DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Uranus evolution models with simple thermal boundary layers

Abstract

The strikingly low luminosity of Uranus (Teff ≃ Teq) constitutes a long-standing challenge to our understanding of Ice Giant planets. Here we present the first Uranus structure and evolution models that are constructed to agree with both the observed low luminosity and the gravity field data. Here, our models make use of modern ab initio equations of state at high pressures for the icy components water, methane, and ammonia. Proceeding step by step, we confirm that adiabatic models yield cooling times that are too long, even when uncertainties in the ice:rock ratio (I:R) are taken into account. We then argue that the transition between the ice/rock-rich interior and the H/He-rich outer envelope should be stably stratified. Therefore, we introduce a simple thermal boundary and adjust it to reproduce the low luminosity. Due to this thermal boundary, the deep interior of the Uranus models are up to 2–3 warmer than adiabatic models, necessitating the presence of rocks in the deep interior with a possible I:R of 1 × solar. Finally, we allow for an equilibrium evolution (Teff ≃ Teq) that begun prior to the present day, which would therefore no longer require the current era to be a ”special time” inmore » Uranus’ evolution. In this scenario, the thermal boundary leads to more rapid cooling of the outer envelope. When Teff ≃ Teq is reached, a shallow, subadiabatic zone in the atmosphere begins to develop. Its depth is adjusted to meet the luminosity constraint. This work provides a simple foundation for future Ice Giant structure and evolution models, that can be improved by properly treating the heat and particle fluxes in the diffusive zones.« less

Authors:
 [1]; ORCiD logo [2];  [3]; ORCiD logo [4]; ORCiD logo [5];  [6];  [7]
  1. Univ. of Rostock (Germany). Inst. of Physics; Univ. of California, Santa Cruz, CA (United States). Dept. of Astronomy and Astrophysics
  2. Castilleja High School, Palo Alto, CA (United States); Univ. of California, Santa Cruz, CA (United States). Science Internship Program
  3. Univ. of Rostock (Germany). Inst. of Physics
  4. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  5. Saratoga High School, Saratoga, CA (United States); Univ. of California, Santa Cruz, CA (United States). Science Internship Program
  6. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Univ. of California, Santa Cruz, CA (United States). Dept. of Astronomy and Astrophysics
  7. Univ. of California, Santa Cruz, CA (United States). Dept. of Astronomy and Astrophysics
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1497277
Report Number(s):
LLNL-JRNL-738448
Journal ID: ISSN 0019-1035; 891299
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Icarus
Additional Journal Information:
Journal Volume: 275; Journal Issue: C; Journal ID: ISSN 0019-1035
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; Astronomy and AstroPhysics; Uranus; Neptune; Planetary Evolution

Citation Formats

Nettelmann, N., Wang, K., Fortney, J. J., Hamel, S., Yellamilli, S., Bethkenhagen, M., and Redmer, R. Uranus evolution models with simple thermal boundary layers. United States: N. p., 2016. Web. doi:10.1016/j.icarus.2016.04.008.
Nettelmann, N., Wang, K., Fortney, J. J., Hamel, S., Yellamilli, S., Bethkenhagen, M., & Redmer, R. Uranus evolution models with simple thermal boundary layers. United States. https://doi.org/10.1016/j.icarus.2016.04.008
Nettelmann, N., Wang, K., Fortney, J. J., Hamel, S., Yellamilli, S., Bethkenhagen, M., and Redmer, R. Tue . "Uranus evolution models with simple thermal boundary layers". United States. https://doi.org/10.1016/j.icarus.2016.04.008. https://www.osti.gov/servlets/purl/1497277.
@article{osti_1497277,
title = {Uranus evolution models with simple thermal boundary layers},
author = {Nettelmann, N. and Wang, K. and Fortney, J. J. and Hamel, S. and Yellamilli, S. and Bethkenhagen, M. and Redmer, R.},
abstractNote = {The strikingly low luminosity of Uranus (Teff ≃ Teq) constitutes a long-standing challenge to our understanding of Ice Giant planets. Here we present the first Uranus structure and evolution models that are constructed to agree with both the observed low luminosity and the gravity field data. Here, our models make use of modern ab initio equations of state at high pressures for the icy components water, methane, and ammonia. Proceeding step by step, we confirm that adiabatic models yield cooling times that are too long, even when uncertainties in the ice:rock ratio (I:R) are taken into account. We then argue that the transition between the ice/rock-rich interior and the H/He-rich outer envelope should be stably stratified. Therefore, we introduce a simple thermal boundary and adjust it to reproduce the low luminosity. Due to this thermal boundary, the deep interior of the Uranus models are up to 2–3 warmer than adiabatic models, necessitating the presence of rocks in the deep interior with a possible I:R of 1 × solar. Finally, we allow for an equilibrium evolution (Teff ≃ Teq) that begun prior to the present day, which would therefore no longer require the current era to be a ”special time” in Uranus’ evolution. In this scenario, the thermal boundary leads to more rapid cooling of the outer envelope. When Teff ≃ Teq is reached, a shallow, subadiabatic zone in the atmosphere begins to develop. Its depth is adjusted to meet the luminosity constraint. This work provides a simple foundation for future Ice Giant structure and evolution models, that can be improved by properly treating the heat and particle fluxes in the diffusive zones.},
doi = {10.1016/j.icarus.2016.04.008},
journal = {Icarus},
number = C,
volume = 275,
place = {United States},
year = {Tue Apr 19 00:00:00 EDT 2016},
month = {Tue Apr 19 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 61 works
Citation information provided by
Web of Science

Figures / Tables:

Figure 1 Figure 1: Isotherms for 2000 K (solid) and 6000 K (dashed) of the ab initio EOS for NH3 (violet), CH4 (cyan), and H2O (blue). For water, ab initio data are used for pressures higher or equal to the points marked by diamonds . The black curves are for the linearmore » mixing approximation and mass mixing ratios H2O: CH4 : NH3 ≈ 7.7 : 4 : 1.« less

Save / Share:

Works referenced in this record:

Exploring exoplanet populations with NASA's Kepler Mission
journal, July 2014


Superionic Phases of the 1:1 Water–Ammonia Mixture
journal, October 2015

  • Bethkenhagen, Mandy; Cebulla, Daniel; Redmer, Ronald
  • The Journal of Physical Chemistry A, Vol. 119, Issue 42
  • DOI: 10.1021/acs.jpca.5b07854

Chemical processes in the deep interior of Uranus
journal, February 2011

  • Chau, Ricky; Hamel, Sebastien; Nellis, William J.
  • Nature Communications, Vol. 2, Issue 1
  • DOI: 10.1038/ncomms1198

The D/H ratio in the atmospheres of Uranus and Neptune from Herschel -PACS observations
journal, March 2013


Planetary Radii across Five Orders of Magnitude in Mass and Stellar Insolation: Application to Transits
journal, April 2007

  • Fortney, J. J.; Marley, M. S.; Barnes, J. W.
  • The Astrophysical Journal, Vol. 659, Issue 2
  • DOI: 10.1086/512120

A Framework for Characterizing the Atmospheres of Low-Mass Low-Density Transiting Planets
journal, September 2013

  • Fortney, Jonathan J.; Mordasini, Christoph; Nettelmann, Nadine
  • The Astrophysical Journal, Vol. 775, Issue 1
  • DOI: 10.1088/0004-637X/775/1/80

Self-Consistent Model Atmospheres and the Cooling of the Solar System'S Giant Planets
journal, February 2011


The Interior Structure, Composition, and Evolution of Giant Planets
journal, December 2009


THE FALSE POSITIVE RATE OF KEPLER AND THE OCCURRENCE OF PLANETS
journal, March 2013

  • Fressin, François; Torres, Guillermo; Charbonneau, David
  • The Astrophysical Journal, Vol. 766, Issue 2
  • DOI: 10.1088/0004-637X/766/2/81

Vertical temperature gradients on Uranus: Implications for layered convection
journal, December 1987

  • Gierasch, Peter J.; Conrath, Barney J.
  • Journal of Geophysical Research: Space Physics, Vol. 92, Issue A13
  • DOI: 10.1029/JA092iA13p15019

The structure and evolution of Jupiter - The fluid contraction stage
journal, July 1975

  • Graboske, H. C. , Jr.; Olness, R. J.; Pollack, J. B.
  • The Astrophysical Journal, Vol. 199
  • DOI: 10.1086/153689

THE INTERIORS OF GIANT PLANETS: Models and Outstanding Questions
journal, May 2005


Effect of Radiative Transport on the Evolution of Jupiter and Saturn
journal, September 1995

  • Guillot, T.; Chabrier, G.; Gautier, D.
  • The Astrophysical Journal, Vol. 450
  • DOI: 10.1086/176156

Interior Models of Uranus and Neptune
journal, December 2010


Polymerization and diamond formation from melting methane and their implications in ice layer of giant planets
journal, May 2009

  • Hirai, Hisako; Konagai, Keisuke; Kawamura, Taro
  • Physics of the Earth and Planetary Interiors, Vol. 174, Issue 1-4
  • DOI: 10.1016/j.pepi.2008.06.011

Comparative thermal evolution of Uranus and Neptune
journal, August 1978


Structure and evolution of Uranus and Neptune
journal, January 1980

  • Hubbard, W. B.; MacFarlane, J. J.
  • Journal of Geophysical Research: Solid Earth, Vol. 85, Issue B1
  • DOI: 10.1029/JB085iB01p00225

Optimized Jupiter, Saturn, and Uranus interior models
journal, March 1989


Layered convection as the origin of Saturn’s luminosity anomaly
journal, April 2013

  • Leconte, Jérémy; Chabrier, Gilles
  • Nature Geoscience, Vol. 6, Issue 5
  • DOI: 10.1038/ngeo1791

The atmosphere of Uranus: Results of radio occultation measurements with Voyager 2
journal, January 1987

  • Lindal, G. F.; Lyons, J. R.; Sweetnam, D. N.
  • Journal of Geophysical Research, Vol. 92, Issue A13
  • DOI: 10.1029/JA092iA13p14987

How Thermal Evolution and Mass-Loss Sculpt Populations of Super-Earths and Sub-Neptunes: Application to the Kepler-11 System and Beyond
journal, November 2012


On the Luminosity of Young Jupiters
journal, January 2007

  • Marley, Mark S.; Fortney, Jonathan J.; Hubickyj, Olenka
  • The Astrophysical Journal, Vol. 655, Issue 1
  • DOI: 10.1086/509759

Explaining why the uranian satellites have equatorial prograde orbits despite the large planetary obliquity
journal, June 2012


Characterization of exoplanets from their formation: I. Models of combined planet formation and evolution
journal, November 2012


THERMAL EVOLUTION AND STRUCTURE MODELS OF THE TRANSITING SUPER-EARTH GJ 1214b
journal, April 2011


New indication for a dichotomy in the interior structure of Uranus and Neptune from the application of modified shape and rotation data
journal, March 2013


Ab Initio Equation of State Data for Hydrogen, Helium, and Water and the Internal Structure of Jupiter
journal, August 2008

  • Nettelmann, Nadine; Holst, Bastian; Kietzmann, André
  • The Astrophysical Journal, Vol. 683, Issue 2
  • DOI: 10.1086/589806

The Effects of Snowlines on c/o in Planetary Atmospheres
journal, November 2011


The albedo, effective temperature, and energy balance of Uranus, as determined from Voyager IRIS data
journal, March 1990


Comparative models of Uranus and Neptune
journal, December 1995


Formation of the Giant Planets by Concurrent Accretion of Solids and Gas
journal, November 1996

  • Pollack, James B.; Hubickyj, Olenka; Bodenheimer, Peter
  • Icarus, Vol. 124, Issue 1
  • DOI: 10.1006/icar.1996.0190

The phase diagram of water and the magnetic fields of Uranus and Neptune
journal, January 2011


A Framework for Quantifying the Degeneracies of Exoplanet Interior Compositions
journal, March 2010


Turbulent Mixing and Layer Formation in Double-Diffusive Convection: Three-Dimensional Numerical Simulations and Theory
journal, March 2011


Turbulent models of ice giant internal dynamics: Dynamos, heat transfer, and zonal flows
journal, May 2013


Numerical dynamo models of Uranus' and Neptune's magnetic fields
journal, October 2006


Cosmochemistry and structure of the giant planets and their satellites
journal, April 1985


Convection and Mixing in Giant Planet Evolution
journal, April 2015


Liquid water oceans in ice giants
journal, February 2007


Diffusivity of heavy elements in Jupiter and Saturn
journal, April 2015


Comparative models of Uranus and Neptune
journal, December 1995


Numerical dynamo models of Uranus' and Neptune's magnetic fields
journal, October 2006


Further investigations of random models of Uranus and Neptune
journal, February 2000


Superionic Phases of the 1:1 Water–Ammonia Mixture
journal, October 2015

  • Bethkenhagen, Mandy; Cebulla, Daniel; Redmer, Ronald
  • The Journal of Physical Chemistry A, Vol. 119, Issue 42
  • DOI: 10.1021/acs.jpca.5b07854

Monte Carlo interior models for Uranus and Neptune
journal, January 1995

  • Marley, Mark S.; Gómez, Percy; Podolak, Morris
  • Journal of Geophysical Research, Vol. 100, Issue E11
  • DOI: 10.1029/95je02362

Dissociation of methane under high pressure
journal, October 2010

  • Gao, Guoying; Oganov, Artem R.; Ma, Yanming
  • The Journal of Chemical Physics, Vol. 133, Issue 14
  • DOI: 10.1063/1.3488102

Equation of state and phase diagram of ammonia at high pressures from ab initio simulations
journal, June 2013

  • Bethkenhagen, Mandy; French, Martin; Redmer, Ronald
  • The Journal of Chemical Physics, Vol. 138, Issue 23
  • DOI: 10.1063/1.4810883

On the Luminosity of Young Jupiters
journal, January 2007

  • Marley, Mark S.; Fortney, Jonathan J.; Hubickyj, Olenka
  • The Astrophysical Journal, Vol. 655, Issue 1
  • DOI: 10.1086/509759

What do we Really know About Uranus and Neptune?
journal, October 2012


Self-Consistent Model Atmospheres and the Cooling of the Solar System's Giant Planets
text, January 2011


NOTE: Explaining why the Uranian satellites have equatorial prograde orbits despite the large planetary obliquity
text, January 2012


A Framework for Characterizing the Atmospheres of Low-Mass Low-Density Transiting Planets
text, January 2013


Works referencing / citing this record:

Laser-driven shock compression of “synthetic planetary mixtures” of water, ethanol, and ammonia
journal, July 2019


Explaining the low luminosity of Uranus: a self-consistent thermal and structural evolution
journal, January 2020


Thermal evolution of Uranus and Neptune: I. Adiabatic models
journal, December 2019


Consequences of Giant Impacts on Early Uranus for Rotation, Internal Structure, Debris, and Atmospheric Erosion
journal, July 2018

  • Kegerreis, J. A.; Teodoro, L. F. A.; Eke, V. R.
  • The Astrophysical Journal, Vol. 861, Issue 1
  • DOI: 10.3847/1538-4357/aac725

Viscosity and Prandtl Number of Warm Dense Water as in Ice Giant Planets
journal, August 2019


Acceleration of Cooling of Ice Giants by Condensation in Early Atmospheres
journal, May 2017


Evidence for Crystalline Structure in Dynamically-Compressed Polyethylene up to 200 GPa
text, January 2019

  • Hartley, N. J.; Brown, S.; Cowan, T. E.
  • GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt
  • DOI: 10.15120/gsi-2019-00575

In Situ Formation of Icy Moons of Uranus and Neptune
journal, November 2018

  • Szulágyi, Judit; Cilibrasi, Marco; Mayer, Lucio
  • The Astrophysical Journal, Vol. 868, Issue 1
  • DOI: 10.3847/2041-8213/aaeed6

Formation of diamonds in laser-compressed hydrocarbons at planetary interior conditions
journal, August 2017


Planetary Ices and the Linear Mixing Approximation
journal, October 2017


Electronic transport in partially ionized water plasmas
journal, September 2017

  • French, Martin; Redmer, Ronald
  • Physics of Plasmas, Vol. 24, Issue 9
  • DOI: 10.1063/1.4998753

Bifurcation in the history of Uranus and Neptune: the role of giant impacts
journal, November 2019

  • Reinhardt, Christian; Chau, Alice; Stadel, Joachim
  • Monthly Notices of the Royal Astronomical Society, Vol. 492, Issue 4
  • DOI: 10.1093/mnras/stz3271

Characterizing equation of state and optical properties of dynamically pre-compressed materials
journal, April 2019

  • Guarguaglini, M.; Hernandez, J. -A.; Benuzzi-Mounaix, A.
  • Physics of Plasmas, Vol. 26, Issue 4
  • DOI: 10.1063/1.5060732

Stabilization of ammonia-rich hydrate inside icy planets
journal, August 2017

  • Naden Robinson, Victor; Wang, Yanchao; Ma, Yanming
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 34
  • DOI: 10.1073/pnas.1706244114

Effect of non-adiabatic thermal profiles on the inferred compositions of Uranus and Neptune
journal, May 2019

  • Podolak, Morris; Helled, Ravit; Schubert, Gerald
  • Monthly Notices of the Royal Astronomical Society, Vol. 487, Issue 2
  • DOI: 10.1093/mnras/stz1467

High-pressure chemistry of hydrocarbons relevant to planetary interiors and inertial confinement fusion
journal, May 2018

  • Kraus, D.; Hartley, N. J.; Frydrych, S.
  • Physics of Plasmas, Vol. 25, Issue 5
  • DOI: 10.1063/1.5017908

Thermal conductivity of dissociating water—an ab initio study
journal, February 2019


The Exchange of Mass and Angular Momentum in the Impact Event of Ice Giant Planets: Implications for the Origin of Uranus
journal, December 2018


Bifurcation in the history of Uranus and Neptune: the role of giant impacts
text, January 2020

  • Reinhardt, Christian; Chau, Alice; Stadel, Joachim
  • Oxford University Press
  • DOI: 10.5167/uzh-182773

Effect of non-adiabatic thermal profiles on the inferred compositions of Uranus and Neptune
text, January 2019

  • Podolak, Morris; Helled, Ravit; Schubert, Gerald
  • Oxford University Press
  • DOI: 10.5167/uzh-182777

Evidence for Crystalline Structure in Dynamically-Compressed Polyethylene up to 200 GPa
journal, March 2019


Thermal evolution of Uranus and Neptune: II. Deep thermal boundary layer
journal, June 2021


In Situ Formation of Icy Moons of Uranus and Neptune
text, January 2018


Acceleration of Cooling of Ice Giants by Condensation in Early Atmospheres
text, January 2017


Bifurcation in the history of Uranus and Neptune: the role of giant impacts
text, January 2019


Thermal evolution of Uranus and Neptune I: adiabatic models
text, January 2019


Uranus and Neptune: Origin, Evolution and Internal Structure
journal, March 2020


Laser-driven shock compression of “synthetic planetary mixtures” of water, ethanol, and ammonia
journal, July 2019


The interiors of Uranus and Neptune: current understanding and open questions
journal, November 2020

  • Helled, Ravit; Fortney, Jonathan J.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2187
  • DOI: 10.1098/rsta.2019.0474

Unusual chemistry of the C-H-N-O system under pressure and implications for giant planets
text, January 2020


On stable H-C-N-O compounds at high pressure
preprint, January 2020