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REVIEW 3 major objections 5 minor 1 cited by

Rossby number regime, convection suppression, and dynamo-generated magnetism in inflated hot Jupiters

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper argues that when the extra heat that inflates hot Jupiters is deposited in the outer envelope rather than in the deep dynamo region, convection in the dynamo region is suppressed and the resulting surface magnetic fields drop to…

desk verdict A clean MESA demonstration that where inflation heat is deposited controls whether hot Jupiter dynamos stay strong or collapse; the missing piece is a self-consistent Ohmic heating profile. read the letter →

arxiv 2507.05202 v1 pith:B7POIEGP submitted 2025-07-07 astro-ph.EP

Albert Elias-López , Matteo Cantiello , Daniele Viganò , Fabio Del Sordo , Simranpreet Kaur , Clàudia Soriano-Guerrero This is my paper
classification astro-ph.EP
keywords exoplanetmagneticfieldshotJupitersdynamoscalinglawsRossbynumberconvectionsuppressionOhmicheatingcoherentradioemissionradiusinflation
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

Hot Jupiters are usually assumed to be the most magnetic exoplanets, with dynamo fields up to an order of magnitude stronger than Jupiter's, which is why they have been the main targets in searches for coherent radio emission. This paper uses one-dimensional evolutionary models to ask where the extra heat that inflates these planets is deposited, and what that does to their internal convection. The central result is conditional: if the heat is spread through the deep dynamo region, the models reproduce the familiar strong fields; but if the heat is deposited in the outer envelope, as electrical-resistance (Ohmic) heating models predict, convection in the dynamo region shuts off and the predicted surface dipole fields drop to Jovian values or below, mostly below the $\sim$3.5 G threshold for ground-based radio detection. That would explain why decades of radio searches have found nothing.

What carries the argument

The operative machinery is a one-dimensional evolutionary model of an irradiated giant planet in which the heating geometry is chosen by hand. The code computes convective velocities and fluxes; the Rossby number $\mathrm{Ro}=P_{\mathrm{orb}}v_{\mathrm{conv}}/H_\rho$ fixes which dynamo regime applies, and the Christensen scaling law $B^2/2\mu_0 = c f_{\mathrm{ohm}}\langle\rho\rangle^{1/3}(Fq_o)^{2/3}$ converts the volume-averaged convective heat flux of the metallic-hydrogen shell into a field strength. The decisive input is deposition geometry: heat deposited outside the dynamo shell inverts the radiative gradient and creates a positive entropy gradient, stalling convection and driving the convective flux $q_c$ toward zero.

What would settle it

A confirmed detection of coherent cyclotron radio emission above 10 MHz from an inflated hot Jupiter would directly contradict the prediction that most such planets have surface dipole fields below the 3.5 G cutoff; so would an updated electrical-resistance heating model whose peak deposition lies below the 1-Mbar metallic-hydrogen boundary while still inflating the radius.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that magnetic-field estimates for inflated hot Jupiters are controlled less by how much heat is added than by where it is added. Extended heat deposition through the dynamo shell leaves almost all hot Jupiters in the fast-rotator regime, with Rossby numbers $\mathrm{Ro}\lesssim0.1$, and recovers the canonical picture: dynamo-region fields of order 900 G and equatorial surface dipole fields near 100 G for the most inflated planets. Outer deposition, the geometry expected of Ohmic heating, stabilizes the deep layers, suppresses convection, and cuts the convective heat flux that feeds the dynamo; the derived surface dipolar fields fall to Jovian values or below, and the corresponding coherent radio fluxes fall below the ionospheric cutoff. The authors present this as a possible resolution of the long-standing failure to detect radio emission from hot Jupiters.

Load-bearing premise

The entire suppression argument rests on the assumption that the extra heat responsible for inflation is deposited mostly in the outer envelope, above the deep metallic-hydrogen layer where a dynamo can operate, rather than deeper; if realistic heating models ever move that heat downward, the predicted strong fields return.

Editorial extensions

If this is right

  • If the outer-heating scenario is right, inflated hot Jupiters are generically weak radio emitters, so the null results of radio surveys are expected rather than puzzling.
  • The best remaining radio and star-planet interaction targets shift to massive, long-period, tidally locked planets whose interiors resist inflation and whose Rossby numbers can exceed 0.1.
  • Even in the optimistic extended-heating case, surface dipole fields are far below dynamo-region fields because inflation swells the outer layers and the dipole decays as the cube of radius.
  • The mechanism can feed back on itself: a strong dynamo field drives more Ohmic heating, which suppresses convection, weakens the field, and reduces the heating, possibly producing oscillatory behaviour.
  • The suppression mechanism parallels the accepted explanation for Venus lacking an active dynamo: a blanketing layer that stabilizes the interior and stalls convective cooling.

Reading between the lines

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

  • The authors do not state it this way, but their two scenarios imply an observable anti-correlation: at fixed equilibrium temperature, the most inflated planets should show the weakest magnetic indicators.
  • Their logic generalizes to non-Ohmic inflation mechanisms: any heat source that peaks above the dynamo shell should suppress the deep dynamo by the same gradient-inversion mechanism.
  • A three-dimensional test is the natural next step: day-night asymmetric deposition might keep localized convection alive in some sectors even when the spherical average is stably stratified.
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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 / 5 minor

Summary. The paper uses the MESA stellar-evolution code (version 24.08.1) to compute one-dimensional evolutionary models of irradiated, inflated hot Jupiters, with the extra heating rate set by the Thorngren & Fortney (2018) efficiency law. After arguing that hot Jupiters are tidally synchronized, the authors compute internal Rossby number profiles Ro(r) for a grid of orbital periods, planetary masses, and host-star types. With heat deposited throughout the envelope down to the dynamo region, the dynamo region stays in the fast-rotator regime (Ro below about 0.1) for almost all models, and the Christensen et al. (2009) scaling yields dynamo-region fields of order 900 G and surface dipole fields of order 100 G, consistent with Yadav & Thorngren (2017). With heat deposited only between the dynamo boundary Rdyn (defined by P_dyn = 1 Mbar) and the irradiation depth, the MESA models develop a subadiabatic, radiative zone that suppresses convection in the metallic-hydrogen region; the predicted surface dipole fields then fall to or below Jovian values, which the paper offers as an explanation for the absence of confirmed coherent radio emission from hot Jupiters.

Significance. The paper's conditional claim is physically clear and of substantial interest: if the heating responsible for inflation is deposited outside the dynamo region, deep convection and dynamo-generated fields are strongly suppressed, which would resolve the long-standing tension between optimistic radio flux predictions and the null results of observing campaigns. The calculation is transparent and largely reproducible: the code version, structure equations, irradiation implementation, and the two heating geometries are all specified, and the field estimates are genuine predictions rather than fits to the nondetections. The paper also makes specific, falsifiable target predictions for massive, long-period planets (GJ 86 b, HD 72892 b, TIC 393818343 b), and it honestly flags the sensitivity of its magnetic-field integral to Rdyn. The main weakness is that the physically decisive choice between the two heating scenarios depends on an imported Ohmic deposition profile that is never computed, quantified, or varied in this work, and the quantitative field values in the suppressed regime employ a scaling law in a regime whose validity the authors themselves question.

major comments (3)
  1. [Section 3.2 and Section 6] The bridge between the two idealized heating scenarios and real Ohmic dissipation is the load-bearing input of the paper, and it is never quantified. In the 'outer' scenario, heat is deposited as a step function between Rdyn and Rirr with exactly zero heating below Rdyn, and no run in the paper varies the fraction of the deposited power that lies below Rdyn, even though every physical heating profile (Ohmic, tidal, or turbulent) has some finite tail at depth. Because the deep convective luminosity carries the interior cooling flux, which is small compared with the deposited heating, a deep fraction of even a few percent of the dissipated power could restore a convective flux comparable to the unheated value, moving the predicted surface fields from sub-Jovian back toward the Jovian range and potentially crossing the ~3.5 G radio cutoff. The authors should either implement published Ohmic dissipation profiles directly in their models, or add a scenario that deposits a fraction f of the heat below Rdyn and present Bdyn and Bdip,surf as functions of f. Without this, the headline conclusion rests on an untested edge of the parameter space.
  2. [Section 5.1, Eqs. (14)-(16)] The quantitative prediction that the suppressed models fall below the coherent-radio cutoff is less secure than the qualitative suppression result. The Christensen et al. (2009) scaling is applied in a regime where the convective flux in the integration shell is vanishing; the manuscript itself concedes that 'it might not be accurate to estimate the magnetic field strength created in these shallower convective layers with the same scaling laws,' and that Eq. (15) is 'very sensitive to both the assumed definition of Rdyn, and the radial interval used in the outer heating.' No sensitivity test to the metallization pressure is provided, even though Section 3.1 notes that the 1 Mbar value is an approximation with temperature dependence. Varying Pdyn over the plausible range given by French et al. (2012) and Bonitz et al. (2024) would change both the integration limits of Eq. (15) and the location of the heating cutoff, thereby changing the surviving deep convective flux. The authors should quantify these two sensitivities; until then, the sub-Jovian field values should be presented as a scenario-dependent estimate rather than a robust prediction.
  3. [Sections 3.2 and 6 (cited Ohmic profiles)] The assertion that realistic Ohmic models predict essentially all dissipation above the dynamo region is supported by citations rather than by any quantity shown in this paper. A normalized dissipation profile from at least one published Ohmic model, plotted against pressure with Rdyn marked, is needed to verify that the step function between Rdyn and Rirr is a faithful approximation in the region that matters. One of the four cited pillars, Viganò et al. (2025), is a submitted manuscript that shares co-authors with this paper, so it does not provide an independent check. This is a case of missing support for a load-bearing input; the gap is fixable within the scope of the manuscript if the authors extract and display the relevant profiles.
minor comments (5)
  1. [Section 1 and Section 4] The dynamo-regime transition is quoted as Ro ~ 0.12 in the introduction, while the abstract, figures, and summary statements use the threshold Ro <= 0.1; the adopted value should be stated consistently.
  2. [Section 5.2, Eq. (17)] In the sentence 'we simply assume a representative solar value, Mdot_star = Mdot_sun ~ 400 km s^-1', the quantity 400 km s^-1 is the wind speed V_W, not a mass-loss rate; this typo should be corrected.
  3. [Section 3.2] The sentence 'the results are almost indistinguishable results from the first one' contains a duplicated word, and the parenthetical list of radii and scenarios would be easier to follow if split into separate sentences.
  4. [Section 5.1] The agreement with Yadav & Thorngren (2017) for the extended-heating branch should be framed as a consistency check rather than an independent confirmation, since both calculations assume that the inflation heat is carried by the convective flux that powers the dynamo.
  5. [Section 2] Given the recent magnetic-torque asynchronization mechanism proposed by Wazny & Menou (2025), a sentence explaining why this effect does not change the Ro conclusions beyond the scope statement would strengthen the tidal-locking argument.

Circularity Check

0 steps flagged · score 2.0 of 10

No material circularity: the low-field suppression branch is an emergent MESA result given an imported (not fitted) heat-deposition profile; self-citations are present but non-load-bearing.

full rationale

The paper's derivation chain is: adopted heat-deposition profile (scenario 1: extended below Rdyn; scenario 2: outer, above Rdyn) yields MESA 1D structure via the energy equation and MLT, which yields qc, which feeds the externally calibrated Christensen et al. (2009) scaling to produce Bdyn and Bdip,surf. No link equates an output to an input by construction: the convection suppression below Rdyn in scenario 2 is computed from the radiative-versus-adiabatic gradient comparison and the resulting sub-dynamo luminosity, not assumed; the field values are post-processed, and no magnetic or radio observable is fitted anywhere. The extended-heating branch 'recovers' the Yadav & Thorngren (2017) values, but the paper states this explicitly ('we recover ... compatible with the work of Yadav & Thorngren (2017) ... conceptually similar to our extended heat case'), so it is a disclosed consistency check rather than a renamed prediction. The genuinely load-bearing premise is that Ohmic heating deposits most of its power above Rdyn; that premise is imported from published external models (Batygin et al. 2011; Ginzburg & Sari 2016; Knierim et al. 2022), with the submitted co-authored Viganò et al. (2025) appearing alongside them in the citation chain. Because the claim survives without the self-citation, the self-citation is not load-bearing, and the 'as realistic Ohmic models predict' bridge is an external physical input, not a circular reduction. The manuscript itself flags the sensitivity of the field integral (Eq. 15) to the assumed Rdyn and the outer-heating radial interval (Sec. 5.1), the purely phenomenological character of the Thorngren & Fortney (2018) efficiency fit (Sec. 3.2), and the possible dynamo-Ohmic feedback loop (Sec. 6); these are honestly disclosed correctness risks and model-dependence concerns, not circular steps. Overall, the central derivation is self-contained given its inputs, and the self-citations are minor, so the circularity score is 2 rather than 0.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

All quantitative outputs depend on externally fitted or assumed inputs: the empirical heating efficiency, the fixed dynamo boundary, the scaling-law normalization, and the outer-heating profile. The paper contributes the MESA evolution runs and the two-scenario comparison, not new physical constants or entities.

free parameters (7)
  • Heating efficiency Gaussian (epsilon_max, peak, width) = 2.37%, log10(Firr/F0)=0.14, sigma=0.37
    Fitted by Thorngren & Fortney (2018) to the observed radius-inflation trend; sets the total heat input in every model.
  • Planetary albedo A_B = 0
    Chosen for simplicity in Eq. (2); affects equilibrium temperature and irradiation.
  • Irradiation absorption column Sigma_star = 200 g/cm^2
    Chosen to correspond to grey opacity 5e-3 cm^2/g; sets the depth of atmospheric heating.
  • Dynamo boundary pressure P_dyn = 1 Mbar
    Fixed metallization pressure; the real transition is temperature dependent.
  • Core mass and density = 10 Earth masses, 10 g/cm^3
    Assumed rocky core; sets R_core.
  • Christensen scaling-law normalization c and f_ohm = c=0.63, f_ohm=1
    Calibrated externally to Earth, Jupiter, and low-mass stars; used in Eqs. (14)-(15).
  • Radio flux stellar wind parameters = Solar mass-loss rate and 400 km/s wind
    Representative solar values assumed in Eq. (17); set the absolute radio flux scale.
assumptions (7)
  • domain assumption All hot Jupiters in the sample are tidally locked, so rotation period equals orbital period
    Section 2 uses Eq. (4) with conservative parameters but sets aside Wazny & Menou (2025) magnetic-torque asynchronization.
  • domain assumption Realistic Ohmic (and other) heat deposition is concentrated in the outer envelope, above the dynamo region
    Section 3.2 defines the 'outer' scenario and Section 6 states it as the realistic case, citing Batygin et al. (2011), Ginzburg & Sari (2016), Knierim et al. (2022), and submitted Viganò et al. (2025).
  • domain assumption MESA one-dimensional mixing-length theory describes convection and convective heat flux adequately
    Section 3.1 and 3.4; no 3D effects, day/night asymmetries, or magnetic feedback on convection are modeled.
  • domain assumption Christensen et al. (2009) heat-flux scaling law applies to hot Jupiter dynamo regions
    Section 5.1; calibrated on Earth, Jupiter, and low-mass stars, with authors noting brown dwarfs are outliers and suppressed-convection cases may violate assumptions.
  • domain assumption Thorngren & Fortney (2018) heating efficiency from Eq. (10) is representative of the population
    Section 3.2; the fit has large scatter and degeneracy with heavy-element mass fraction.
  • domain assumption The hydrogen metallization boundary is at a fixed pressure of 1 Mbar
    Section 3.1; the transition is actually temperature dependent, which affects Rdyn and the dynamo volume.
  • domain assumption Stellar irradiation is constant in time and deposited uniformly through the outermost 200 g/cm^2 column
    Section 3.1; neglects stellar luminosity evolution and non-uniform day/night heating.

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Cite this review

Pith. "Pith review of Rossby number regime, convection suppression, and dynamo-generated magnetism in inflated hot Jupiters." pith.science (2026). https://pith.science/paper/B7POIEGP

@misc{pith2026250705202,
  author       = {Pith},
  title        = {Pith review of: Rossby number regime, convection suppression, and dynamo-generated magnetism in inflated hot Jupiters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B7POIEGP}},
  note         = {Machine review of arXiv:2507.05202}
}
abstract

Hot Jupiters (HJs) are commonly thought to host the strongest dynamo-generated magnetic fields among exoplanets, up to one order of magnitude larger than Jupiter. Thus, they have often been regarded as the most promising exoplanets to display magnetic star-planet interaction signals and magnetically-driven coherent radio emission, which unfortunately remains elusive, despite many diversified observational campaigns. In this work, we investigate the evolution of the internal convection and dynamo properties of HJs via one-dimensional models. We explore the dependency on orbital distance, planetary and stellar masses, and types of heat injection. We employ one-dimensional evolutionary models to obtain internal convective structures. Specifically, we obtain the Rossby number $\mathrm{Ro}$ as a function of planetary depth and orbital period, after showing that tidal synchronization is likely valid for all HJs. When the heat is applied uniformly, the convective layers of almost all HJs remain in the fast rotator regime, $\mathrm{Ro} \lesssim 0.1$, except possibly the most massive planets with large orbital distances (but still tidally locked). We recover magnetic field strengths for inflated HJs by applying well-known scaling laws for fast rotators. When strong heat sources are applied mostly in the outer envelope and outside the dynamo region, as realistic Ohmic models predict, convection in the dynamo region often breaks down. Consequently, the heat flux and the derived surface magnetic fields can be greatly reduced to or below Jovian values, contrary to what is commonly assumed, thus negatively affecting estimates for coherent radio emission, and possibly explaining the failure in detecting it so far.

Figures

Figures reproduced from arXiv: 2507.05202 by the authors.

Figure 1
Figure 1. Population properties for the confirmed gas giant exoplanet population with mass MP > 0.2 MJ, considering the host star effective temperature and radius to obtain the irradiation flux Firr, and the corresponding equilibrium temperature Teq. Data is extracted from the NASA exoplanet archivea (Christiansen et al. 2025). Colors indicate the main-sequence stellar type of the host star. Errors are not shown, for the sake… view at source ↗
Figure 2
Figure 2. Dynamo outer surface radius Rdyn (green), RCB radius Rrcb (gray), bottom of the irradiated region Rirr (dashed), and planetary radius RP (solid black), for a 1 MJ planet orbiting a 1 M⊙ star, at 5 Gyr, as a function of or￾bital period, for both heated (upper lines) and non-heated models (lower lines). The gray area shows the outer radius uncertainty for the heated models, accounting for the range of parameters quote… view at source ↗
Figure 3
Figure 3. Radial profiles of temperature, density, convective velocity, heat convective flux, and density scale height, for 1 MJ planets orbiting a 1 M⊙ star at 5 Gyr with different Porb. Models without and with extra heating (below Rdyn) are shown by solid and dashed lines, respectively. Rirr is marked with a cross, RRCB is the transition from thick to thin lines, and Rdyn is marked with a dot [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Radial profiles of extended and outer heating models for a 1 MJ planet orbiting a 1 M⊙ star at 5 Gyr, with Porb= 1.47 d. Top panels: Total logarithmic tempera￾ture gradient ∇ (black solid line), with the adiabatic (green dashed line) and radiative (red dashed line) tem…
Figure 5
Figure 5. Figure 5: Rossby number as a function of radius or pressure for 1 MJ planets orbiting a solar-like G2 star, comparing heated (left panels) and non-heated (right panels) models. The different radii introduced in [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: Similar to [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Rossby number as a function of pressure for dif￾ferent mass planets orbiting a G2 star with two different pe￾riods, comparing models with the extended heating (dashed) with only irradiated models (solid). Earth, Jupiter, and fully-convective fast-rotating main￾sequence…
Figure 8
Figure 8. Figure 8: Magnetic field estimates for 1 MJ planets orbiting a 1 M⊙ main-sequence star (same models as [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Estimates for Jovian-like coherent radio flux (top, for a 10 pc away HJ) and SPI available power (bottom), as a function of age and Porb, for the same models shown in [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Similar to [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]

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Cited by 1 Pith paper

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

  1. Inflated hot Jupiters: Inferring average atmospheric velocity via Ohmic models coupled with internal dynamo evolution

    astro-ph.EP 2025-07 conditional novelty 6.0 of 10

    Ohmic heating models with an evolving dynamo field reproduce observed hot Jupiter radii only for sub-10-bar winds of 0.01 to 1 km/s that decline steeply with temperature and roughly linearly with mass.

Reference graph

Works this paper leans on

98 extracted references · 8 canonical work pages · cited by 1 Pith paper

  1. [1]

    2006, ApJ, 650, 394, doi: 10.1086/506011

    Arras, P., & Bildsten, L. 2006, ApJ, 650, 394, doi: 10.1086/506011

    doi:10.1086/506011 2006

  2. [2]

    S., Dulk, G

    Bastian, T. S., Dulk, G. A., & Leblanc, Y. 2000, ApJ, 545, 1058, doi: 10.1086/317864

    doi:10.1086/317864 2000

  3. [3]

    2018, AJ, 155, 178, doi: 10.3847/1538-3881/aab54e

    Batygin, K. 2018, AJ, 155, 178, doi: 10.3847/1538-3881/aab54e

    doi:10.3847/1538-3881/aab54e 2018

  4. [4]

    Batygin, K., & Stevenson, D. J. 2010, The Astrophysical Journal Letters, 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, ApJ, 738, 1, doi: 10.1088/0004-637X/738/1/1

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

  6. [6]

    2024, Physics of Plasmas, 31, 110501, doi: 10.1063/5.0219405

    Bonitz, M., Vorberger, J., Bethkenhagen, M., et al. 2024, Physics of Plasmas, 31, 110501, doi: 10.1063/5.0219405

    doi:10.1063/5.0219405 2024

  7. [7]

    Burrows, A., Hubeny, I., Budaj, J., & Hubbard, W. B. 2007, ApJ, 661, 502, doi: 10.1086/514326

    doi:10.1086/514326 2007

  8. [8]

    R., Shimwell, T

    Callingham, J. R., Shimwell, T. W., Vedantham, H. K., et al. 2023, A&A, 670, A124, doi: 10.1051/0004-6361/202245567

    doi:10.1051/0004-6361/202245567 2023

Show all 98 references
  1. [9]

    W., & Ostlie, D

    Carroll, B. W., & Ostlie, D. A. 2017, An introduction to modern astrophysics, Second Edition

    2017

  2. [10]

    W., Shkolnik, E

    Cauley, P. W., Shkolnik, E. L., Llama, J., & Lanza, A. F. 2019, Nature Astronomy, 3, 1128, doi: 10.1038/s41550-019-0840-x

    2019 doi

  3. [11]

    2007, ApJL, 661, L81, doi: 10.1086/518473

    Chabrier, G., & Baraffe, I. 2007, ApJL, 661, L81, doi: 10.1086/518473

    2007 doi

  4. [12]

    R., & Aubert, J

    Christensen, U. R., & Aubert, J. 2006, Geophysical Journal International, 166, 97, doi: 10.1111/j.1365-246X.2006.03009.x

    2006 arXiv

  5. [13]

    R., Holzwarth, V., & Reiners, A

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

    2009 doi

  6. [14]

    L., McElroy, D

    Christiansen, J. L., McElroy, D. L., Harbut, M., et al. 2025, arXiv e-prints, arXiv:2506.03299, doi: 10.48550/arXiv.2506.03299

    2025 doi arXiv

  7. [15]

    P., & Giuli, R

    Cox, J. P., & Giuli, R. T. 1968, Principles of stellar structure

    1968

  8. [16]

    H., & Musielak, Z

    Cuntz, M., Saar, S. H., & Musielak, Z. E. 2000, ApJL, 533, L151, doi: 10.1086/312609

    2000 doi

  9. [17]

    B., Schwartz, J

    Dang, L., Cowan, N. B., Schwartz, J. C., et al. 2018, Nature Astronomy, 2, 220, doi: 10.1038/s41550-017-0351-6

    2018 doi

  10. [18]

    Davidson, P. A. 2013, Geophysical Journal International, 195, 67, doi: 10.1093/gji/ggt167 de Gasperin, F., Brunetti, G., Bruggen, M., et al. 2020, doi: 10.26093/cds/vizier.36420085

    2013 doi

  11. [19]

    J., et al

    Dietrich, W., Kumar, S., Poser, A. J., et al. 2022, MNRAS, 517, 3113, doi: 10.1093/mnras/stac2849

    2022 doi

  12. [20]

    Dulk, G. A. 1985, ARA&A, 23, 169, doi: 10.1146/annurev.aa.23.090185.001125 Elias-L´ opez, A., Del Sordo, F., Vigan` o, D., et al. 2025, A&A, 696, A161, doi: 10.1051/0004-6361/202453372

    1985

  13. [21]

    P., Vogt, S

    Feng, F., Butler, R. P., Vogt, S. S., et al. 2022, ApJS, 262, 21, doi: 10.3847/1538-4365/ac7e57

    2022 doi

  14. [22]

    J., Dawson, R

    Fortney, J. J., Dawson, R. I., & Komacek, T. D. 2021, Journal of Geophysical Research (Planets), 126, e06629, doi: 10.1029/2020JE006629

    2021 doi

  15. [23]

    J., Marley, M

    Fortney, J. J., Marley, M. S., & Barnes, J. W. 2007, ApJ, 659, 1661, doi: 10.1086/512120

    2007 doi

  16. [24]

    2012, The Astrophysical Journal Supplement Series, 202, 5, doi: 10.1088/0067-0049/202/1/5

    French, M., Becker, A., Lorenzen, W., et al. 2012, The Astrophysical Journal Supplement Series, 202, 5, doi: 10.1088/0067-0049/202/1/5

    2012 doi

  17. [25]

    2023, in AAS/Division for Planetary Sciences Meeting

    Fuentes, R., Cumming, A., Anders, E., & Hindman, B. 2023, in AAS/Division for Planetary Sciences Meeting

    2023

  18. [26]

    X., Wang, S., et al

    Gan, T., Wang, S. X., Wang, S., et al. 2023, AJ, 165, 17, doi: 10.3847/1538-3881/ac9b12

    2023 doi

  19. [27]

    2015, ApJ, 803, 111, doi: 10.1088/0004-637X/803/2/111 18 —

    Ginzburg, S., & Sari, R. 2015, ApJ, 803, 111, doi: 10.1088/0004-637X/803/2/111 18 —. 2016, ApJ, 819, 116, doi: 10.3847/0004-637X/819/2/116

    2015 doi

  20. [28]

    1966, Icarus, 5, 375, doi: 10.1016/0019-1035(66)90051-0 Grießmeier, J

    Goldreich, P., & Soter, S. 1966, Icarus, 5, 375, doi: 10.1016/0019-1035(66)90051-0 Grießmeier, J. M., Zarka, P., & Spreeuw, H. 2007, A&A, 475, 359, doi: 10.1051/0004-6361:20077397

    1966 doi

  21. [29]

    1996, ApJL, 459, L35, doi: 10.1086/309935

    Saumon, D. 1996, ApJL, 459, L35, doi: 10.1086/309935

    1996 doi

  22. [30]

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

    2002 doi

  23. [31]

    Heng, K., & Showman, A. P. 2015, Annual Review of Earth and Planetary Sciences, 43, 509, doi: 10.1146/annurev-earth-060614-105146

    2015 doi

  24. [32]

    2021, ApJ, 908, 77, doi: 10.3847/1538-4357/abd8d1

    Hori, Y. 2021, ApJ, 908, 77, doi: 10.3847/1538-4357/abd8d1

    2021 doi

  25. [33]

    A., Rubie, D

    Jacobson, S. A., Rubie, D. C., Hernlund, J., Morbidelli, A., & Nakajima, M. 2017, Earth and Planetary Science Letters, 474, 375, doi: 10.1016/j.epsl.2017.06.023

    2017 doi

  26. [34]

    S., & Cantiello, M

    Jermyn, A. S., & Cantiello, M. 2020, ApJ, 900, 113, doi: 10.3847/1538-4357/ab9e70

    2020 doi

  27. [35]

    S., Bauer, E

    Jermyn, A. S., Bauer, E. B., Schwab, J., et al. 2023, ApJS, 265, 15, doi: 10.3847/1538-4365/acae8d

    2023 doi

  28. [36]

    2015, A&A, 577, A27, doi: 10.1051/0004-6361/201425300

    Brott, I. 2015, A&A, 577, A27, doi: 10.1051/0004-6361/201425300

    2015 doi

  29. [37]

    Jones, C. A. 2011, Annual Review of Fluid Mechanics, 43, 583, doi: 10.1146/annurev-fluid-122109-160727

    2011 doi

  30. [38]

    M., Hallinan, G., Pineda, J

    Kao, M. M., Hallinan, G., Pineda, J. S., et al. 2016, ApJ, 818, 24, doi: 10.3847/0004-637X/818/1/24

    2016 doi

  31. [39]

    2018, ApJS, 237, 25, doi: 10.3847/1538-4365/aac2d5

    Burgasser, A. 2018, ApJS, 237, 25, doi: 10.3847/1538-4365/aac2d5

    2018 doi

  32. [40]

    A., Allan, A., & Kubyshkina, D

    Kilmetis, K., Vidotto, A. A., Allan, A., & Kubyshkina, D. 2024, MNRAS, 535, 3646, doi: 10.1093/mnras/stae2505

    2024 doi

  33. [41]

    2022, A&A, 658, L7, doi: 10.1051/0004-6361/202142588

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

    2022 doi

  34. [42]

    A., Charbonneau, D., Allen, L

    Knutson, H. A., Charbonneau, D., Allen, L. E., et al. 2007, Nature, 447, 183, doi: 10.1038/nature05782

    2007 doi

  35. [43]

    2020, ApJ, 893, 36, doi: 10.3847/1538-4357/ab7eb4

    Ginzburg, S. 2020, ApJ, 893, 36, doi: 10.3847/1538-4357/ab7eb4

    2020 doi

  36. [44]

    D., & Youdin, A

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

    2017 doi

  37. [45]

    1986, A&A, 160, 116

    Kuhfuss, R. 1986, A&A, 160, 116

    1986

  38. [46]

    J., Sch¨ ottler, M., et al

    Kumar, S., Poser, A. J., Sch¨ ottler, M., et al. 2021, PhRvE, 103, 063203, doi: 10.1103/PhysRevE.103.063203

    2021 doi

  39. [47]

    Lanza, A. F. 2013, A&A, 557, A31, doi: 10.1051/0004-6361/201321790

    2013 doi

  40. [48]

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

    2011 doi

  41. [49]

    Lazovik, Y. A. 2023, MNRAS, 520, 3749, doi: 10.1093/mnras/stad394

    2023 doi

  42. [50]

    2010, ApJ, 725, 1146, doi: 10.1088/0004-637X/725/1/1146

    Li, J., & Goodman, J. 2010, ApJ, 725, 1146, doi: 10.1088/0004-637X/725/1/1146

    2010 doi

  43. [51]

    D., & Fortney, J

    Lopez, E. D., & Fortney, J. J. 2016, ApJ, 818, 4, doi: 10.3847/0004-637X/818/1/4

    2016 doi

  44. [52]

    2012, ApJ, 745, 138, doi: 10.1088/0004-637X/745/2/138

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

    2012 doi

  45. [53]

    D., & Dermott, S

    Murray, C. D., & Dermott, S. F. 1999, doi: 10.1017/CBO9781139174817

    1999 doi

  46. [54]

    H., et al

    Narang, M., Puravankara, M., Ishwara Chandra, C. H., et al. 2024, MNRAS, 529, 1161, doi: 10.1093/mnras/stae536

    2024 doi

  47. [55]

    2002, Geology, 30, 987, doi: 10.1130/0091- 7613(2002)030⟨0987:WDVLAM⟩2.0.CO;2

    Nimmo, F. 2002, Geology, 30, 987, doi: 10.1130/0091- 7613(2002)030⟨0987:WDVLAM⟩2.0.CO;2

    2002 doi

  48. [56]

    Parker, E. N. 1965, SSRv, 4, 666, doi: 10.1007/BF00216273

    1965 doi

  49. [57]

    2011, ApJS, 192, 3, doi: 10.1088/0067-0049/192/1/3

    Paxton, B., Bildsten, L., Dotter, A., et al. 2011, ApJS, 192, 3, doi: 10.1088/0067-0049/192/1/3

    2011 doi

  50. [58]

    2013, ApJS, 208, 4, doi: 10.1088/0067-0049/208/1/4

    Paxton, B., Cantiello, M., Arras, P., et al. 2013, ApJS, 208, 4, doi: 10.1088/0067-0049/208/1/4

    2013 doi

  51. [59]

    2015, ApJS, 220, 15, doi: 10.1088/0067-0049/220/1/15

    Paxton, B., Marchant, P., Schwab, J., et al. 2015, ApJS, 220, 15, doi: 10.1088/0067-0049/220/1/15

    2015 doi

  52. [60]

    B., et al

    Paxton, B., Schwab, J., Bauer, E. B., et al. 2018, ApJS, 234, 34, doi: 10.3847/1538-4365/aaa5a8

    2018 doi

  53. [61]

    2019, ApJS, 243, 10, doi: 10.3847/1538-4365/ab2241 P´ erez-Torres, M., G´ omez, J

    Paxton, B., Smolec, R., Schwab, J., et al. 2019, ApJS, 243, 10, doi: 10.3847/1538-4365/ab2241 P´ erez-Torres, M., G´ omez, J. F., Ortiz, J. L., et al. 2021, A&A, 645, A77, doi: 10.1051/0004-6361/202039052

    2019 doi

  54. [62]

    2010a, ApJ, 724, 313, doi: 10.1088/0004-637X/724/1/313 —

    Perna, R., Menou, K., & Rauscher, E. 2010a, ApJ, 724, 313, doi: 10.1088/0004-637X/724/1/313 —. 2010b, ApJ, 719, 1421, doi: 10.1088/0004-637X/719/2/1421

    doi

  55. [63]

    Reiners, A., Basri, G., & Christensen, U. R. 2009, ApJ, 697, 373, doi: 10.1088/0004-637X/697/1/373

    2009 doi

  56. [64]

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

    2010 doi

  57. [65]

    Reiners, A., Sch¨ ussler, M., & Passegger, V. M. 2014, ApJ, 794, 144, doi: 10.1088/0004-637X/794/2/144

    2014 doi

  58. [66]

    J., et al

    Reiners, A., Shulyak, D., K¨ apyl¨ a, P. J., et al. 2022, A&A, 662, A41, doi: 10.1051/0004-6361/202243251 S´ anchez-Lavega, A. 2004, ApJL, 609, L87, doi: 10.1086/422840

    2022 doi

  59. [67]

    D., & Molli` ere, P

    Sarkis, P., Mordasini, C., Henning, T., Marleau, G. D., & Molli` ere, P. 2021, A&A, 645, A79, doi: 10.1051/0004-6361/202038361

    2021 doi

  60. [68]

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

    1995 doi

  61. [69]

    2013, A&A, 552, A119, doi: 10.1051/0004-6361/201118179

    Simon, S. 2013, A&A, 552, A119, doi: 10.1051/0004-6361/201118179

    2013 doi

  62. [70]

    Scharf, C. A. 2010, ApJ, 722, 1547, doi: 10.1088/0004-637X/722/2/1547 19

    2010 doi

  63. [71]

    M., Marsden, S

    Seach, J. M., Marsden, S. C., Carter, B. D., et al. 2020, MNRAS, 494, 5682, doi: 10.1093/mnras/staa1107

    2020 doi

  64. [72]

    2018, A&A, 616, A76, doi: 10.1051/0004-6361/201731454

    Sestovic, M., Demory, B.-O., & Queloz, D. 2018, A&A, 616, A76, doi: 10.1051/0004-6361/201731454

    2018 doi

  65. [73]

    A., Dalba, P

    Sgro, L. A., Dalba, P. A., Esposito, T. M., et al. 2024, AJ, 168, 26, doi: 10.3847/1538-3881/ad5096

    2024 doi

  66. [74]

    P., Fortney, J

    Showman, A. P., Fortney, J. J., Lian, Y., et al. 2009, ApJ, 699, 564, doi: 10.1088/0004-637X/699/1/564

    2009 doi

  67. [75]

    P., & Guillot, T

    Showman, A. P., & Guillot, T. 2002, A&A, 385, 166, doi: 10.1051/0004-6361:20020101

    2002 doi

  68. [76]

    2023, MNRAS, 525, 626, doi: 10.1093/mnras/stad2311

    Palenzuela, C. 2023, MNRAS, 525, 626, doi: 10.1093/mnras/stad2311

    2023 doi

  69. [77]

    2025, arXiv e-prints, arXiv:2505.14342, doi: 10.48550/arXiv.2505.14342

    Soriano-Guerrero, C., Vigan` o, D., Perna, R., Elias-L´ opez, A., & Beltz, H. 2025, arXiv e-prints, arXiv:2505.14342, doi: 10.48550/arXiv.2505.14342

    2025 doi arXiv

  70. [78]

    S., & Burrows, A

    Spiegel, D. S., & Burrows, A. 2013, ApJ, 772, 76, doi: 10.1088/0004-637X/772/1/76

    2013 doi

  71. [79]

    G., Collins, K

    Stassun, K. G., Collins, K. A., & Gaudi, B. S. 2017, AJ, 153, 136, doi: 10.3847/1538-3881/aa5df3

    2017 doi

  72. [80]

    Stevens, I. R. 2005, MNRAS, 356, 1053, doi: 10.1111/j.1365-2966.2004.08528.x

    2005

  73. [81]

    2016, ApJ, 833, 140, doi: 10.3847/1538-4357/833/2/140

    Strugarek, A. 2016, ApJ, 833, 140, doi: 10.3847/1538-4357/833/2/140

    2016 doi

  74. [82]

    Thorngren, D. P. 2024, arXiv e-prints, arXiv:2405.05307, doi: 10.48550/arXiv.2405.05307

    2024 doi

  75. [83]

    P., & Fortney, J

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

    2018 doi

  76. [84]

    Lopez, E. D. 2016, ApJ, 831, 64, doi: 10.3847/0004-637X/831/1/64

    2016 doi

  77. [85]

    2024, A&A, 688, A66, doi: 10.1051/0004-6361/202450095

    Mauduit, E. 2024, A&A, 688, A66, doi: 10.1051/0004-6361/202450095

    2024 doi

  78. [86]

    D., Zarka, P., Grießmeier, J.-M., et al

    Turner, J. D., Zarka, P., Grießmeier, J.-M., et al. 2021, A&A, 645, A59, doi: 10.1051/0004-6361/201937201 Vigan` o, D., Sengupta, S., Soriano-Guerrero, C., et al. 2025, A&A submitted

    2021 doi

  79. [87]

    M., Hubbard, W

    Wahl, S. M., Hubbard, W. B., Militzer, B., et al. 2017, Geophys. Res. Lett., 44, 4649, doi: 10.1002/2017GL073160

    2017 doi

  80. [88]

    2025, ApJL, 979, L31, doi: 10.3847/2041-8213/ada954

    Wazny, M., & Menou, K. 2025, ApJL, 979, L31, doi: 10.3847/2041-8213/ada954

    2025 doi

  81. [89]

    M., Marcy, G

    Weiss, L. M., Marcy, G. W., Rowe, J. F., et al. 2013, ApJ, 768, 14, doi: 10.1088/0004-637X/768/1/14

    2013 doi

  82. [90]

    2005, ApJL, 628, L143, doi: 10.1086/432716

    Redfield, S. 2005, ApJL, 628, L143, doi: 10.1086/432716

    2005 doi

  83. [91]

    E., M¨ uller, H.-R., Redfield, S., et al

    Wood, B. E., M¨ uller, H.-R., Redfield, S., et al. 2021, ApJ, 915, 37, doi: 10.3847/1538-4357/abfda5

    2021 doi

  84. [92]

    2013, ApJ, 763, 13, doi: 10.1088/0004-637X/763/1/13

    Wu, Y., & Lithwick, Y. 2013, ApJ, 763, 13, doi: 10.1088/0004-637X/763/1/13

    2013 doi

  85. [93]

    K., Gastine, T., Christensen, U

    Yadav, R. K., Gastine, T., Christensen, U. R., & Duarte, L. D. V. 2013, ApJ, 774, 6, doi: 10.1088/0004-637X/774/1/6

    2013 doi

  86. [94]

    K., & Thorngren, D

    Yadav, R. K., & Thorngren, D. P. 2017, ApJL, 849, L12, doi: 10.3847/2041-8213/aa93fd Yıldız, M., C ¸ elik Orhan, Z.,¨Ortel, S., & C ¸ akır, T. 2024, MNRAS, 528, 6881, doi: 10.1093/mnras/stae476

    2017 doi

  87. [95]

    N., & Mitchell, J

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

    2010 doi

  88. [96]

    Zarka, P. 1998, J. Geophys. Res., 103, 20159, doi: 10.1029/98JE01323

    1998 doi

  89. [97]

    A., Ryabov, B

    Zarka, P., Treumann, R. A., Ryabov, B. P., & Ryabov, V. B. 2001, Ap&SS, 277, 293, doi: 10.1023/A:1012221527425

    2001 doi

  90. [98]

    K., & Howard, A

    Zink, J. K., & Howard, A. W. 2023, ApJL, 956, L29, doi: 10.3847/2041-8213/acfdab 20 APPENDIX A. ROSSBY NUMBER DEPENDENCE ON STELLAR TYPE To evaluate the dependence of Ro on stellar type, we use the properties of the specific stars shown in Table 1. Note that, by construction, ...

    2023 doi

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