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

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that reproducing the observed inflated radii of hot Jupiters through Ohmic dissipation requires average wind speeds of 0.01–1 km/s in the $p < 10$ bar region, declining roughly linearly with mass and much more steeply…

desk verdict The paper's wind-speed constraints are a calibrated fit, not an independent measurement, but the time-varying dynamo coupling and updated conductivity make it a useful framework. read the letter →

arxiv 2507.13991 v2 pith:6RC3ALFZ submitted 2025-07-18 astro-ph.EP astro-ph.SR

Daniele Viganò , Soumya Sengupta , Clàudia Soriano-Guerrero , Rosalba Perna , Albert Elias-López , Sandeep Kumar , Taner Akgün This is my paper
classification astro-ph.EPastro-ph.SR
keywords hotJupitersOhmicdissipationradiusinflationmagneticdynamoatmosphericwindselectricalconductivityplanetaryevolutionexoplanetatmospheres
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

The paper targets the long-standing puzzle of why hundreds of hot Jupiters are larger than cooling models predict. It argues that Ohmic dissipation—Joule heating from electrical currents induced when atmospheric winds drag the planet's magnetic field—can explain the inflated radii, provided the average wind speed in the region $p < 10$ bar lies between 0.01 and 1 km/s. That wind speed must decline roughly linearly with planetary mass and much more steeply with equilibrium temperature, consistent with magnetic drag being stronger in hotter and heavier planets. A second claim is that the Ohmic heating efficiency is not constant in time: as the planet cools, the deep dynamo field weakens, so the efficiency drops by at least an order of magnitude from 0.1 to 10 Gyr, with strong heating able to suppress convection and feed back on the field itself.

What carries the argument

The central object is the effective average wind speed $v_{\rm avg}$, which sets the atmospheric current density through $J = \sigma_{\rm atm} v_{\rm avg} B_{\rm atm}$ in the region $p < 10$ bar. The background field $B_{\rm atm}$ is derived from a dynamo scaling law that relates the deep field to the convective heat flux integrated over the region at pressures above $10^6$ bar, and the conductivity $\sigma$ is taken from updated tables for thermal alkali ionisation at low density and pressure ionisation at high density. The current profile below the wind region is reconstructed by patching piecewise power-law solutions of the induction equation shell by shell, so that the shape of heating is set by the steepness of the conductivity gradient rather than by the assumed wind or field geometry.

What would settle it

Direct measurements of surface magnetic fields or of wind speeds in the $p < 10$ bar layer of a hot Jupiter would settle the claim: a field an order of magnitude below the scaling-law prediction, or a measured wind above about 1 km/s in a hot, massive planet, would contradict the inferred values and trends.

Watch

Extended reading notes

Core claim

The central claim is that matching the observed radii of hot Jupiters requires average atmospheric wind speeds in the $p < 10$ bar layer of roughly 0.01–1 km/s, decreasing approximately linearly with planetary mass and much more steeply with equilibrium temperature. Because the induced currents are proportional to the deep dynamo field, and that field decays as the planet cools, the Ohmic heating efficiency declines by at least an order of magnitude between 0.1 and 10 Gyr—unlike prior models with constant efficiency. In strongly heated cases the Ohmic heat suppresses the convection that sustains the dynamo, creating a feedback loop that can make the field and radius oscillate rather than settle.

Load-bearing premise

The load-bearing premise is that the dynamo scaling law, calibrated on fully convective bodies, gives the correct deep magnetic field for hot Jupiters even when Ohmic heating fragments the convection into thin layers, because the inferred wind speeds scale directly with that field.

Editorial extensions

If this is right

  • The observed radius versus insolation and mass trends of hot Jupiters become a constraint on sub-10-bar wind speeds, with heavier and hotter planets requiring slower flows.
  • Ohmic efficiency declines with age, so models that assume a constant efficiency overestimate how long inflation lasts; old hot Jupiters should be closer to their cooling radii.
  • The dynamo–induction feedback can produce intermittent convection and oscillatory field strength, implying that some radius scatter at fixed mass and temperature is intrinsic.
  • When the host star's luminosity rises on the main sequence, late re-inflation becomes possible, matching hints that some planets grow at gigayear ages.

Reading between the lines

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

  • If the framework holds, replacing the constant $v_{\rm avg}$ parameter with a magnetic-drag prescription would let the model predict wind speeds rather than fit them, and could soften the oscillatory feedback.
  • The same approach could be applied to warm Jupiters and hot Saturns, where the inferred declining efficiency may help explain the absence of strong inflation in cooler planets.
  • The predicted steep decline of wind speed with equilibrium temperature can be tested statistically with a large sample of Doppler wind measurements from high-resolution spectroscopy.
  • The comparable magnitudes of atmospherically induced and dynamo-generated currents suggest hot-Jupiter dynamo simulations should be run with current-carrying boundary conditions rather than the usual current-free ones.
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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

4 major / 5 minor

Summary. This paper presents one-dimensional MESA evolutionary models of hot Jupiters with a parameterized Ohmic heating prescription, coupled to a deep-seated dynamo field whose strength evolves through the Christensen et al. (2009) scaling law. The headline result is that reproducing the observed radius distribution requires a sub-10-bar atmospheric wind speed v_avg of order 0.01-1 km/s, with a roughly linear decrease with planetary mass and a much steeper decrease with equilibrium temperature. The paper also reports that Ohmic efficiency declines by at least an order of magnitude between 0.1 and 10 Gyr, that feedback between Ohmic heating and convective heat flux can produce oscillatory dynamo behavior, and that a slowly brightening host star can cause late-time reinflation. The model is described in detail, the code is released, and the authors are unusually candid about the many physical and numerical caveats.

Significance. If the calibration were robust, the paper would provide a novel mapping from the observed radius distribution of hot Jupiters to average atmospheric wind speeds, with testable predictions for circulation models and for the mass and temperature dependence of Ohmic inflation. The strengths are the public, machine-checkable MESA implementation; the use of updated conductivity tables for both thermal and pressure ionization; the semi-analytic current reconstruction; and the explicit discussion of limitations in Sections 5.2, 6, and Appendix A. However, the central quantitative claim is a one-parameter calibration: v_avg is adjusted so that model tracks fall inside observed radius bands, and the paper does not propagate the dominant systematic uncertainties, most importantly the factor-of-several uncertainty in the dynamo field scaling law. The stress-test concern about B_dyn therefore lands directly: Appendix A itself shows that an equally standard scaling law gives B_dyn roughly three times lower, which would shift the inferred v_avg range by the same factor.

major comments (4)
  1. [Section 4.3 and Appendix A (Eqs. 18, A.1)] The quantitative headline in the abstract, v_avg = 0.01-1 km/s, is not robust to the acknowledged order-unity uncertainty in the dynamo field. Equation (10) sets J_atm proportional to v_avg B_atm, and since Ohmic heating is quadratic in J, a factor-3 lower B_dyn from Eq. (A.1) requires a factor-3 higher v_avg to produce the same radii. The paper itself notes this discrepancy in Fig. A.1 but does not propagate it into the inferred range. The authors should either rerun representative tracks with the alternative scaling law, or explicitly rescale the reported v_avg values and state the resulting range in the abstract and conclusions. The same applies to the f_ohm = 0.5 choice in Eq. (18), whose plausible range f_ohm ~ 0.3-0.8 is discussed but not propagated.
  2. [Section 5.1, Eq. (20), and Fig. 5] The claimed trend of v_avg with mass and equilibrium temperature is partly imposed by the choice of parameter grid. Equation (20) defines a stability limit scaling as 1/[(M/Mj)(Teq/1500K)^6], and the values shown in Fig. 5 are explicitly chosen as {0,1000,2000,3000} m/s divided by exactly this same denominator. It is therefore unsurprising that the tracks that match the observed radius bands correspond to v_avg values decreasing with M and Teq. To establish that the inferred scalings are a property of the model rather than of the sampling, the authors should show results for a fixed set of absolute v_avg values across the M-Teq grid, or perform a formal inversion (e.g., a chi-square map over v_avg for each bin) with uncertainties. Without this, the phrase 'we infer that v_avg decreases roughly linearly with mass' overstates what is a calibrated fit.
  3. [Section 5.1 and Fig. 5] The paper presents the range of v_avg as a definite inference but does not quantify how well individual tracks match the observed radius bands, nor how the spread of observed radii maps onto a spread of v_avg. The grey bands are the observed mean plus or minus one standard deviation, but no goodness-of-fit is reported, and the many other free parameters that are fixed in the main grid (core mass, core density, composition, f_dip, p_atm, Sigma_star) would also shift the required v_avg. A sensitivity study or an explicit statement that the reported range is a 'calibration range under fixed assumptions' is needed before the abstract's quantitative claim can be accepted.
  4. [Section 4.3, Eq. (19), and Section 5.2] The assumed dipolarity factor f_dip = 0.1, constant in time, enters linearly into the atmospheric field B_atm and hence quadratically into the Ohmic heating rate. The authors note that a time-varying f_dip could overestimate the surface field at early ages. Because the time evolution of the Ohmic efficiency, and hence the claimed secular decline and the oscillatory feedback, depend on this choice, the paper should provide a sensitivity test with f_dip varied within the range suggested by the cited dynamo simulations. The self-acknowledged numerical sensitivity of the oscillations in Section 5.2 is not by itself a flaw, but it currently prevents the oscillatory behavior from being a robust, quantitative result.
minor comments (5)
  1. [Section 5.1, Fig. 5 legend] The legend states v_avg = {0,1000,2000,3000}/[(M/Mj)(Teq/1500K)^6] m/s, which is easy to misread as absolute values. Please state explicitly that these are the tested values relative to the stability-limit scaling of Eq. (20).
  2. [Appendix A, Fig. A.1] The factor-of-three difference between the two scaling laws is a central caveat and deserves a sentence in Section 4.3 or the conclusions, not only in the appendix.
  3. [Section 4.2.2, Eq. (17)] The notation j_{l+l_w} in Eq. (17) is ambiguous: l_w and l_b are introduced but the convolution is not made explicit. A clearer definition of the multipole weight index would improve readability.
  4. [Section 4.4] The time-averaging of the Ohmic heat source is described only as 'an interval much smaller than the typical cooling timescales.' Please give the actual averaging window or the numerical criterion used, since this directly affects the interpretation of the oscillations in Section 5.2.
  5. [Abstract and Section 5.1] The abstract quotes 0.01-1 km/s, while Section 5.1 says 'v_avg ~ km/s in the lightest, moderately irradiated planets, and one or two orders of magnitude less' at the highest M and Teq. Please align the wording so the reader can see that these are the same range.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the inferred wind range is a calibrated inverse model output, with acknowledged scaling-law sensitivity, not a definitional reduction.

full rationale

The derivation chain is a forward model with an inverse step: v_avg is a free parameter in Eq. (10), and the paper tunes it so that MESA tracks fall in the observed radius bands of Fig. 5, then reports the tuned values as an inference (Sec. 5.1 and abstract). This is a calibration of a free parameter to data, not a prediction from a fitted quantity, and the mapping from radius to v_avg is nontrivial via the MESA evolution, the conductivity profiles, and the deep-current reconstruction. The dynamo field enters through the external Christensen et al. (2009) scaling law with f_ohm=0.5 and f_dip=0.1; Appendix A explicitly documents that an alternative Reiners et al. (2009) law gives roughly a factor-3 lower B_dyn, which would rescale the inferred v_avg, but this is a robustness/correctness concern rather than circularity. The self-citations to Elias-López et al. (2025a,b) set the fast-rotation regime and the dipolarity parameter, but the paper also calibrates against Jupiter's surface field and discusses the sensitivity in Appendix A; these are not a uniqueness argument that suppresses alternatives. The paper's own phrase 'circular relation' (Sec. 6) refers to a physical feedback loop between Ohmic dissipation, convective heat flux, and dynamo magnetic field, not to a logical circularity in the derivation. No load-bearing step reduces by construction to its own inputs.

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

The central inference of wind speeds depends on a handful of free parameters, most importantly v_avg, and on the Christensen et al. scaling law and conductivity interpolation. No new physical entities are introduced; the oscillatory behavior is an emergent outcome of the assumed coupling.

free parameters (7)
  • v_avg = 0.01-1 km/s, decreasing with increasing M and T_eq
    Average wind speed at p<10 bar, free parameter in eq. (10) J_atm = sigma_atm v_avg B_atm. Its value is calibrated so that MESA models match observed radius bands in Fig. 5.
  • f_ohm = 0.5
    Fraction of Ohmic to total dissipation in the dynamo region in eq. (18), chosen mid-range of 0.3-0.8 from dynamo simulations; sets normalization of B_dyn.
  • f_dip = 0.1
    Effective dipolarity at dynamo surface in eq. (19), B_atm = f_dip B_dyn (R_dyn/R)^3, chosen constant in time from Elias-Lopez et al. (2025b) range.
  • p_atm = 10 bar
    Pressure boundary dividing the parametrized wind region from the deeper induction solution in Sect. 4.2; sets the normalization of J_atm and hence the meaning of v_avg.
  • v_stab_avg = 3000 (M_j/M)(1500 K/T_eq)^6 m/s
    Empirical numerical stability limit in eq. (20) found by exploring parameters; used to choose tested v_avg range, not physically derived.
  • Sigma_star = 250 g/cm2
    Absorbing column mass for irradiation in Sect. 3.3; tests in Appendix C show a few percent effect on radius at gigayear ages.
  • core_mass_and_density = M_c=10(M/M_j) M_earth, rho_c=10(M/M_j) g/cm3
    Prescription in Sect. 3.2 to avoid unphysical central density; effects on radius are minor as shown in Appendix C.
assumptions (7)
  • domain assumption The Christensen-Aubert scaling law, eq. (18), with f_ohm=0.5, correctly gives B_dyn of hot Jupiters from convective heat flux integrated over p>10^6 bar.
    Section 4.3. Calibrated on solar system dynamos and stars; the paper's own Appendix A notes brown dwarf outliers and excluded planets, and that HJ convection may be fragmented by heating.
  • domain assumption Stationary induction equation balances advection against resistive diffusion and neglects Hall and ambipolar terms, eq. (7).
    Section 4.2. The paper states these non-ideal terms are neglected, citing that they may matter in shallow layers but are not expected to affect the radius.
  • ad hoc to paper The wind region is characterized by a single average conductivity sigma_atm and a single velocity v_avg constant in time, eq. (10)-(11).
    Section 4.2.1. Explicitly a parametrization of a complex 3D pattern; v_avg constancy neglects magnetic drag feedback, acknowledged in Sect. 4.2.1 and 6.
  • domain assumption The conductivity profile is obtained by linear interpolation in log(rho)-log(T) of Kumar et al. (2021) and Bonitz et al. (2024) tables, including a sparse intermediate region.
    Section 4.1. The paper notes few available points at T less than about 10^4 K, the regime of interest, making interpolation uncertain.
  • standard math Piecewise power-law fits reproduce sigma(r) to a few percent and eq. (14) gives the correct multipole solution of the induction equation in each shell.
    Section 4.2.2. The derivation of the alpha exponents is mathematically straightforward; the approximation is the power-law fit to the conductivity profile.
  • domain assumption The planetary structure equations and MESA EOS, with fixed core, solar composition, and no H-He immiscibility, capture the radius evolution.
    Section 3.1-3.2. Standard assumptions; the paper lists neglected physics (immiscibility, double-diffusive convection, mass loss) and discusses their limited relevance for the hottest sample.
  • ad hoc to paper Ohmic heating source is linearly activated between 5 and 20 Myr and time-averaged to stabilize the code.
    Section 4.4. Chosen for numerical convenience; the paper states it does not affect gigayear radius trends, but it shapes early evolution and can damp or alter the oscillatory behavior.

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Cite this review

Pith. "Pith review of Inflated hot Jupiters: Inferring average atmospheric velocity via Ohmic models coupled with internal dynamo evolution." pith.science (2026). https://pith.science/paper/6RC3ALFZ

@misc{pith2026250713991,
  author       = {Pith},
  title        = {Pith review of: Inflated hot Jupiters: Inferring average atmospheric velocity via Ohmic models coupled with internal dynamo evolution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6RC3ALFZ}},
  note         = {Machine review of arXiv:2507.13991}
}
abstract

The inflated radii observed in hundreds of hot Jupiters (HJ) represent a long-standing open issue. In this study, we quantitatively investigate this phenomenon within the framework of Ohmic dissipation arising from magnetic induction in the atmosphere, one of the most promising mechanisms for explaining the radius anomaly. We simulate the evolution of irradiated giant planets with MESA, spanning the observed range of masses and equilibrium temperatures, incorporating an internal source of Ohmic dissipation that extends to deep layers of the envelope. We infer average atmospheric wind intensities, averaged in the region $p < 10$ bar, in the range 0.01-1 km/s in order to reproduce the range of observed radii, decreasing roughly linearly with planetary mass, and much more steeply with equilibrium temperature. This is consistent with the expected effects of magnetic drag from the induced field, which is higher for more intense irradiation, via conductivity, and for larger masses, which have higher dynamo fields. Due to the evolution of the dynamo field and the proportionality of the induced currents on it, the Ohmic efficiency typically decreases by at least one order of magnitude from 0.1 to 10 Gyr, at contrast with the common assumption of a constant-in-time value. Notably, the extent of the main convective region, and the associated heat flux supporting the dynamo, is reduced in the presence of strong Ohmic dissipation, which in turn depends on the dynamo field strength, generating a non-trivial coupling of the latter with the atmospheric induction, potentially leading to an oscillatory behaviour of the field strength. These findings remain generally valid even when accounting for a long-term increase in the main-sequence host star luminosity, although this case can more readily lead to HJ re-inflation, consistent with previous studies.

Figures

Figures reproduced from arXiv: 2507.13991 by the authors.

Figure 1
Figure 1. Hot Jupiter inflated radii observational trends for the 424 Jupiter-like exoplanets in the database with available estimated mass M ≥ 0.5 Mj ; age t ≥ 100 Myr; radius, R; and equilibrium temperature, Teq. We consider only the planets with relative errors in a radius of less than 25% and available uncertainties for the mass. We also excluded seven planets younger than 100 Myr. Top: Planetary radius, R, versus, Teq, o… view at source ↗
Figure 2
Figure 2. shows the conductivity profiles obtained at three ages (t ∼ 0.4, 1.1, 5 Gyr) for four different models: Teq = 1500, 2000 K, and with (blue and red lines) or without (black and grey lines) the inclusion of Ohmic heating (see below). While in the external part the values are highly sensitive to the local tem￾perature, which is higher for highly irradiated and/or internally heated cases, at p ≳ 105 bar the curves tend … view at source ↗
Figure 3
Figure 3. Profiles as a function of pressure of the induced currents, J (top), and Ohmic specific (middle) and cumulative (bottom) heat rate. We show the same heated cases and ages as in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Current reconstruction for the two models with heating consid￾ered in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Evolution of the radius, R, for planets with a given Teq = 1750, 2000, 2250 K (from left to right), different masses (M = 0.7, 1, 2, 4 Mj in blue, green, orange, and purple, respectively), and different values of vavg, marked by increasingly darker shades: vavg = {0, 1…
Figure 6
Figure 6. Figure 6: Evolution of radii (top row, with dots indicating the dynamo radius and the solid the planetary radius), estimated magnetic field produced in the dynamo region (second row, with dots for Bdyn and solid lines for the planetary surface, Batm, assuming fdip = 0.1), Ohmic …
Figure 7
Figure 7. Figure 7: Effects of the feedback of Batm. We take into account two representative models, both with M = 1Mj , Teq = 1750 K and vavg = 793 m/s: one with an evolving Batm (grey) and the other with a fixed Batm = 5 G. Left: Evolution of the pressure values delimiting the deep (sol…
Figure 9
Figure 9. Figure 9: Typical radial profiles of |∇ × B|/(¯κB) (top) and 1/κ¯ (bottom), averaged over the spherical surface at each radius, from 3D dynamo simulations with the code MagIC. In order to explore the sensitivity to the free parameters. All models have the same boundary condition…

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.