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From Tides to Currents: Unraveling the Mechanism That Powers WASP-107b's Internal Heat Flux

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper proposes that Ohmic dissipation—currents induced as atmospheric winds sweep through WASP-107b's magnetic field—maintains the planet's inflated radius and high internal heat, with tidal heating ruled out by dynamical arguments.

desk verdict The tidal argument is likely right and the Ohmic proposal is an honestly qualified hypothesis; the paper deserves a serious referee mainly for the dynamics. read the letter →

arxiv 2505.01581 v1 pith:6APXLBLN submitted 2025-05-02 astro-ph.EP

Konstantin Batygin This is my paper · ORCID
classification astro-ph.EP
keywords exoplanetsWASP-107bOhmicdissipationhotJupiterinflationtidalheatingsuper-puffplanetsplanetarymagneticfieldsatmosphericcirculation
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

WASP-107b is a low-density sub-Jovian planet whose JWST spectra show methane depletion, implying an interior heated from below to roughly $T_{\rm eff} \sim 400$ K. The paper argues that the usual explanation—tidal heating from the planet's eccentric orbit—cannot work: it would require an implausibly dissipative interior with tidal quality factor $Q \sim 30$, and the outer companion WASP-107c cannot sustain the eccentricity against ~2 Myr circularization over the system's 3.4 Gyr age. Instead, the paper proposes that electrical currents generated when atmospheric zonal winds move a partially ionized gas through the planet's magnetic field deposit heat in the interior (Ohmic dissipation). Under nominal assumptions for the wind speed, field strength, and ionization chemistry, the predicted heating corresponds to $T_{\rm eff} \approx 400$ K, matching the JWST-inferred value. If correct, this removes the need for an anomalously low tidal $Q$ and explains how a metal-rich, Jupiter-radius planet can remain inflated.

What carries the argument

The load-bearing object is a global induction model: a dipole magnetic field aligned with the rotation axis, a single zonal jet whose velocity rises parabolically from zero at the 2-bar pressure level to $\tilde v=0.25$ km/s at 1 bar, and an electrical conductivity profile $\sigma(r)$ set by thermal ionization of potassium and other alkali metals plus hydrogen. The induced electric potential $\Phi$ satisfies $\nabla\cdot(\sigma\nabla\Phi)=\nabla\cdot(\mathbf v\times\mathbf B)$ in the circulation layer, with the right-hand side vanishing below it; solutions are matched at the base of the weather layer and at the core, and the heating rate is $\int J^2/\sigma\,dV$. The result is a compact scaling, $T_{\rm eff}\propto\sqrt{\tilde v\tilde B}$, which makes the final answer depend mainly on two inputs: the wind speed and the surface field strength.

What would settle it

A direct measurement or tight upper limit on WASP-107b's surface magnetic field would settle the claim: because Ohmic heating scales as $B^2$, a field below roughly 20–30 G would drop the predicted $T_{\rm eff}$ below the JWST lower bound of 345 K, even at the nominal wind speed and conductivity. Radio emission from the planet's magnetosphere or spectropolarimetric detection of Zeeman signatures in its atmosphere could provide such a constraint.

Watch

Extended reading notes

Core claim

The paper's central claim is that WASP-107b's high intrinsic luminosity is maintained by Ohmic heating, not tides. In the proposed mechanism, a single zonal jet with speed $\tilde v = 0.25$ km/s at the 1-bar level drags a weakly ionized, alkali-rich atmosphere through a pole-aligned dipole field of strength $\tilde B \approx 70$ G, inducing currents that close through the deep envelope. The resistive dissipation of those currents, computed by solving the induction equation for the electric potential and integrating $J^2/\sigma$ over the interior, yields $T_{\rm eff}\approx 400$ K, consistent with the JWST-based estimates of $460\pm40$ K and $>345$ K. The tidal alternative is rejected on dynamical grounds: sustaining the same luminosity requires $Q_b\sim30$, which circularizes the orbit in $\tau_e\lesssim2$ Myr, and neither coplanar secular forcing nor inclined configurations that excite eccentricity-inclination oscillations (von Zeipel-Lidov-Kozai cycles) driven by WASP-107c can maintain the required eccentricity over gigayear timescales.

Load-bearing premise

The weakest load-bearing premise is the assumed surface magnetic field strength of about 70 G, taken from a scaling relation that links internal heat flow to dynamo-generated fields; if the planet's slow, synchronized rotation keeps its field far weaker, the Ohmic heating, which grows as the square of the field strength, would not reach the observed 345–500 K interior temperature.

Editorial extensions

If this is right

  • If Ohmic dissipation powers WASP-107b, the observed eccentricity no longer needs constant tidal pumping; it can be a relic of slow circularization, implying a tidal quality factor $Q_b$ of a few $\times 10^4$ or higher, in line with values inferred for solar-system giants.
  • The planet's high atmospheric metallicity and extended scale height may steepen the conductivity increase with depth, making Ohmic heating more efficient in metal-rich sub-Jovians than in the typical hot-Jupiter population.
  • Radius inflation in sub-Jovian planets likely has multiple causes: Ohmic dissipation may dominate for WASP-107b, while obliquity tides, delayed contraction from high opacity, or other energy sources may inflate other super-puffs.
  • Parameter degeneracy is built into the mechanism: extending the induction region deeper and reducing the wind speed (e.g., 40 m/s to 10 bars) gives the same heating rate, so atmospheric observations alone may not pin down the exact flow geometry.

Reading between the lines

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

  • Because the heating scales as $\tilde B^2$, a future radio or spectropolarimetric search for WASP-107b's magnetic field would sharply discriminate between this model and tidal heating.
  • If Ohmic dissipation commonly powers super-puff inflation, JWST methane-depletion surveys should find inflated radii preferentially in metal-rich, highly irradiated sub-Jovians—a population correlation that could be tested with a modest sample.
  • The same induction calculation could be exported to other warm sub-Neptunes, where deeper, more conductive atmospheres might make Ohmic heating efficient even at lower irradiation levels; the paper does not explore this application.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The manuscript addresses the elevated internal heat flux inferred for WASP-107b from JWST methane depletion. It first argues against tidal heating: matching the observed luminosity requires Q≈30, the tidal circularization timescale is only about 2 Myr, and neither coplanar secular forcing (equilibrium eccentricity ≈3e-4) nor high-inclination von Zeipel-Lidov-Kozai cycles (N-body runs) can sustain the required eccentricity over Gyr timescales. The paper then proposes Ohmic dissipation: a zonal flow of 0.25 km/s between the 1 and 2 bar levels, interacting with a dipolar field of about 70 G in a partially ionized, high-metallicity envelope, yields Teff≈400 K, matching the JWST estimates of Sing et al. (2024) and Welbanks et al. (2024). Section 4 acknowledges that the calculation is deliberately stylized and lists parameter degeneracies.

Significance. The tidal analysis is a solid and useful contribution: the equilibrium eccentricity calculation, the N-body test of inclined configurations, and the robustness of the low-Q inference to interior-model choices are clearly presented and internally consistent. The Ohmic proposal is physically motivated and consistent with population-level inflation mechanisms, but as presented it is a plausibility demonstration rather than a quantitative prediction. The main weaknesses are the dependence of the field estimate on the observed luminosity, the questionable applicability of the dynamo scaling to a spin-synchronized planet, and a numerical inconsistency in Eq. (9). If these are repaired or the claims are appropriately conditioned, the paper would be a valuable case study for super-puff inflation scenarios.

major comments (3)
  1. [§3.2, Eq. (9)] As printed, the radius factor (R_sun/R_b)^(6/7) does not yield the stated B≈70 G. With the paper's nominal numbers (m_b≈30.5 M_earth, L_b from Teff≈440 K and R_b≈0.95 R_J, so R_b/R_sun≈0.095), Eq. (9) gives B≈35 G rather than 70 G; the value 70 G is recovered if the radius exponent is -7/6, i.e., (R_b/R_sun)^(-7/6). Because Teff_Ohm is proportional to B^(1/2) in Eq. (11), the printed equation would give Teff_Ohm≈280 K, below the Welbanks et al. lower bound of 345 K. This is load-bearing, since Eq. (9) is the only estimate of B and the numerical claim in Section 3.3 depends directly on it.
  2. [§3.2–3.3, Eqs. (9)–(11)] The estimate of B through Eq. (9) uses L_b, i.e., the observed internal luminosity, as an input. The Ohmic heating calculation then returns a Teff that is compared to the same L_b. The relation is not an identity—Teff_Ohm scales as L_b^(1/6), which is sublinear—but it is a consistency condition rather than an independent confirmation. The abstract's statement that Ohmic heating 'readily accounts' for the thermal state therefore overstates the evidence, even though Section 4 honestly labels the calculation a proof-of-concept. I recommend either deriving B from an input that does not involve L_b, or explicitly framing the result as 'if B≈70 G, then Teff≈400 K' and presenting the required B as a function of Teff.
  3. [§3.2, Eq. (9) and surrounding text] The Christensen/Reiners scaling is calibrated for rapidly rotating, fully convective dynamos. WASP-107b is spin-orbit synchronized with P=5.7 d, and the manuscript does not demonstrate that its convective dynamo lies in the regime described by Eq. (9). This matters quantitatively because the heating rate scales as B^2: reducing B from 70 G to about 35–40 G (a factor of 2) lowers Teff_Ohm to roughly 280–300 K, below the Welbanks et al. lower bound, and a factor of 3 reduces it to about 230 K. A concrete test would be to evaluate a rotation-dependent dynamo scaling or to quote a plausible range of B from independent hot-Jupiter field constraints; absent that, the fiducial agreement is not robust.
minor comments (6)
  1. [§1, first paragraph] 'subsequent observations' should be capitalized because it begins a sentence.
  2. [§2.3 heading] The heading contains a typo: 'von Zeiplel-Lidov-Kozai' should be 'von Zeipel-Lidov-Kozai'.
  3. [§3.1, text above Eq. (6)] 'reduced Plank constant' should be 'reduced Planck constant'.
  4. [Eq. (9)] Please define whether R_b is the 1-bar radius and clarify the radius exponent; if the intended scaling is (R_b/R_sun)^(-7/6), write it that way so the equation reproduces B≈70 G.
  5. [§3.3] The paper quotes Teff≈400 K without an uncertainty or a plausible range, which makes the comparison to 460±40 K and >345 K difficult to assess; a short sensitivity range would be useful.
  6. [Abstract and §4] The abstract's 'readily accounts' should be softened to 'can account under the assumed fiducial parameters' to match the proof-of-concept caveat stated in Section 4.

Circularity Check

1 steps flagged · score 4.0 of 10

The fiducial Ohmic match is partly circular: Eq. (9) sets B from the observed luminosity, so Teff≈400 K is a weak L_b^{1/6} self-consistency relation rather than an independent prediction; the tidal analysis is independent.

  1. fitted input called prediction [Sec. 3.2, Eq. (9); Sec. 3.3, Eq. (11); Sec. 4]
    "To estimate the strength of the magnetic field, we adopt the scaling relation of Reiners & Christensen (2010), which relates the surface field strength to the heat-flux via the expression: \tilde B =B_0 (m_b/M_\odot)^{1/6}(L_b/L_\odot)^{1/3}(R_\odot/R_b)^{6/7} ... This fiducial estimate yields a surface field of \tilde B\approx 70 G. ... With our fiducial estimates enumerated above, we obtain T_eff\approx 400 K, in agreement with JWST inferences of Sing et al. (2024); Welbanks et al. (2024)."

    Eq. (9) sets B from the observed luminosity L_b, i.e., from the observed Teff (L_b = 4πR_b²σ_sbT_eff⁴, as used in Sec. 2.1). The paper's Sec. 4 states the heating rate scales as the square of B, and Eq. (11) gives T_eff ∝ √(ṽ B̃). Substituting Eq. (9) makes the predicted Teff proportional to L_b^{1/6}. Thus the nominal 400 K agreement is a weak consistency relation with the same observable used as an input, not an independent prediction. The paper also concedes that B, wind speed, and layer depth can be traded off to give identical results, so the fiducial match is not unique.

full rationale

The tidal-heating rejection is self-contained and not circular: Eq. (1) uses the observed Teff to infer the required Q_b, and the subsequent secular and N-body calculations independently show that WASP-107c cannot maintain the eccentricity needed to sustain that luminosity. That argument does not presuppose the Ohmic conclusion. The main circularity is confined to the Ohmic positive claim. The surface field in Eq. (9) is not an independent observable; it is estimated from the very luminosity the Ohmic calculation purports to reproduce. Because P_Ohmic ∝ B² and B ∝ L_b^{1/3}, the resulting Teff scales only as L_b^{1/6}, so the exercise is a self-consistency check rather than a falsifiable prediction. The paper is transparent about this degeneracy in Sec. 4, and the self-citations to Batygin & Stevenson (2010) and Batygin et al. (2011) supply a published model rather than a load-bearing uniqueness claim. The Ohmic result therefore has partial circularity, but the tidal dynamics and the conductivity modeling add independent content. Score 4 reflects a central prediction that is partly fed by its own target observable without being a full tautology.

Assumptions & free parameters 5 free parameters · 11 assumptions · 0 invented entities

The Ohmic heating estimate relies on a chain of adopted parameters: a fitted polytropic interior, a chosen wind profile and depth, a conductivity model, and a magnetic field strength set by a scaling relation that uses the observed heat flux. No fundamentally new physical entities are introduced, but the circularity in the field-strength estimate and the hand-picked circulation parameters mean the central positive claim rests on plausibility assumptions rather than independent predictions.

free parameters (5)
  • Envelope polytropic index eta = 1.29 (zeta ~ 7/2)
    Adjusted in Appendix A to match WASP-107b's measured mass and radius; sets k2b = 0.015 and hence the tidal Q bound.
  • Envelope density at core boundary rho0 = 5.8 g/cc
    Fit to the observed mass and radius in the polytropic model; controls the planetary radius.
  • Wind speed at 1 bar, v = 0.25 km/s
    Chosen from hot Jupiter GCM literature (e.g., Kataria et al. 2014); Ohmic heating scales as v^2, so this is a key amplitude choice.
  • Circulation depth (wind vanishes at 2 bars) = delta corresponding to 1-2 bar pressure difference
    Chosen from Elsasser-number arguments that the Lorentz force becomes dominant below 2 bars; deeper layers with slower winds produce equivalent heating, as stated in Sec 4.
  • Surface magnetic field B = ~70 G
    Derived from Eq 9 using the observed luminosity L_b and scaling constant B0 = 0.48 T. Because the target luminosity enters the field estimate, this parameter partially calibrates the model to the predicted quantity.
assumptions (11)
  • domain assumption Envelope pressure-density relation P = K rho^eta (polytropic EOS), Appendix A.
    Adopted to build an interior model. The index eta is fitted to the observed mass and radius, so the polytropic form itself is an assumption about the equation of state.
  • standard math The planet is in hydrostatic equilibrium and is spherically symmetric.
    Standard for planetary structure calculations.
  • domain assumption Constant-density solid core with Murnaghan EOS and R_c/R_earth = (M_c/M_earth)^(1/4).
    Assumed composition and EOS for the core; the 12 M_earth core mass is taken from retrieval models.
  • domain assumption Magnetic field is a pole-aligned dipole.
    Eq 8 prescribes the field geometry for the induction calculation. A multipolar or tilted field would change the heating distribution.
  • ad hoc to paper Zonal wind profile is a single jet with velocity increasing parabolically with altitude, vanishing at 2 bars.
    Eq 8 is a stylized circulation model chosen for analytic tractability rather than derived from GCMs.
  • ad hoc to paper Conductivity in the circulation region is approximated by an exponential matched to the polytropic profile.
    Introduced to enable an analytic solution of the induction equation. The paper states this is a convenient parameterization.
  • domain assumption The planet is in pseudo-synchronized spin and the spin rate equals the mean motion.
    Used for the tidal luminosity formula and the Elsasser number estimate.
  • domain assumption The outer planet's orbital elements (e_c, i_c) are nearly constant because the angular momentum ratio is small (Eq B9).
    Justified by the system's hierarchical architecture; standard in secular theory.
  • domain assumption Saha equilibrium with potassium ionization and a potassium abundance that scales with inferred metallicity.
    Gives the electron fraction and conductivity profile. The paper notes the square-root dependence dilutes the sensitivity to this assumption.
  • domain assumption Magnetic field strength follows the Christensen/Reiners scaling B proportional to L_b^(1/3).
    This scaling is calibrated on convective dynamos. Using the observed L_b to set B introduces a mild circularity into the Ohmic heating estimate.
  • domain assumption Tidal dissipation is described by a constant Q and the equilibrium tide formula (Eq 1).
    Standard parameterization used to relate Q to the observed luminosity and to the circularization timescale.

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Cite this review

Pith. "Pith review of From Tides to Currents: Unraveling the Mechanism That Powers WASP-107b's Internal Heat Flux." pith.science (2026). https://pith.science/paper/6APXLBLN

@misc{pith2026250501581,
  author       = {Pith},
  title        = {Pith review of: From Tides to Currents: Unraveling the Mechanism That Powers WASP-107b's Internal Heat Flux},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6APXLBLN}},
  note         = {Machine review of arXiv:2505.01581}
}
abstract

The sub-Jovian exoplanet WASP-107b ranks among the best-characterized low-density worlds, featuring a Jupiter-like radius and a mass that lies firmly in the sub-Saturn range. Recently obtained JWST spectra reveal significant methane depletion in the atmosphere, indicating that WASP-107b's envelope has both a high metallicity and an elevated internal heat flux. Together with a detected non-zero orbital eccentricity, these data have been interpreted as evidence of tidal heating. However, explaining the observed luminosity with tidal dissipation requires an unusually low tidal quality factor of $Q \sim 100$. Moreover, we find that secular excitation by the RV-detected outer companion WASP-107c, generally cannot sustain WASP-107b's eccentricity in steady state against tidal circularization. As an alternative explanation, we propose that Ohmic dissipation -- generated by interactions between zonal flows and the planetary magnetic field in a partially ionized atmosphere -- maintains the observed thermal state. Under nominal assumptions for the field strength, atmospheric circulation, and ionization chemistry, we show that Ohmic heating readily accounts for WASP-107b's inflated radius and anomalously large internal entropy.

Figures

Figures reproduced from arXiv: 2505.01581 by the authors.

Figure 1
Figure 1. Eccentricity evolution of WASP-107b under various dynamical configurations. Panel A depicts the results from secular perturbation theory, showing the orbital eccentricity of WASP-107b as a function of time (in units of the tidal circularization timescale τe ≈ 6 Myr) for different mutual inclinations of the planetary orbits: 0 deg (black), 20 deg (purple), 40 deg (red), 60 deg (green), and 80 deg (blue). The coplanar… view at source ↗
Figure 2
Figure 2. Electrical conductivity profile of WASP-107b’s atmosphere and upper interior as a function of radius (in units of Rb). The gray curve (labeled “K-only”) shows the conductivity resulting from thermal ionization of potassium alone, while the purple curve (“H + Alkali metals”) incorpo￾rates multiple alkali species and hydrogen ionization, leading to a significantly higher conductivity in deeper layers. The vertical sha… view at source ↗
Figure 3
Figure 3. Schematic, to-scale representation of the geome￾try of the induced currents (colored arrows) within WASP￾107b’s interior, resulting from atmospheric circulation (indi￾cated by circles with dots and crosses marking flow into and out of the page, respectively) interacting with a pole-aligned magnetic dipole field (black curves). The outer circle de￾notes the 1-bar pressure level, and the gray band highlights the layer… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Density profile of WASP-107b’s polytropic enve￾lope, extending from the core to the outer radius, defined by matching the atmospheric temperature the irradiation equi￾librium value. The purple curve shows the full numerical hy￾drostatic solution, while the black curve …

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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. Continuous helium absorption from the leading and trailing tails of WASP-107b

    astro-ph.EP 2025-05 conditional novelty 7.0 of 10

    Continuous JWST observations of WASP-107b reveal metastable helium absorption beginning 1.5 hours before ingress, evidence of an extended ellipsoidal thermosphere, with spot-corrected water abundance log10 H2O = -2.5 ± 0.6.

Reference graph

Works this paper leans on

65 extracted references · 4 canonical work pages · cited by 1 Pith paper

  1. [1]

    x ?s`|sa 0! ` C jC@b1 D p G?؜q 14N#uB A,#@ R

    thebibliography [1] 20pt to REFERENCES 6pt =0pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command Each re...

    2017

  2. [2]

    & Socrates, A.\ 2010, , 714, 1

    Arras, P. & Socrates, A.\ 2010, , 714, 1. doi:10.1088/0004-637X/714/1/1

    doi:10.1088/0004-637x/714/1/1 2010

  3. [3]

    doi:10.1088/0004-637X/704/1/L49

    Batygin, K., Bodenheimer, P., & Laughlin, G.\ 2009, , 704, L49. doi:10.1088/0004-637X/704/1/L49

    doi:10.1088/0004-637x/704/1/l49 2009

  4. [4]

    & Stevenson, D

    Batygin, K. & Stevenson, D. J.\ 2010, , 714, L238. doi:10.1088/2041-8205/714/2/L238

    doi:10.1088/2041-8205/714/2/l238 2010

  5. [5]

    J., & Bodenheimer, P

    Batygin, K., Stevenson, D. J., & Bodenheimer, P. H.\ 2011, , 738, 1. doi:10.1088/0004-637X/738/1/1

    doi:10.1088/0004-637x/738/1/1 2011

  6. [6]

    & Stevenson, D

    Batygin, K. & Stevenson, D. J.\ 2013, , 769, L9. doi:10.1088/2041-8205/769/1/L9

    doi:10.1088/2041-8205/769/1/l9 2013

  7. [7]

    Bodenheimer, P., Lin, D. N. C., & Mardling, R. A.\ 2001, , 548, 466. doi:10.1086/318667

    doi:10.1086/318667 2001

  8. [8]

    doi:10.1086/514326

    Burrows, A., Hubeny, I., Budaj, J., et al.\ 2007, , 661, 502. doi:10.1086/514326

    doi:10.1086/514326 2007

Show all 65 references
  1. [9]

    W., Shkolnik, E

    Cauley, P. W., Shkolnik, E. L., Llama, J., et al.\ 2019, Nature Astronomy, 3, 1128. doi:10.1038/s41550-019-0840-x

    2019 doi

  2. [10]

    M., Latham, D

    Charbonneau, D., Brown, T. M., Latham, D. W., et al.\ 2000, , 529, L45. doi:10.1086/312457

    2000 doi

  3. [11]

    Chandrasekhar, S.\ 1939, Chicago, Ill., The University of Chicago press [1939]

    1939

  4. [12]

    & Rogers, L

    Chen, H. & Rogers, L. A.\ 2016, , 831, 180. doi:10.3847/0004-637X/831/2/180

    2016 doi

  5. [13]

    R., Holzwarth, V., & Reiners, A.\ 2009, , 457, 167

    Christensen, U. R., Holzwarth, V., & Reiners, A.\ 2009, , 457, 167. doi:10.1038/nature07626

    2009 doi

  6. [14]

    & Winn, J

    Dai, F. & Winn, J. N.\ 2017, , 153, 205. doi:10.3847/1538-3881/aa65d1

    2017 doi

  7. [15]

    J., Mordasini, C., Nettelmann, N., et al.\ 2013, , 775, 80

    Fortney, J. J., Mordasini, C., Nettelmann, N., et al.\ 2013, , 775, 80. doi:10.1088/0004-637X/775/1/80

    2013 doi

  8. [16]

    doi:10.1093/mnras/stw609

    Fuller, J., Luan, J., & Quataert, E.\ 2016, , 458, 3867. doi:10.1093/mnras/stw609

    2016 doi

  9. [17]

    E., & Sari, R.\ 2016, , 825, 29

    Ginzburg, S., Schlichting, H. E., & Sari, R.\ 2016, , 825, 29. doi:10.3847/0004-637X/825/1/29

    2016 doi

  10. [18]

    & Sari, R.\ 2016, , 819, 116

    Ginzburg, S. & Sari, R.\ 2016, , 819, 116. doi:10.3847/0004-637X/819/2/116

    2016 doi

  11. [19]

    & Batygin, K.\ 2024, , 413, 116014

    Goldberg, M. & Batygin, K.\ 2024, , 413, 116014. doi:10.1016/j.icarus.2024.116014

    2024

  12. [20]

    & Showman, A

    Guillot, T. & Showman, A. P.\ 2002, , 385, 156. doi:10.1051/0004-6361:20011624

    2002 doi

  13. [21]

    doi:10.1088/2041-8205/748/1/L17

    Heng, K.\ 2012, , 748, L17. doi:10.1088/2041-8205/748/1/L17

    2012 doi

  14. [22]

    W., Marcy, G

    Henry, G. W., Marcy, G. W., Butler, R. P., et al.\ 2000, , 529, L41. doi:10.1086/312458

    2000 doi

  15. [23]

    P., Fortney, J

    Kataria, T., Showman, A. P., Fortney, J. J., et al.\ 2014, , 785, 92. doi:10.1088/0004-637X/785/2/92

    2014 doi

  16. [24]

    doi:10.1051/0004-6361/202142588

    Knierim, H., Batygin, K., & Bitsch, B.\ 2022, , 658, L7. doi:10.1051/0004-6361/202142588

    2022 doi

  17. [25]

    & Helled, R.\ 2024, , 977, 227

    Knierim, H. & Helled, R.\ 2024, , 977, 227. doi:10.3847/1538-4357/ad8dd0

    2024 doi

  18. [26]

    Komacek, T. D. & Youdin, A. N.\ 2017, , 844, 94. doi:10.3847/1538-4357/aa7b75

    2017 doi

  19. [27]

    J., Sch \"o ttler, M., et al.\ 2021, , 103, 063203

    Kumar, S., Poser, A. J., Sch \"o ttler, M., et al.\ 2021, , 103, 063203. doi:10.1103/PhysRevE.103.063203

    2021 doi

  20. [28]

    C.\ 2011, , 729, L7

    Laughlin, G., Crismani, M., & Adams, F. C.\ 2011, , 729, L7. doi:10.1088/2041-8205/729/1/L7

    2011 doi

  21. [29]

    doi:10.1038/nature08108

    Lainey, V., Arlot, J.-E., Karatekin, \"O ., et al.\ 2009, , 459, 957. doi:10.1038/nature08108

    2009 doi

  22. [30]

    G., Fuller, J., et al.\ 2020, Nature Astronomy, 4, 1053

    Lainey, V., Casajus, L. G., Fuller, J., et al.\ 2020, Nature Astronomy, 4, 1053. doi:10.1038/s41550-020-1120-5

    2020 doi

  23. [31]

    M., & Stevenson, D

    Liu, J., Goldreich, P. M., & Stevenson, D. J.\ 2008, , 196, 653. doi:10.1016/j.icarus.2007.11.036

    2008 doi

  24. [32]

    Lopez, E. D. & Fortney, J. J.\ 2014, , 792, 1. doi:10.1088/0004-637X/792/1/1

    2014 doi

  25. [33]

    Mardling, R. A. & Lin, D. N. C.\ 2002, , 573, 829. doi:10.1086/340752

    2002 doi

  26. [34]

    A.\ 2007, , 382, 1768

    Mardling, R. A.\ 2007, , 382, 1768. doi:10.1111/j.1365-2966.2007.12500.x

    2007

  27. [35]

    A.\ 2010, , 407, 1048

    Mardling, R. A.\ 2010, , 407, 1048. doi:10.1111/j.1365-2966.2010.16814.x

    2010

  28. [36]

    & Queloz, D.\ 1995, , 378, 355

    Mayor, M. & Queloz, D.\ 1995, , 378, 355. doi:10.1038/378355a0

    1995 doi

  29. [37]

    doi:10.1088/0004-637X/745/2/138

    Menou, K.\ 2012, , 745, 138. doi:10.1088/0004-637X/745/2/138

    2012 doi

  30. [38]

    \ 2024, PNAS, 121, 49 doi:10.1073/pnas.2403981121

    Militzer, B. \ 2024, PNAS, 121, 49 doi:10.1073/pnas.2403981121

    2024 doi

  31. [39]

    & Laughlin, G.\ 2019, Nature Astronomy, 3, 424

    Millholland, S. & Laughlin, G.\ 2019, Nature Astronomy, 3, 424. doi:10.1038/s41550-019-0701-7

    2019 doi

  32. [40]

    doi:10.3847/1538-4357/ab959c

    Millholland, S., Petigura, E., & Batygin, K.\ 2020, , 897, 7. doi:10.3847/1538-4357/ab959c

    2020 doi

  33. [41]

    doi:10.1088/0004-637X/724/1/313

    Perna, R., Menou, K., & Rauscher, E.\ 2010, , 724, 313. doi:10.1088/0004-637X/724/1/313

    2010 doi

  34. [42]

    A., Livingston, J., Batygin, K., et al.\ 2020, , 159, 2

    Petigura, E. A., Livingston, J., Batygin, K., et al.\ 2020, , 159, 2. doi:10.3847/1538-3881/ab5220

    2020 doi

  35. [43]

    A., et al.\ 2021, , 161, 70

    Piaulet, C., Benneke, B., Rubenzahl, R. A., et al.\ 2021, , 161, 70. doi:10.3847/1538-3881/abcd3c

    2021 doi

  36. [44]

    H., Teukolsky, S

    Press, W. H., Teukolsky, S. A., Vetterling, W. T., et al.\ 1992, Cambridge: University Press, |c1992, 2nd ed

    1992

  37. [45]

    I., & Marley, M

    Podolak, M., Podolak, J. I., & Marley, M. S.\ 2000, , 48, 143. doi:10.1016/S0032-0633(99)00088-4

    2000 doi

  38. [46]

    B., Hubickyj, O., Bodenheimer, P., et al.\ 1996, , 124, 62

    Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al.\ 1996, , 124, 62. doi:10.1006/icar.1996.0190

    1996

  39. [47]

    & Valencia, D.\ 2017, , 846, 47

    Pu, B. & Valencia, D.\ 2017, , 846, 47. doi:10.3847/1538-4357/aa826f

    2017 doi

  40. [48]

    & Wolf, A

    Ragozzine, D. & Wolf, A. S.\ 2009, , 698, 1778. doi:10.1088/0004-637X/698/2/1778

    2009 doi

  41. [49]

    & Christensen, U

    Reiners, A. & Christensen, U. R.\ 2010, , 522, A13. doi:10.1051/0004-6361/201014251

    2010 doi

  42. [50]

    Rogers, T. M. & Showman, A. P.\ 2014, , 782, L4. doi:10.1088/2041-8205/782/1/L4

    2014 doi

  43. [51]

    A., Dai, F., Howard, A

    Rubenzahl, R. A., Dai, F., Howard, A. W., et al.\ 2021, , 161, 119. doi:10.3847/1538-3881/abd177

    2021 doi

  44. [52]

    doi:10.1051/0004-6361/202038361

    Sarkis, P., Mordasini, C., Henning, T., et al.\ 2021, , 645, A79. doi:10.1051/0004-6361/202038361

    2021 doi

  45. [53]

    M.\ 1995, , 99, 713

    Saumon, D., Chabrier, G., & van Horn, H. M.\ 1995, , 99, 713. doi:10.1086/192204

    1995 doi

  46. [54]

    P., Tan, X., & Parmentier, V.\ 2020, , 216, 139

    Showman, A. P., Tan, X., & Parmentier, V.\ 2020, , 216, 139. doi:10.1007/s11214-020-00758-8

    2020 doi

  47. [55]

    K., Rustamkulov, Z., Thorngren, D

    Sing, D. K., Rustamkulov, Z., Thorngren, D. P., et al.\ 2024, , 630, 831. doi:10.1038/s41586-024-07395-z

    2024 doi

  48. [56]

    E.\ 1939, , 99, 451

    Sterne, T. E.\ 1939, , 99, 451. doi:10.1093/mnras/99.5.451

    1939 doi

  49. [57]

    Thorngren, D. P. & Fortney, J. J.\ 2018, , 155, 214. doi:10.3847/1538-3881/aaba13

    2018 doi

  50. [58]

    Tittemore, W. C. & Wisdom, J.\ 1988, , 74, 172. doi:10.1016/0019-1035(88)90038-3

    1988 doi

  51. [59]

    J., et al.\ 2017, , 841, 30

    Tremblin, P., Chabrier, G., Mayne, N. J., et al.\ 2017, , 841, 30. doi:10.3847/1538-4357/aa6e57

    2017 doi

  52. [60]

    & Wordsworth, R.\ 2020, , 891, 7

    Wang, H. & Wordsworth, R.\ 2020, , 891, 7. doi:10.3847/1538-4357/ab6dcc

    2020 doi

  53. [61]

    & Menou, K.\ 2024, arXiv:2409.07651

    Wazny, M. & Menou, K.\ 2024, arXiv:2409.07651. doi:10.48550/arXiv.2409.07651

    2024 doi arXiv

  54. [62]

    J., Beatty, T

    Welbanks, L., Bell, T. J., Beatty, T. G., et al.\ 2024, , 630, 836. doi:10.1038/s41586-024-07514-w

    2024 doi

  55. [63]

    & Frail, D

    Wolszczan, A. & Frail, D. A.\ 1992, , 355, 145. doi:10.1038/355145a0

    1992 doi

  56. [64]

    Youdin, A. N. & Mitchell, J. L.\ 2010, , 721, 1113. doi:10.1088/0004-637X/721/2/1113

    2010 doi

  57. [65]

    & Dai, F.\ 2024, , 972, 159

    Yu, H. & Dai, F.\ 2024, , 972, 159. doi:10.3847/1538-4357/ad5ffb

    2024 doi

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.