Date: 2019-10-29
Web Publishing Date: 2020-03-01

Measurements of Jupiter's gravity field by Juno have been acquired with unprecedented precision, but uncertainties in the planet’s hydrogen–helium equation of state (EOS) and the hydrogen–helium phase separation have meant that differences remain in the interior model predictions. We deduce an empirical EOS from Juno gravity field observations in terms of the hydrostatic equation and then investigate the structure and composition of Jupiter by comparison of the empirical EOS with Jupiter's adiabats obtained from the physical EOS. The deduced helium mass fraction suggests depletion of helium in the outermost atmosphere and helium concentration in the inner molecular hydrogen region, which is a signature of helium rain in Jupiter's interior. The deduced envelope metallicity (the heavy-element mass fraction) is as high in the innermost envelope as 11–13 times the solar value. Such a high metallicity provides sharp support to the dilute core model with the heavy elements dissolved in hydrogen and expanded outward. No matter how the core mass is varied, the empirical EOS derived from the two-layer interior model generally suggests higher densities in the innermost envelope than does the best-fit Jupiter's adiabat; this result is, again, a signature of dilute cores in Jupiter's interior. Moreover, no matter the core mass, the empirical EOS is found to exhibit an inflexion point in the deep interior, around 10 Mbar, which can be explained as the combined effect of helium concentration in the upper part and dilute cores in the lower part.

Key words: Jupiter, interior; abundances, interiors; geophysics

Anderson, J. D., and Schubert, G. (2007). Saturn's gravitational field, internal rotation, and interior structure. Science, 317(5843), 1384–1387.

Becker, A., Lorenzen, W., Fortney, J. J., Nettelmann, N., Schöttler, M., and Redmer, R. (2014). Ab initio equations of state for hydrogen (H-REOS.3) and helium (He-REOS.3) and their implications for the interior of brown dwarfs. Astrophys. J. Suppl. Ser., 215(2), 21.

Bolton, S. J., Adriani, A., Adumitroaie, V., Allison, M., Anderson, J., Atreya, S., Bloxham, J., Brown, S., Connerney, P. J. E., … Wilson, R. (2017). Jupiter's interior and deep atmosphere: The initial pole-to-pole passes with the Juno spacecraft. Science, 356(6340), 821–825.

Debras, F., and Chabrier, G. (2019). New models of Jupiter in the context of Juno and Galileo. Astrophys. J., 872(1), 100.

Folkner, W. M., Iess, L., Anderson, J. D., Asmar, S. W., Buccino, D. R., Durante, D., Feldman, M., Gomez Casajus, L., Gregnanin, M., … Levin, S. M. (2017). Jupiter gravity field estimated from the first two Juno orbits. Geophys. Res. Lett., 44(10), 4694–4700.

Fortney, J. J., and Nettelmann, N. (2010). The interior structure, composition, and evolution of giant planets. Space Sci. Rev., 152(1-4), 423–447.

French, M., Becker, A., Lorenzen, W., Nettelmann, N., Bethkenhagen, M., Wicht, J., and Redmer, R. (2012). Ab initio simulations for material properties along the Jupiter adiabat. Astrophys. J. Suppl. Ser., 202(1), 5.

Galileo probe archive. (2002). Available at\&volume=gp\_0001222

Guillot, T., and Morel P. (1995). CEPAM: a code for modeling the interiors of giant planets. Astron. Astrophys. Suppl. Ser., 109, 109–123.

Guillot, T., Gautier, D., and Hubbard, W. B. (1997). New constraints on the composition of Jupiter from Galileo measurements and interior models. Icarus, 130(2), 534–539.

Guillot, T. (1999). A comparison of the interiors of Jupiter and Saturn. Planet. Space Sci., 47(10-11), 1183–1200.

Guillot, T. (2005). The interiors of giant planets: Models and outstanding questions. Annu. Rev. Earth Planet. Sci., 33(1), 493–530.

Guillot, T., Miguel, Y., Militzer, B., Hubbard, W. B., Kaspi, Y., Galanti, E., Cao, H., Helled, R., Wahl, S. M., .. Bolton, S. J. (2018). A suppression of differential rotation in Jupiter's deep interior. Nature, 555(7695), 227–230.

Helled, R., Schubert, G., and Anderson, J. D. (2009). Empirical models of pressure and density in Saturn's interior: implications for the helium concentration, its depth dependence, and Saturn's precession rate. Icarus, 199(2), 368–377.

Helled, R., Anderson, J. D., Schubert, G., and Stevenson, D. J. (2011). Jupiter's moment of inertia: a possible determination by Juno. Icarus, 216(2), 440–448.

Helled, R., Galanti, E., and Kaspi, Y. (2015). Saturn's fast spin determined from its gravitational field and oblateness. Nature, 520(7546), 202–204.

Hubbard, W. B. (1968). Thermal structure of Jupiter. Astrophys. J., 152, 745–754.

Hubbard, W. B. (1999). Gravitational signature of Jupiter's deep zonal flows. Icarus, 137(2), 357–359.

Hubbard, W. B., Burrows, A., and Lunine, J. I. (2002). Theory of giant planets. Annu. Rev. Astron. Astrophys., 40, 103–136.

Hubbard, W. B., and Militzer, B. (2016). A preliminary Jupiter model. Astrophys. J., 820(1), 80.

Iess, L., Folkner, W. M., Durante, D., Parisi, M., Kaspi, Y., Galanti, E., Guillot, T., Hubbard, W. B., Stevenson, D. J., … Bolton, S. J. (2018). Measurement of Jupiter's asymmetric gravity field. Nature, 555(7695), 220–222.

Kong, D. L., Zhang, K. K., and Schubert, G. (2016). A fully self-consistent multi-layered model of Jupiter. Astrophys. J., 826(2), 127.

Kong, D. L., Zhang, K. K., Schubert, G., and Anderson, J. D. (2018). Origin of Jupiter's cloud-level zonal winds remains a puzzle even after Juno. Proc Natl Acad Sci USA, 115(34), 8499–8504.

Lodders, K. (2003). Solar system abundances and condensation temperatures of the elements. Astrophys. J., 591(2), 1220–1247.

Lyon, S. P., and Johnson, J. D. (1992). LANL Rep. LA-UR-92-3407 (Los Alamos: LANL).222

McMahon, J. M., Morales, M. A., Pierleoni, C., and Ceperley, D. M. (2012). The properties of hydrogen and helium under extreme conditions. Rev. Mod. Phys., 84(4), 1607–1653.

Miguel, Y., Guillot, T., and Fayon, L. (2016). Jupiter internal structure: the effect of different equations of state. A&A, 596, A114.

Militzer, B., Hubbard, W. B., Vorberger, J., Tamblyn, I., and Bonev, S. A. (2008). A massive core in Jupiter predicted from first-principles simulations. Astrophys. J. Lett., 688(1), L45.

Militzer, B., and Hubbard, W. B. (2013). Ab initio equation of state for hydrogen-helium mixtures with recalibration of the giant-planet mass-radius relation. Astrophys. J., 774(2), 148.

Militzer, B., Soubiran, F., Wahl, S. M., and Hubbard, W. (2016). Understanding Jupiter's interior. J. Geophys. Res. Planets, 121(9), 1552–1572.

Nettelmann, N., Holst, B., Kietzmann, A., French, M., Redmer, R., and Blaschke, D. (2008). Ab initio equation of state data for hydrogen, helium, and water and the internal structure of Jupiter. Astrophys. J., 683(2), 1217–1228.

Nettelmann, N., Becker, A., Holst, B., and Redmer, R. (2012). Jupiter models with improved Ab initio hydrogen equation of state (H-REOS.2). Astrophys. J., 750(1), 52.

Ni, D. D. (2018). Empirical models of Jupiter's interior from Juno data: moment of inertia and tidal Love number k2. A&A, 613, A32.

Ni, D. D. (2019). Understanding Jupiter's deep interior: the effect of a dilute core. A&A, 632, A76.

Saumon, D., Chabrier, G., and van Horn, H. M. (1995). An equation of state for low-mass stars and giant planets. Astrophys. J. Suppl. Ser., 99, 713–741.

Saumon, D., and Guillot, T. (2004). Shock compression of deuterium and the interiors of Jupiter and Saturn. Astrophys. J., 609(2), 1170–1180.

Serenelli, A. M., and Basu, S. (2010). Determining the initial helium abundance of the sun. Astrophys. J., 719(1), 865–872.

Vazan, A., Helled, R., Kovetz, A., and Podolak, M. (2015). Convection and mixing in giant planet evolution. Astrophys. J., 803(1), 32.

Wahl, S. M., Hubbard, W. B., and Militzer, B. (2016). Tidal response of preliminary Jupiter model. Astrophys. J., 831(1), 14.

Wahl, S. M., Hubbard, W. B., Militzer, B., Guillot, T., Miguel, Y., Movshovitz, N., Kaspi, Y., Helled, R., Reese, D., … Bolton, S. J. (2017). Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core. Geophys. Res. Lett., 44(10), 4649–4659.

Zharkov, V. N., and Trubitsyn, V. P. (1975). Fifth-approximation system of equations for the theory of figure. Soviet Astron., 19, 366.

Zharkov, V. N., and Trubitsyn, V. P. (1978). Physics of Planetary Interiors. Tucson: Pachart Pub. House.222


Stuart Crampin, Yuan Gao, 2018: Evidence supporting New Geophysics, Earth and Planetary Physics, 2, 173-188. doi: 10.26464/epp2018018

Article Metrics
  • PDF Downloads()
  • Abstract views()
  • HTML views()
  • Cited by(0)

Figures And Tables

Signature of helium rain and dilute cores in Jupiter's interior from empirical equations of state

DongDong Ni