Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

Ab Initio Entropy Calculations of Water Predict the Interiors of Uranus and Neptune to be 15-30% Colder than Previous Models

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Water's entropy at extreme pressure makes Uranus and Neptune 15-30% colder inside than prior models, favoring diamond rain and phase-separated ices.

desk verdict Ab initio entropy of water yields a crisp, novel prediction for colder ice giant interiors, but the corrupted text means the DFT validation can't be audited — the referee should check that first. read the letter →

arxiv 2508.16754 v1 pith:LMN7RWUF submitted 2025-08-22 astro-ph.EP astro-ph.IMcond-mat.mtrl-sci

Burkhard Militzer This is my paper · ORCID
classification astro-ph.EPastro-ph.IMcond-mat.mtrl-sci
keywords abinitiofreeenergywaterentropyUranusNeptuneicegiantinteriorssuperionicadiabatictemperatureprofilediamondrain
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the deep interiors of Uranus and Neptune are 15-30% colder than the standard models used to interpret them. The reason is the entropy of water, which the author computes for liquid and superionic water—a high-pressure state with mobile hydrogen inside a solid oxygen lattice—using quantum-mechanical free-energy calculations over the pressures and temperatures of ice-giant mantles. Those entropy values make the adiabatic temperature-pressure profiles much shallower than earlier model adiabats, so following them inward from the known outer conditions reaches much cooler depths. If right, the mantle conditions are cold enough that diamond rain and the recently predicted phase separation of planetary ices become more likely. The models also match the measured gravity harmonics, so the colder interiors are consistent with the existing gravity constraints.

What carries the argument

The load-bearing object is the ab initio entropy surface S(P,T) for liquid and superionic water, derived from free-energy calculations. That surface determines the slope of an adiabat: along a constant-entropy path, the temperature rise with pressure is controlled by dT/dP at fixed S, so a flatter entropy surface produces a colder deep interior at a given pressure. The paper inserts this water equation of state into the Concentric MacLaurin Spheroid method, a rotating-planet interior scheme that iterates density layers until the computed gravity harmonics match observations.

What would settle it

Recompute the entropy of water at a representative mantle condition, for example 100 GPa and 3000 K, with a different quantum mechanical approximation or with nuclear quantum effects included. If the slope of entropy with pressure is materially steeper than in this paper, the shallow adiabat and the 15-30% cooling disappear. A future precise measurement of the planets' intrinsic heat flow that requires hotter deep interiors would also contradict the model.

Watch

Extended reading notes

Core claim

The central claim is that the entropy surface S(P,T) of water, obtained from first-principles (ab initio) free-energy calculations, sets the shape of the adiabat in the mantles of Uranus and Neptune, and that this shape is much flatter in pressure-temperature space than the adiabats adopted in earlier interior models. Because an adiabat follows constant entropy, a shallower entropy surface means each step in pressure adds less temperature, so the same outer boundary conditions connect to a substantially colder deep interior. The paper builds rotating interior models with the Concentric MacLaurin Spheroid method that match the measured gravity moments, comparing fully convective models with m

Load-bearing premise

The conclusion depends on the computed entropy of water being accurate enough that the internal temperature profile really is flatter than older models assumed; a hidden error in the quantum mechanical calculation would shrink or erase the predicted 15-30% cooling.

Editorial extensions

If this is right

  • The deep mantles of Uranus and Neptune sit at lower temperatures than previously inferred, so estimates of how fast the planets cool and how much heat they still radiate need to be revised downward.
  • Cold enough conditions make diamond rain and the predicted phase separation of planetary ices more likely, meaning rain or layering may be active in the mantles rather than a well-mixed fluid.
  • Gravity data alone do not determine the warm interior profiles; the new models match the measured gravity harmonics with colder adiabats.
  • A thermal boundary between liquid and superionic water is compatible with the gravity data, giving a concrete, testable structural variation for future studies.
  • The released atmosphere code lets later models treat para/ortho hydrogen and helium consistently, so the outer boundary condition can be improved alongside the interior equation of state.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the entropy surface is the real control, then the precise 15-30% figure is tied to the current ab initio method; replacing the exchange-correlation functional or adding nuclear quantum effects will shift the number while probably preserving a shallower adiabat than earlier models.
  • The same entropy-based adiabat construction could be applied to other water-rich worlds, such as ocean exoplanets or icy moons, where the depth of the ocean-ice transition depends on the same S(P,T) surface.
  • A colder deep interior changes the thermal contraction history of Uranus and Neptune: the planets' present-day heat flows may be explained by slower cooling, which could be checked by future precise measurements of luminosity and atmospheric temperatures.
  • If rain layers form more readily, the distribution of heavy elements becomes stratified, so the bulk water abundance inferred from gravity alone would need reinterpretation.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper claims to derive the entropy of liquid and superionic water from ab initio free energy calculations over pressure-temperature conditions relevant to Uranus and Neptune. It then uses these entropies to construct shallower adiabats than those adopted in previous interior models, leading to interiors that are 15-30% colder, and it builds CMS-based interior models that match measured gravity for both fully convective and convective-boundary cases. The abstract also announces the release of an atmosphere code for para/ortho hydrogen and helium. The central claim is clear and potentially important. However, the submitted full text is largely unreadable because of character corruption, so the methods, numerical details, validation tables, and equations cannot be audited from the supplied material.

Significance. If the entropy calculations are converged and adequately benchmarked, the paper would make a substantive contribution: it replaces parameterized adiabats with physically derived ones, changes the predicted deep temperatures of ice giants by 15-30%, and has direct implications for diamond rain and phase-separated ice mantles. The approach is established in computational planetary science, and the promised code release is a practical strength. The gravity-matched interior modeling is also appropriate. The main limitation is that the quantitative result hinges entirely on the accuracy of the ab initio entropy S(P,T); neither the exchange-correlation functional, the thermodynamic-integration path, the finite-size extrapolation, nor the comparison with experimental/shock data is visible in the supplied text.

major comments (3)
  1. [Abstract and full-text methods] The 15-30% colder temperature is an integrated consequence of the ab initio entropy surface S(P,T). A small systematic error in the computed entropy can shift the adiabat slope and produce the claimed temperature change. The submitted text does not report the exchange-correlation functional, the thermodynamic-integration scheme, the number of k-points, the system size, finite-size corrections, or convergence tolerances. The unlabeled table in the full text appears to list entropy/adiabat values, but without these details and without error bars the central quantitative claim cannot be checked.
  2. [CMS interior models and gravity matching] Gravity data constrain the density distribution, not the temperature directly. The claim that the interior is 15-30% colder than previous models therefore requires a sensitivity analysis showing that the temperature reduction is driven by the ab initio adiabat rather than by the assumed layer compositions, the H/He-to-rock-to-ice ratios, or the placement of a convective boundary. The abstract states that fully convective and boundary-containing models are compared, but the supplied text does not show how parameter degeneracy propagates into the quoted temperature change.
  3. [Validation against experimental and shock data] Because the central claim depends on the quantitative accuracy of S(P,T), the paper should include a benchmark comparison of the computed entropy or derived Hugoniot against available experimental data on water at high pressure, and ideally against previous ab initio results. No such validation is visible in the supplied full text. The readable fragments contain tables but no uncertainties or comparison columns, so the accuracy of the entropy calculation remains unverified.
minor comments (4)
  1. [Full text] The body text is heavily corrupted and unreadable in places; equations, tables, and figures cannot be identified reliably. A clean manuscript is required for review.
  2. [Full text, inserted line] The text contains the unrelated line 'arXiv:2508.16753v4 [cs.CL] 22 Jan 2026'. This does not belong to the manuscript and should be removed or explained.
  3. [Abstract] The phrase 'wide range of conditions' should be quantified with the actual pressure-temperature range considered in the ab initio calculations, since the relevant range is roughly 10-800 GPa and 1000-8000 K.
  4. [Atmosphere code] The abstract announces a code for para/ortho hydrogen and helium atmospheres, but the readable text does not describe its inputs, outputs, or relation to the interior models. This needs a reference or a brief description.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: entropy is computed from ab initio free energy, and gravity matching constrains density, not the predicted temperatures.

full rationale

The paper's central chain is: ab initio free energy calculations -> entropy S(P,T) -> adiabatic temperature profiles -> interior models matched to gravity -> comparison with earlier models. None of these steps is defined in terms of the target result. The entropy is a thermodynamic derivative of the computed free energy, not a parameter fitted to Uranus/Neptune temperatures. The CMS gravity matching adjusts composition and boundaries to reproduce measured gravity, which constrains density; the 15-30% colder interior temperatures are consequences of the entropy-based adiabats, not fitted targets. The mention of diamond rain and phase separation is an implication, not an input. The provided full text is heavily corrupted (mojibake), so methodology details cannot be inspected, but no quotable equation or passage exhibits a reduction of a prediction to its own inputs. Under the rule requiring specific quoted evidence for circularity, none is present. Concerns about DFT exchange-correlation accuracy, finite-size effects, or missing convergence tests are correctness risks, not circularity.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

From the abstract, the main free parameters are the interior composition structure and any convective boundary, adjusted to match gravity. The core axioms are the adiabatic assumption and the accuracy of the DFT entropy calculations, neither of which is verifiable from the abstract alone.

free parameters (2)
  • Interior layer composition fractions (H/He, water, rock, core) = not stated in abstract
    Interior models constructed with the Concentric MacLaurin Spheroid method are adjusted to match gravity measurements, so composition and density jumps are fitted parameters.
  • Pressure/temperature location of the convective boundary between liquid and superionic water = not stated in abstract
    The abstract compares models with and without a convective boundary, so the boundary's pressure and the entropy jump across it are model parameters.
assumptions (3)
  • domain assumption Uranus and Neptune interiors are approximately adiabatic in the convective regions
    The paper derives adiabats and builds interior models assuming convective (isentropic) structure; this is the standard assumption for well-mixed giant planet envelopes.
  • domain assumption Density functional theory free energies are accurate for liquid and superionic water at planetary interior conditions
    The entire entropy derivation rests on ab initio free energy calculations; the abstract does not state the functional or its validation.
  • domain assumption The ab initio thermodynamic integrations are converged with respect to system size and simulation time
    Entropy from free energy calculations is only reliable if finite-size and sampling errors are controlled; the abstract gives no convergence data.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Ab Initio Entropy Calculations of Water Predict the Interiors of Uranus and Neptune to be 15-30% Colder than Previous Models." pith.science (2026). https://pith.science/paper/LMN7RWUF

@misc{pith2026250816754,
  author       = {Pith},
  title        = {Pith review of: Ab Initio Entropy Calculations of Water Predict the Interiors of Uranus and Neptune to be 15-30% Colder than Previous Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LMN7RWUF}},
  note         = {Machine review of arXiv:2508.16754}
}
read the original abstract

Ab initio free energy calculations are employed to derive the entropy of liquid and superionic water over a wide range of conditions in the interiors of Uranus and Neptune. The resulting adiabats are much shallower in pressure-temperature space than those adopted for earlier models of Uranus and Neptune. Our models for their interiors are thus much colder, increasing the likelihood that diamond rain or the recently predicted phase separation of planetary ices has occurred in the mantles of ice giant planets. Based on our ab initio data, we construct interior models for Uranus and Neptune with the Concentric MacLaurin Spheroid method that match the existing gravity measurements. We compare fully convective models with models that include a convective boundary between liquid and superionic water. We also share a code to characterize giant planet atmospheres where para and ortho hydrogen as well as helium are present.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Uncoupled high-latitude wave models in COAMPS

    physics.ao-ph 2025-08 unverdicted novelty 4.0 of 10

    A report of six uncoupled SWAN/WW3 high-latitude hindcasts within COAMPS tests a new ice-thickness-dependent wave dissipation formula; external verification exists for only two of the six cases.

Reference graph

Works this paper leans on

73 extracted references · 63 canonical work pages · cited by 1 Pith paper

  1. [1]

    1987, Computer Simulation of Liquids (New York: Oxford University Press)

    Allen, M., & Tildesley, D. 1987, Computer Simulation of Liquids (New York: Oxford University Press)

    work page 1987

  2. [2]

    Bailey, E., & Stevenson, D. J. 2021, The Planetary Science Journal, 2, 64, 10.3847/PSJ/abd1e0

    doi:10.3847/psj/abd1e0 2021

  3. [3]

    2015, The Journal of Physical Chemistry A, 119, 10582

    Bethkenhagen, M., Cebulla, D., Redmer, R., & Hamel, S. 2015, The Journal of Physical Chemistry A, 119, 10582

    work page 2015

  4. [4]

    L., Scandolo, S., et al

    Cavazzoni, C., Chiarotti, G. L., Scandolo, S., et al. 1999, Nature, 283, 44

    work page 1999

  5. [5]

    Chau, R., Hamel, S., & Nellis, W. J. 2011, Nature Communications, 2, 203, 10.1038/ncomms1198

    work page doi:10.1038/ncomms1198 2011

  6. [6]

    1995, Annual Review Of Earth And Planetary Sciences, Volume 23, pp

    Christensen, U. 1995, Annual Review Of Earth And Planetary Sciences, Volume 23, pp. 65-88., 23, 65

    work page 1995

  7. [7]

    2023, Nature Communications, 14, 7580

    de Villa, K., Gonz \'a lez-Cataldo, F., & Militzer, B. 2023, Nature Communications, 14, 7580

    work page 2023

  8. [8]

    2025, Contributions to Plasma Physics, e70015

    ---. 2025, Contributions to Plasma Physics, e70015

    work page 2025

Show all 73 references
  1. [9]

    A., Kresse, G., & Gillan, M

    de Wijs, G. A., Kresse, G., & Gillan, M. J. 1998, Phys. Rev. B, 57, 8223

    1998

  2. [10]

    R., Nettelmann, N., & Redmer, R

    French, M., Mattsson, T. R., Nettelmann, N., & Redmer, R. 2009, Phys. Rev. B, 79, 054107

    2009

  3. [11]

    G., Hedman, M

    French, R. G., Hedman, M. M., Nicholson, P. D., Longaretti, P.-Y., & McGhee-French, C. A. 2024, Icarus, 411, 115957

    2024

  4. [12]

    S., Bykova, E., et al

    Frost, M., McWilliams, R. S., Bykova, E., et al. 2024, Nature astronomy, 8, 174

    2024

  5. [13]

    F., & Militzer, B

    Gonz \' a lez-Cataldo, F., Wilson, H. F., & Militzer, B. 2014, The Astrophysical Journal, 787, 79

    2014

  6. [14]

    J., Hubbard , W

    Guillot , T., Stevenson , D. J., Hubbard , W. B., & Saumon , D. 2004, The interior of Jupiter , ed. D. T. E. . M. W. B. Bagenal, F., 35--57

    2004

  7. [15]

    2014, The Astrophysical Journal, 789, 69, 10.1088/0004-637X/789/1/69

    Helled, R., & Bodenheimer, P. 2014, The Astrophysical Journal, 789, 69, 10.1088/0004-637X/789/1/69

    2014 doi

  8. [16]

    2020, Space Science Reviews, 216, 38, 10.1007/s11214-020-00660-3

    Helled, R., Nettelmann, N., & Guillot, T. 2020, Space Science Reviews, 216, 38, 10.1007/s11214-020-00660-3

    2020 doi

  9. [17]

    Hubbard, W. B. 1984, Planetary Interiors (Tucson, AZ: University of Arizona Press)

    1984

  10. [18]

    2013, The Astrophysical Journal, 768, 43

    ---. 2013, The Astrophysical Journal, 768, 43

    2013

  11. [19]

    B., & MacFarlane, J

    Hubbard, W. B., & MacFarlane, J. J. 1980, Journal of Geophysical Research: Solid Earth, 85, 225

    1980

  12. [20]

    B., & Militzer, B

    Hubbard, W. B., & Militzer, B. 2016, Astrophys. J., 820, 80

    2016

  13. [21]

    2013, Molecular spectra and molecular structure: IV

    Huber, K. 2013, Molecular spectra and molecular structure: IV. Constants of diatomic molecules (Springer Science & Business Media)

    2013

  14. [22]

    J., & Voth, G

    Izvekov, S., Parrinello, M., Burnham, C. J., & Voth, G. A. 2003, J. Chem. Phys., 120, 10896

    2003

  15. [23]

    2017, Nature Astronomy, 1, 606

    Kraus, D., Vorberger, J., Pak, A., et al. 2017, Nature Astronomy, 1, 606

    2017

  16. [24]

    1996, Phys

    Kresse, G., & Furthm\" u ller, J. 1996, Phys. Rev. B, 54, 11169

    1996

  17. [25]

    1999, Phys

    Kresse, G., & Joubert, D. 1999, Phys. Rev. B, 59, 1758, 10.1103/PhysRevB.59.1758

    1999 doi

  18. [26]

    2012, Astronomy & Astrophysics, 540, A20

    Leconte, J., & Chabrier, G. 2012, Astronomy & Astrophysics, 540, A20

    2012

  19. [27]

    Lin, Z., Seager, S., & Weiss, B. P. 2025, The Planetary Science Journal, 6, 27

    2025

  20. [28]

    2022, Proceedings of the National Academy of Sciences, 119, e2203397119

    Matusalem, F., Santos Rego, J., & de Koning, M. 2022, Proceedings of the National Academy of Sciences, 119, e2203397119

    2022

  21. [29]

    2013, Physical Review B, 87, 014202

    Militzer, B. 2013, Physical Review B, 87, 014202

    2013

  22. [30]

    2016, High Energy Density Physics, 21, 8

    ---. 2016, High Energy Density Physics, 21, 8

    2016

  23. [31]

    2023 a , The Astrophysical Journal, 953, 111, 10.3847/1538-4357/ace1f1

    ---. 2023 a , The Astrophysical Journal, 953, 111, 10.3847/1538-4357/ace1f1

    2023 doi

  24. [32]

    2023 b , Quadratic Monte Carlo, 03-08-23, Zenodo, 10.5281/zenodo.8038144

    ---. 2023 b , Quadratic Monte Carlo, 03-08-23, Zenodo, 10.5281/zenodo.8038144

    2023 doi

  25. [33]

    2024 a , Proceedings of the National Academy of Sciences, 121, e2403981121

    ---. 2024 a , Proceedings of the National Academy of Sciences, 121, e2403981121

    2024

  26. [34]

    2024 b , Quadratic Monte Carlo 2024, Zenodo, 10.5281/zenodo.13961175

    ---. 2024 b , Quadratic Monte Carlo 2024, Zenodo, 10.5281/zenodo.13961175

    2024 doi

  27. [35]

    Ideal Mixture of Hydrogen and Helium

    ---. 2025 a , "Ideal Mixture of Hydrogen and Helium", Zenodo, DOI 10.5281/zenodo.15848727 , Zenodo, 10.5281/zenodo.15848727

    2025 doi

  28. [36]

    2025 b , Computer Physics Communications, 307, 109424

    ---. 2025 b , Computer Physics Communications, 307, 109424

    2025

  29. [37]

    H2O Equation of State and Interior Models of Uranus and Neptune

    ---. 2025 c , "H2O Equation of State and Interior Models of Uranus and Neptune", Zenodo, DOI 10.5281/zenodo.15848859 , Zenodo, 10.5281/zenodo.15848859

    2025 doi

  30. [38]

    Militzer, B., & Hubbard, W. B. 2007, AIP Conf. Proc., 955, 1395

    2007

  31. [39]

    2013, Astrophys

    ---. 2013, Astrophys. J., 774, 148

    2013

  32. [40]

    2024, Icarus, 411, 115955, https://doi.org/10.1016/j.icarus.2024.115955

    ---. 2024, Icarus, 411, 115955, https://doi.org/10.1016/j.icarus.2024.115955

    2024

  33. [41]

    H., Vorberger, J., Tamblyn, I., & Bonev, S

    Militzer, B., Hubbard, W. H., Vorberger, J., Tamblyn, I., & Bonev, S. A. 2008, Astrophys. J. Lett., 688, L45

    2008

  34. [42]

    Militzer, B., Wahl, S., & Hubbard, W. B. 2019, The Astrophysical Journal, 879, 78, 10.3847/1538-4357/ab23f0

    2019 doi

  35. [43]

    2018, AIP Conference Proceedings, 1979, 050012

    Militzer, B., & Zhang, S. 2018, AIP Conference Proceedings, 1979, 050012

    2018

  36. [44]

    B., Wahl, S., et al

    Militzer, B., Hubbard, W. B., Wahl, S., et al. 2022, Planet. Sci. J., 3, 185

    2022

  37. [45]

    R., et al

    Millot, M., Coppari, F., Rygg, J. R., et al. 2019, Nature, 569, 251

    2019

  38. [46]

    A., Schwegler, E., Ceperley, D., et al

    Morales, M. A., Schwegler, E., Ceperley, D., et al. 2009, Proceedings of the National Academy of Sciences, 106, 1324

    2009

  39. [47]

    Movshovitz, N., & Fortney, J. J. 2022, The Planetary Science Journal, 3, 88

    2022

  40. [48]

    NASA. 2021. https://science.nasa.gov/wp-content/uploads/2023/10/uranus-orbiter-and-probe.pdf

    2021

  41. [49]

    2013, Planetary and Space Science, 77, 143, https://doi.org/10.1016/j.pss.2012.06.019

    Nettelmann, N., Helled, R., Fortney, J., & Redmer, R. 2013, Planetary and Space Science, 77, 143, https://doi.org/10.1016/j.pss.2012.06.019

    2013 doi

  42. [50]

    A., M \"u ller, S., & Helled, R

    Neuenschwander, B. A., M \"u ller, S., & Helled, R. 2024, Astron. and Astrophys., in press, arXiv preprint arXiv:2401.11769, in press

    2024 arXiv

  43. [51]

    NIST. 2025. http://webbook.nist.gov/cgi/cbook.cgi?ID=C1333740&Units=SI&Mask=1000#Diatomic

    2025

  44. [52]

    1984, Journal of Chemical Physics, 81, 511

    Nos \'e , S. 1984, Journal of Chemical Physics, 81, 511

    1984

  45. [53]

    P., Burke, K., & Ernzerhof, M

    Perdew, J. P., Burke, K., & Ernzerhof, M. 1996, Phys. Rev. Lett., 77, 3865

    1996

  46. [54]

    1995, Planetary and Space Science, 43, 1517, https://doi.org/10.1016/0032-0633(95)00061-5

    Podolak, M., Weizman, A., & Marley, M. 1995, Planetary and Space Science, 43, 1517, https://doi.org/10.1016/0032-0633(95)00061-5

    1995 doi

  47. [55]

    B., Holtgrewe, N., Lobanov, S

    Prakapenka, V. B., Holtgrewe, N., Lobanov, S. S., & Goncharov, A. F. 2021, Nature Physics, 17, 1233

    2021

  48. [56]

    R., Nettelmann, N., & French, M

    Redmer, R., Mattsson, T. R., Nettelmann, N., & French, M. 2011, Icarus, 211, 798, https://doi.org/10.1016/j.icarus.2010.08.008

    2011 doi

  49. [57]

    1981, Nature, 292, 435

    Ross, M. 1981, Nature, 292, 435

    1981

  50. [58]

    1991, Icarus, 93, 82

    Ruzmaikin, A., & Starchenko, S. 1991, Icarus, 93, 82

    1991

  51. [59]

    1991, Physical Review A, 44, 5122

    Saumon, D., & Chabrier, G. 1991, Physical Review A, 44, 5122

    1991

  52. [60]

    1992, Phys

    ---. 1992, Phys. Rev. A, 46 , 2084

    1992

  53. [61]

    A., & Turcotte, D

    Schubert, G., Yuen, D. A., & Turcotte, D. L. 1975, Geophysical Journal International, 42, 705

    1975

  54. [62]

    2013, Icarus, 224, 97

    Soderlund, K., Heimpel, M., King, E., & Aurnou, J. 2013, Icarus, 224, 97

    2013

  55. [63]

    2020, Philosophical Transactions of the Royal Society A, 378, 20190479

    Soderlund, K., & Stanley, S. 2020, Philosophical Transactions of the Royal Society A, 378, 20190479

    2020

  56. [64]

    2015, The Astrophysical Journal, 806, 228

    Soubiran, F., & Militzer, B. 2015, The Astrophysical Journal, 806, 228

    2015

  57. [65]

    2004, Nature, 428, 151, 10.1038/nature02376

    Stanley, S., & Bloxham, J. 2004, Nature, 428, 151, 10.1038/nature02376

    2004 doi

  58. [66]

    2006, Icarus, 184, 556

    ---. 2006, Icarus, 184, 556

    2006

  59. [67]

    2021, The Planetary Science Journal, 2, 222

    Stixrude, L., Baroni, S., & Grasselli, F. 2021, The Planetary Science Journal, 2, 222

    2021

  60. [68]

    K., Torquato, S., & Car, R

    Sun, J., Clark, B. K., Torquato, S., & Car, R. 2015, Nature communications, 6, 8156

    2015

  61. [69]

    M., & Militzer, B

    Wahl, S. M., & Militzer, B. 2015, Earth and Planetary Science Letters, 410, 25

    2015

  62. [70]

    M., Wilson, H

    Wahl, S. M., Wilson, H. F., & Militzer, B. 2013, The Astrophysical Journal, 773, 95

    2013

  63. [71]

    F., & Militzer, B

    Wilson, H. F., & Militzer, B. 2012 a , Astrophys. J., 745, 54

    2012

  64. [72]

    2012 b , Phys

    ---. 2012 b , Phys. Rev. Lett., 108, 111101

    2012

  65. [73]

    F., Wong, M

    Wilson, H. F., Wong, M. L., & Militzer, B. 2013, Physical review letters, 110, 151102

    2013

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.