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Ohmic heating in the upper atmosphere of hot exoplanets The influence of a time-varying magnetic field

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Ohmic heating from an orbital-timescale, time-varying stellar-wind magnetic field can reach $10^{-3}$ erg s$^{-1}$ cm$^{-3}$ in hot-exoplanet upper atmospheres and can rival or exceed XUV heating for intermediate planetary fields.

desk verdict A careful 1D treatment that makes a plausible case for Ohmic heating as a thermal term in hot exoplanet upper atmospheres, but the central numbers rest on an idealized sinusoidal driver and unconstrained field strengths. read the letter →

arxiv 2412.14072 v1 pith:3FQH2UIT submitted 2024-12-18 astro-ph.EP

A. Strugarek , A. García Muñoz , A.S. Brun , A. Paul This is my paper · ORCID
classification astro-ph.EP
keywords Ohmicheatinghotexoplanetsupperatmospheretime-varyingmagneticfieldscreeningPedersenconductivityTrappist-1bπMenc
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

Close-in exoplanets are heated by more than the XUV radiation of their host star. This paper argues that the magnetic field of the stellar wind, varying as the planet orbits, induces currents in the upper atmosphere whose Ohmic dissipation can deposit up to $10^{-3}$ erg s$^{-1}$ cm$^{-3}$ locally, comparable to or larger than photochemical XUV heating in favorable cases. That matters because models of thermally escaping atmospheres that include only XUV heating would omit this term. The paper shows the effect is strongest for close-in planets around low-mass, fast-rotating stars, and that strong Ohmic heating also implies efficient screening of the external field by the upper atmosphere.

What carries the argument

The machinery is the 1D induction equation for the vector potential amplitude $A_0(x)$, $\partial_{xx} A_0 + (4\pi i \Omega \sigma_P/c^2) A_0 = 0$, with the time-varying field imposed at the top and zero current at the bottom. The penetration is set by the skin depth $\delta_P = c/\sqrt{2\pi \Omega \sigma_P}$. The volumetric heating is $Q = [\sigma_P/(\sigma_H^2+\sigma_P^2)] (c/(4\pi) \Re(\partial_{xx} A_0))^2$, and in the thin-skin limit it saturates at $Q_{\max} = \Omega B_{\mathrm{sw}}^2/(8\pi)$, independent of the Pedersen conductivity. A key result is that the heating peak need not sit at the conductivity maximum, and that localized conductivity enhancements pull both the screening and the heat deposition toward them.

What would settle it

Run a time-dependent 3D stellar-wind model for Trappist-1 and decompose the magnetic-field fluctuations at the planet's orbit in Fourier space: if the variance is dominated by timescales much shorter than the 1.51-day orbital period (CME crossings or advection past the planet), then the sinusoidal, orbital-frequency assumption at the heart of the skin-depth calculation fails, and the predicted penetration and heating profiles do not apply.

Watch

Extended reading notes

Core claim

The paper's central claim is that the upper atmospheres of hot exoplanets ohmically dissipate a time-varying external magnetic field, and that this dissipation can be a leading term in the local energy budget. Solving the 1D induction equation with ab-initio conductivity profiles, the authors find maximum volumetric heating rates up to $10^{-3}$ erg s$^{-1}$ cm$^{-3}$, with a theoretical cap $Q_{\max} = \Omega B_{\mathrm{sw}}^2/(8\pi)$ that is independent of the Pedersen conductivity once the skin depth is small. For intermediate steady planetary fields, roughly 0.01 to 1 G, the heating can peak near or below the sonic point of the escaping atmosphere; for very small fields the atmosphere screens the external field high up, and for very large fields the field passes through without being dissipated. Applied to Trappist-1 b and $\pi$ Men c, both planets are predicted to experience substantial Ohmic heating.

Load-bearing premise

Everything hangs on treating the magnetic field felt by the planet as a single smooth oscillation repeated once per orbit, with no motion of the wind itself; if the real field varies in sharper bursts or gets swept past the planet, the calculated heating and screening profiles change.

Editorial extensions

If this is right

  • Ohmic heating from an orbital-timescale, time-varying external field can reach $10^{-3}$ erg s$^{-1}$ cm$^{-3}$ in hot-exoplanet upper atmospheres and can locally exceed XUV photochemical heating.
  • For planetary magnetic fields in the roughly 0.01–1 G range, the heating peak can sit close to or below the sonic point of the escaping atmosphere, so it should enter the thermal budget that sets atmospheric mass loss.
  • When Ohmic heating is strong, the upper atmosphere screens the external time-varying field almost completely, so little of it reaches deeper atmospheric layers or the planetary interior.
  • Trappist-1 b and $\pi$ Men c are both predicted to experience substantial Ohmic heating, with the effect becoming important for ambient fields of about 1 G and 0.1 G, respectively.
  • For the known exoplanet population, the maximal heating rate is largest for close-in planets around fast-rotating, low-mass stars.

Reading between the lines

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

  • Editorial inference: if the $Q_{\max}$ saturation is general, then searches for induced radio emission or magnetic star-planet interaction signatures around close-in planets can use $Q_{\max} = \Omega B_{\mathrm{sw}}^2/(8\pi)$ as an upper bound on the energy available to any Ohmic dissipation channel.
  • Editorial inference: the screening result implies that interior-induction heating scenarios for close-in exoplanets must first pass through the upper atmosphere; planets with strong XUV-driven electron densities may block the varying field before it reaches the interior, weakening interior Ohmic heating in exactly the systems where it was previously predicted to be strongest.
  • Editorial inference: atmospheric composition becomes a first-order control on this heating channel—an H2O-dominated upper atmosphere can suppress electron density and therefore conductivity relative to an H-dominated one at comparable XUV flux, so escape and habitability models for M-dwarf planets may need composition-dependent Ohmic heating terms.
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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 / 4 minor

Summary. The paper develops a 1D model for the penetration of an external time-varying magnetic field into the upper atmospheres of hot exoplanets and for the associated Ohmic heating. It solves a diffusion equation for the vector potential with a Pedersen conductivity (Eq. 12), validates the solver against an analytic constant-conductivity solution and against Earth ionospheric conductivities, and applies the framework to Trappist-1 b and π Men c using photochemical upper-atmosphere models. It introduces a saturation heating rate Qmax = ΩBsw^2/(8π) (Eq. 14), compares Ohmic heating with XUV heating at the sonic point, and produces a population-level map of Qmax. The central claim is that Ohmic heating can reach ~10^-3 erg s^-1 cm^-3 and can surpass XUV heating for intermediate planetary field strengths of roughly 0.01-1 G, making it a potentially important term in the thermal budget of escaping atmospheres of close-in planets.

Significance. If the central claim holds, the paper establishes a new heating mechanism that must be included in upper-atmosphere energy balance models of close-in exoplanets. The manuscript has several clear strengths: the diffusion problem is solved with a numerically validated scheme; the conductivity calculations are benchmarked against Earth ionospheric data (Appendix B) and against the analytic constant-conductivity solution (Appendix C); the paper explicitly reconciles its heating-rate saturation with the earlier Cohen et al. (2024) result (Appendix D); and the population-level Qmax map is a simple, falsifiable prediction. These strengths make the paper a useful contribution to the star-planet interaction literature. However, the physical driver of the time variation (the assumed monochromatic orbital-period oscillation) and the neglect of advective induction are load-bearing assumptions that need to be justified or relaxed before the quantitative claims can be considered robust.

major comments (3)
  1. [Eq. (10), Sect. 6] The induction equation used in the paper, ∂xx A0 + (4πiΩσP/c^2) A0 = 0, omits the advective term ∇×(u×B). In the planet's rest frame, the stellar wind generates a motional electric field E = -u×B/c that is present even when ∂B/∂t = 0. The statement in Sect. 6 that a radial outflow makes this term negligible is not quantitatively supported. Using the paper's own numbers for π Men c (σP≈0.4 S/m, u≈10 km/s near the sonic point, L≈100 km), the magnetic Reynolds number is Rm≈500, so advection dominates over diffusion precisely in the region where the heating peaks. Consequently, the computed heating rates and the 'upper limit' Qmax are not robust for a planet embedded in a flowing stellar wind. This limitation is acknowledged in Sect. 7 ('we have neglected so far inductive effects'), but it affects the central quantitative claim of the paper and should be addressed with a quantitative ordering argument or by including the advective term.
  2. [Eq. (14), Sect. 5.2] The population estimate and the claimed maximum heating rate assume a monochromatic oscillation at Ω = 2π/Porb. For a planet orbiting a rotating tilted stellar dipole, the magnetic-field component in the planetary frame varies at the stellar rotation period or at a beat period, and for advected wind structures the characteristic timescale is L/v_wind rather than the orbital period. Since Qmax ∝ Ω, the frequency choice directly sets the peak values in Fig. 7. The paper uses rotation periods of 3 and 30 days only in the scaling law for B⋆ (Eq. 20) and not for Ω, so the population-level heating rates can change by factors of several depending on which physical timescale actually modulates the field. The authors should specify the driver of the time variation and justify the use of the orbital frequency in the population analysis.
  3. [Sect. 5.2 and Fig. 3c] The statement in Sect. 5.2 that 'this Qmax can never be surpassed' is contradicted by the paper's own Fig. 3c, where a localized conductivity enhancement (green curve) produces a peak Ohmic heating rate eight times larger than the corresponding constant-conductivity case, which represents Qmax for those parameters. Appendix C provides the δP >> d limit Q = (σP/σP0)^3 Qmax, and while that particular limit lies below Qmax, the non-uniform-conductivity case in Fig. 3 shows that local volumetric heating can exceed Qmax. Therefore the population estimate in Fig. 7, which uses Eq. (14) as a nominal upper bound, is not a rigorous upper limit for a stratified atmosphere; it is the value for a uniform conductor with skin depth smaller than the layer depth. The text should be corrected to state the conditions under which Qmax applies.
minor comments (4)
  1. [Eq. (19)] The formula for the electron-ion collision frequency is dimensionally unclear as printed: the text states n_i is in g cm^-3, but a collision frequency should scale with number density; please clarify the units or the intended formula.
  2. [Fig. B.1] The label 'Maedea 1977' is a typo for 'Maeda 1977'.
  3. [Sect. 5.2] The choice of Prot = 3 and 30 days for all stars in the population estimate is not clearly justified for the actual stellar sample; the magnetic field scaling of Eq. (20) is sensitive to this parameter, and the paper does not discuss the resulting uncertainty in the Qmax map.
  4. [Sect. 6] The statement that a CME 'sweep[s] an Earth-like planet in a few seconds to a few minutes' is imprecise: for v=3000 km/s and a planet radius of ~6400 km, the crossing time is about 4 seconds; a few minutes would require a much larger structure or a slower speed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Ohmic-heating derivation is self-contained, validated against external benchmarks, and uses no fitted parameter relabeled as a prediction.

full rationale

The paper's derivation chain is self-contained. Eqs. (5)-(12) solve the induction equation with Ohm's law under a monochromatic ansatz (Eqs. 6-7); the conductivity tensor follows from standard Chapman/Norman-Heyvaerts collision-frequency formulae with species densities taken from the independent Garcia Munoz (2023) upper-atmosphere models. The central analytic limit Qmax = Omega Bsw^2/(8 pi) is re-derived in Appendix C from the constant-conductivity solution and matches the independent result of Chyba & Hand (2021); it is an upper bound, not a fit. The 1D solver is validated against the analytical constant-conductivity solution and against the empirical WDC/Maeda Earth conductivity profiles (Appendix B), i.e., external benchmarks. No parameter is fitted to the target heating rates: Bsw and Omega are stated inputs, and the paper scans a (BP, Bsw) grid rather than tuning to make Q exceed Qph. The population estimate uses the Ahuir et al. (2020) scaling law co-authored by two of the present authors, but this empirical scaling is not fitted to Ohmic heating, is externally falsifiable, and the specific Trappist-1 b and pi Men c conclusions rely on observed/estimated Bsw from Reiners & Basri (2010) and Reville et al. (2024). Section 6 explicitly flags the main limitations: 'we have chosen here to neglect the advective component of the induction equation', 'we have considered only perfect oscillators for the external magnetic field', and only a constant planetary field BP; these are scope and robustness limitations, not circular reductions. No load-bearing step reduces to its own input by definition; self-citations are present but not used as unverified uniqueness theorems.

Assumptions & free parameters 3 free parameters · 8 assumptions · 0 invented entities

The Ohmic heating result depends on standard electrodynamics plus a chain of modeling choices: sinusoidal driver, 1D geometry, neglect of advection, constant planetary field, Chapman conductivities, and the Garcia Munoz (2023) atmosphere models. None of these is fitted to the target heating rates; they are approximations with stated scope, but the planet-level conclusions inherit their uncertainty.

free parameters (3)
  • Bsw, ambient oscillating field amplitude = no fit; explored 1 mG to 10 G, estimated 0.07 to 1.4 G for Trappist-1 b, unconstrained for pi Men c
    Set by hand as a scenario input; the central likely conclusion depends on its assumed or estimated value.
  • BP, planetary magnetic field strength = no fit; explored 1 mG to 4 G
    Planetary field is unknown; chosen by hand in the parameter exploration and controls whether heating occurs below the sonic point.
  • Prot, assumed stellar rotation period in the population estimate = 3 and 30 days
    Free inputs in the population Qmax map (Sect. 5.2) that control B* through the Ahuir et al. scaling law.
assumptions (8)
  • standard math Maxwell equations, Ohm's law, and the magnetic diffusion equation (Eqs. 5-12)
    Basis of the induction problem; their use is standard.
  • domain assumption Sinusoidal time dependence of the external field with frequency 2 pi / Porb (Eqs. 6-7)
    The planet is treated as seeing a monochromatic oscillating magnetic field; transients and non-periodic variations are excluded.
  • domain assumption Neglect of the advective term v x B in the induction equation
    Stated in Sect. 6; valid only where the atmospheric flow is radial and slow compared with magnetic diffusion.
  • domain assumption Steady planetary magnetic field is constant with height and aligned with ez
    Used for the conductivity tensor and penetration equation; the authors note real field decays with height (Sect. 6).
  • domain assumption 1D geometry with variations only along x and a field orientation such that only Pedersen conductivity enters the diffusion equation
    Simplified geometry in Fig. 1; ignores 3D current closure and complex field topology.
  • domain assumption Boundary conditions: Neumann top boundary dx A0 = Bsw and no-current bottom boundary dxx A0 = 0
    Define the solution family; the bottom condition matters in the thick-skin limit (Appendix C).
  • domain assumption Chapman conductivity formulas with singly-ionized species and equal temperatures (Eqs. 15-19)
    Standard ionospheric approximation; validated against the Earth WDC model.
  • domain assumption The photochemical atmosphere models of Garcia Munoz (2023) are representative of Trappist-1 b and pi Men c
    Conductivity profiles and Qph are taken from these models; no error bars are propagated.

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Pith. "Pith review of Ohmic heating in the upper atmosphere of hot exoplanets The influence of a time-varying magnetic field." pith.science (2026). https://pith.science/paper/3FQH2UIT

@misc{pith2026241214072,
  author       = {Pith},
  title        = {Pith review of: Ohmic heating in the upper atmosphere of hot exoplanets The influence of a time-varying magnetic field},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3FQH2UIT}},
  note         = {Machine review of arXiv:2412.14072}
}
abstract

Exoplanets on close-in orbit are subject to intense X-ray and ultraviolet (XUV) irradiation from their star. Their atmosphere therefore heats up, sometimes to the point where it thermally escapes from the gravitational potential of the planet. Nonetheless, XUV is not the only source of heating in such atmospheres. Indeed, close-in exoplanets are embedded in a medium (the stellar wind) with strong magnetic fields that can significantly vary along the orbit. The variations of this magnetic field can induce currents in the upper atmosphere, which dissipate and locally heat it up through Ohmic heating. The aim of this work is to quantify Ohmic heating in the upper atmosphere of hot exoplanets due to an external time-varying magnetic field, and to compare it to the XUV heating. Ohmic heating depends strongly on the conductivity properties of the upper atmosphere. A 1D formalism is developed to assess the level and the localization of Ohmic heating depending on the conductivity profile, and applied to the specific cases of Trappist-1 b and $\pi$ Men c. Ohmic heating can reach values up to 10$^{-3}$ erg s$^{-1}$ cm$^{-3}$ in the upper atmospheres of hot exoplanets. It is expected to be stronger the closer the planet is and the lower the central star mass is, as these conditions maximize the strength of the ambient magnetic field around the planet. We confirm that Ohmic heating can play an important role in setting the thermal budget of the upper atmosphere of hot exoplanets, and can even surpass the XUV heating in the most favorable cases. When it is strong, a corollary is that the upper atmosphere screens efficiently time-varying external magnetic fields, preventing them to penetrate deeper in the atmosphere or inside the planet itself. We find that both Trappist-1b and $\pi$ Men c are likely subject to intense Ohmic heating.

Figures

Figures reproduced from arXiv: 2412.14072 by the authors.

Figure 1
Figure 1. Top panel: schematic of the geometry considered in this work. The central star (orange circle) creates a dipole field (gray arrows and lines) in which the planet (blue open circle symbol) orbits (large blue circle). The x axis corresponds to the star-planet direction at all times, and the y axis the direction of the orbit. The z axis (not shown here) is perpendicular to the orbital plane. Bottom panel: the time-vary… view at source ↗
Figure 2
Figure 2. Penetration of time-varying magnetic field Bsw(panels a, c, e) and associated Ohmic heating Q (panels b, d, f) in the case of a constant σP atmospheric layer of 1,000 km, subject to a time-varying magnetic field of 4 mG imposed as a boundary condition at the top of the layer. The Hall conductivity is neglected here (σH = 0) and the Pedersen conductivity is constant in space. The dotted black line in panels a), c) an… view at source ↗
Figure 3
Figure 3. Same experimental setup than in panels e) and f) of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: The three upper panels a-b-c present the profiles of the number density of ions (colored lines) and electrons (black line) as a function of height in the upper atmosphere of the Earth (panel a), π Men c (panel b) and Trappist-1 b (panel c). Panel d) shows the electron …
Figure 5
Figure 5. Figure 5: Conductivities, penetration and Ohmic heating in the atmospheres of Trappist-1 b (top panels) and π Men c (bottom panels). Left panels (a and d) represent the parallel (dotted gray lines), Hall (dashed colored lines) and Pedersen (solid colored lines) conductivities as…
Figure 6
Figure 6. Figure 6: Ohmic heating and field transmission in the upper atmospheres of Trappist-1 b (left column) and π Men c (right column). The upper panels show the heating rate Q at the sonic point rc divided by the heating from photochemistry Qph at the same location, as function of th…
Figure 7
Figure 7. Figure 7: Qmax (Eq. 14) for the population of exoplanets from the exoplanet.eu database, as a function of the orbital distance and the stellar mass. A given rotation rate has been assumed for all stars in each panel, to estimate their magnetic field and the ambient magnetic fiel…

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

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Reference graph

Works this paper leans on

48 extracted references · 44 canonical work pages · cited by 1 Pith paper

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

  3. [3]

    L., et al

    Agol, E., Dorn, C., Grimm, S. L., et al. 2021, PSJ, 2, 1, publisher: IOP ADS Bibcode: 2021PSJ.....2....1A

    work page 2021

  4. [4]

    From Stellar Coron{\ae} to Gyrochronology: a theoretical and observational exploration

    Ahuir, J., Brun, A. S., & Strugarek, A. 2020, A & A, 170, 1, arXiv: 2002.00696

    work page Pith review arXiv 2020

  5. [5]

    H., Marcussen, M

    Albrecht, S. H., Marcussen, M. L., Winn, J. N., Dawson, R. I., & Knudstrup, E. 2021, ApJ, 916, L1, publisher: IOP ADS Bibcode: 2021ApJ...916L...1A

    work page 2021

  6. [6]

    & Stevenson, D

    Batygin, K. & Stevenson, D. J. 2010, ApJ, 714, L238, publisher: IOP ADS Bibcode: 2010ApJ...714L.238B

    work page 2010

  7. [7]

    2022, Rv Geo., 60, e2022RG000792, aDS Bibcode: 2022RvGeo..6000792B

    Bilitza, D., Pezzopane, M., Truhlik, V., et al. 2022, Rv Geo., 60, e2022RG000792, aDS Bibcode: 2022RvGeo..6000792B

    work page 2022

  8. [8]

    Bourrier, V., Osorio, M. R. Z., Allart, R., et al. 2022, A & A, 663, A160, publisher: EDP Sciences

    work page 2022

Show all 48 references
  1. [9]

    S., Strugarek, A., Noraz, Q., et al

    Brun, A. S., Strugarek, A., Noraz, Q., et al. 2022, ApJ, 926, 21, publisher: IOP Publishing

    2022

  2. [10]

    Chapman, S. 1956, N. Cim., 4, 1385, aDS Bibcode: 1956NCim....4S1385C

    1956

  3. [11]

    Christensen, U. R. & Aubert, J. 2006, Geo. J. I., 166, 97, place: AA(Max-Planck-Institut für Sonnensystemforschung, Katlenburg-Lindau, Germany. christensen@mps.mpg.de), AB(Institut de Physique du Globe de Paris, Paris, France)

    2006

  4. [12]

    Chyba, C. F. & Hand, K. P. 2021, ApJL, 922, L38

    2021

  5. [13]

    F., Hand, K

    Chyba, C. F., Hand, K. P., & Thomas, P. J. 2021, Icarus, 360, 114360, aDS Bibcode: 2021Icar..36014360C

    2021

  6. [14]

    2024, ApJ, 962, 157, publisher: IOP ADS Bibcode: 2024ApJ...962..157C

    Cohen, O., Glocer, A., Garraffo, C., et al. 2024, ApJ, 962, 157, publisher: IOP ADS Bibcode: 2024ApJ...962..157C

    2024

  7. [15]

    J., et al

    Dietrich, W., Kumar, S., Poser, A. J., et al. 2022, MNRAS, 517, 3113, aDS Bibcode: 2022MNRAS.517.3113D

    2022

  8. [16]

    H., et al

    Gandolfi, D., Barragán, O., Livingston, J. H., et al. 2018, A & A, 619, L10, aDS Bibcode: 2018A&A...619L..10G

    2018

  9. [17]

    2023, A & A, 672, A77

    García Muñoz, A. 2023, A & A, 672, A77

    2023

  10. [18]

    2021, ApJ, 907, L36, publisher: IOP ADS Bibcode: 2021ApJ...907L..36G

    García Muñoz, A., Fossati, L., Youngblood, A., et al. 2021, ApJ, 907, L36, publisher: IOP ADS Bibcode: 2021ApJ...907L..36G

    2021

  11. [19]

    2020, ApJ, 888, L21, publisher: IOP ADS Bibcode: 2020ApJ...888L..21G

    García Muñoz, A., Youngblood, A., Fossati, L., et al. 2020, ApJ, 888, L21, publisher: IOP ADS Bibcode: 2020ApJ...888L..21G

    2020

  12. [20]

    2023, A & A, 680, A33, aDS Bibcode: 2023A&A...680A..33G

    Gillet, A., García Muñoz, A., & Strugarek, A. 2023, A & A, 680, A33, aDS Bibcode: 2023A&A...680A..33G

    2023

  13. [21]

    Gillon, M., Triaud, A. H. M. J., Demory, B.-O., et al. 2017, Nature, 542, 456, aDS Bibcode: 2017Natur.542..456G

    2017

  14. [22]

    & Petitdemange, L

    Gissinger, C. & Petitdemange, L. 2019, Nat. Astr., 1, 878, arXiv: 1710.08761

    2019 arXiv

  15. [23]

    2022, ApJ, 940, 123

    Hardy, R., Cumming, A., & Charbonneau, P. 2022, ApJ, 940, 123

    2022

  16. [24]

    & Cumming, A

    Huang, X. & Cumming, A. 2012, ApJ, 757, 47

    2012

  17. [25]

    P., Güdel, M., Lammer, H., & Kislyakova, K

    Johnstone, C. P., Güdel, M., Lammer, H., & Kislyakova, K. G. 2018, A & A, 617, arXiv: 1806.06897

    2018 arXiv

  18. [26]

    & Noack, L

    Kislyakova, K. & Noack, L. 2020, A & A, 636, L10, aDS Bibcode: 2020A&A...636L..10K

    2020

  19. [27]

    G., Fossati, L., Johnstone, C

    Kislyakova, K. G., Fossati, L., Johnstone, C. P., et al. 2018, ApJ, 858, 105, publisher: IOP ADS Bibcode: 2018ApJ...858..105K

    2018

  20. [28]

    G., Noack, L., Johnstone, C

    Kislyakova, K. G., Noack, L., Johnstone, C. P., et al. 2017, Nat. Astr., 1, 878, aDS Bibcode: 2017NatAs...1..878K

    2017

  21. [29]

    2022, A & A, 658, L7, aDS Bibcode: 2022A&A...658L...7K

    Knierim, H., Batygin, K., & Bitsch, B. 2022, A & A, 658, L7, aDS Bibcode: 2022A&A...658L...7K

    2022

  22. [30]

    Lu, Y., See, V., Amard, L., Angus, R., & Matt, S. P. 2023, Nat. Astr., 8, 223

    2023

  23. [31]

    2017, ApJ, 851, 94, publisher: IOP ADS Bibcode: 2017ApJ...851...94L

    Luger, R., Lustig-Yaeger, J., & Agol, E. 2017, ApJ, 851, 94, publisher: IOP ADS Bibcode: 2017ApJ...851...94L

    2017

  24. [32]

    1977, JATP, 39, 1041

    Maeda, K.-i. 1977, JATP, 39, 1041

    1977

  25. [33]

    McIntyre, S. R. N., Lineweaver, C. H., & Ireland, M. J. 2019, MNRAS, 4012, 3999, publisher: Oxford University Press

    2019

  26. [34]

    2010, MNRAS, 407, 2269

    Morin, J., Donati, J.-F., Petit, P., et al. 2010, MNRAS, 407, 2269

    2010

  27. [35]

    & Heyvaerts, J

    Norman, C. & Heyvaerts, J. 1985, A & A, 147, 247, aDS Bibcode: 1985A&A...147..247N

    1985

  28. [36]

    Parkinson, W. D. 1983, Introduction to geomagnetism (Scottish Academic Press)

    1983

  29. [37]

    M., Hedin, A

    Picone, J. M., Hedin, A. E., Drob, D. P., & Aikin, A. C. 2002, JGR: Space Physics, 107

    2002

  30. [38]

    & Basri, G

    Reiners, A. & Basri, G. 2010, ApJ, 710, 924, publisher: IOP ADS Bibcode: 2010ApJ...710..924R

    2010

  31. [39]

    J., et al

    Reiners, A., Shulyak, D., Käpylä, P. J., et al. 2022, A & A, 662, A41, aDS Bibcode: 2022A&A...662A..41R

    2022

  32. [40]

    Rogers, T. M. & Komacek, T. D. 2014, ApJ, 794, 132

    2014

  33. [41]

    M., Velli, M., et al

    Réville, V., Jasinski, J. M., Velli, M., et al. 2024, ApJ, 976, 65, publisher: The American Astronomical Society

    2024

  34. [42]

    M., & Glassmeier, K

    Saur, J., Neubauer, F. M., & Glassmeier, K. H. 2010, SSR, 152, 391

    2010

  35. [43]

    & Nagy, A

    Schunk, R. & Nagy, A. 2009, Ionospheres: Physics , Plasma Physics , and Chemistry , 2nd edn. (Cambridge University Press)

    2009

  36. [44]

    Schunk, R. W. & Nagy, A. F. 1980, Rev. Geo., 18, 813

    1980

  37. [45]

    2024, Comptes Rendus Physique, 24, 138, aDS Bibcode: 2024CRPhy..24S.138S

    Strugarek, A. 2024, Comptes Rendus Physique, 24, 138, aDS Bibcode: 2024CRPhy..24S.138S

    2024

  38. [46]

    Strugarek, A., Beaudoin, P., Charbonneau, P., & Brun, A. S. 2018, ApJ, 863, 35, publisher: IOP Publishing

    2018

  39. [47]

    S., & do Nascimento, J.-D

    Strugarek, A., Beaudoin, P., Charbonneau, P., Brun, A. S., & do Nascimento, J.-D. 2017, Science, 357, 185

    2017

  40. [48]

    J., Froning, C

    Wilson, D. J., Froning, C. S., Duvvuri, G. M., et al. 2021, ApJ, 911, 18, publisher: IOP ADS Bibcode: 2021ApJ...911...18W

    2021

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