Pith. sign in

REVIEW 4 major objections 10 minor 78 references

In a rotating magnetised spherical shell, the tidal response depends on magnetic field geometry as much as on field strength: poloidal fields modify the flow at smaller Lehnert numbers and add high-frequency Alfvénic resonances, while a pur

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-03 12:52 UTC pith:AHNQGJGJ

load-bearing objection Systematic linear MHD tidal survey with solid numerics, but the headline viscous-vs-Ohmic claim rests on the Pm=1 assumption and lacks a direct sensitivity check. the 4 major comments →

arxiv 2607.29141 v1 pith:AHNQGJGJ submitted 2026-07-31 astro-ph.EP astro-ph.SRphysics.flu-dyn

Tidal dissipation in magnetised, rotating stars and planets: linear calculations exploring various magnetic field configurations

Shijun Chu , Zhao Guo , Aur\'elie Astoul , Adrian J. Barker , Rainer Hollerbach This is my paper
classification astro-ph.EP astro-ph.SRphysics.flu-dyn
keywords tidal dissipationmagneto-inertial wavesmagnetic field geometryrotating spherical shellOhmic dissipationviscous dissipationAlfvénic resonancesfrequency-averaged tidal power
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to establish that magnetic field geometry—not just field strength—is a controlling parameter for wavelike tidal dissipation in the convective envelopes of stars and planets. Using linear magnetohydrodynamic calculations in a rotating spherical shell, it compares seven background field configurations and shows that fields with a strong poloidal component alter the tidal flow at smaller Lehnert numbers and excite high-frequency Alfvénic resonances, while a purely toroidal field leaves the flow nearly unchanged. It also finds that with turbulent viscosity (Ekman number ≈1e-5, magnetic Prandtl number ≈1), viscous dissipation stays comparable to Ohmic dissipation for strong fields, contrary to earlier small-Pm studies. The frequency-averaged tidal power is largely insensitive to the field in most configurations, with significant exceptions for free-decay poloidal fields. If true, this means tidal evolution models that ignore field geometry may mispredict dissipation at individual frequencies, though secular evolution may be more robust.

Core claim

The paper establishes that in a rotating, magnetised, incompressible spherical-shell model of a convective envelope, the linear tidal response at a given forcing frequency depends strongly on both the strength and the geometry of the background magnetic field. Fields with significant poloidal components—aligned and tilted dipoles, free-decay poloidal dipoles and quadrupoles—modify the flow at smaller Lehnert numbers and create high-frequency Alfvénic resonances outside the inertial frequency band |ω|<2, while a purely toroidal axisymmetric field has little effect. At the adopted turbulent diffusivities (Ek≈1e-5, Pm≈1), viscous dissipation remains comparable to Ohmic dissipation for strong fi

What carries the argument

The central object is the linearised MHD system in an incompressible, uniformly rotating spherical shell with an imposed steady background field, governed by the Lehnert number Le (the ratio of Alfvén speed to rotational velocity), the Ekman number Ek, and the magnetic Ekman number Em. The workhorse is the frequency-dependent tidal power and its decomposition into viscous dissipation, Ohmic dissipation, and the work done by the background Lorentz force; peaks outside the inertial band are matched to eigenfrequencies of the least-damped magneto-inertial modes from the unforced eigenvalue problem. The geometric survey—dipoles, tilted dipoles, a Malkus toroidal field, a Prendergast mixed field,

Load-bearing premise

The load-bearing premise is that the adopted Ekman number Ek≈1e-5 and magnetic Prandtl number Pm≈1 are the appropriate effective turbulent diffusivities of a convective envelope and that the background magnetic field remains perfectly steady; if the real effective Pm is much smaller than unity or the field is not sustained, the claimed comparability of viscous and Ohmic dissipation and the computed resonance spectrum would not carry over.

What would settle it

A decisive calculation: for an aligned dipole at Le=5e-2, Ek=1e-5, and ω=1.1, vary Pm from 1 down to 1e-4 and record the ratio D_ohm/D_vis; if the ratio grows from O(1) to well above 10 at Pm=1e-4 while poloidal-geometry effects persist, then the comparability claim is an artifact of the adopted turbulent Pm and would not apply to microscopic-Pm bodies.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • At a fixed tidal frequency, poloidal field geometries modify tidal flows and dissipation at smaller Le than a purely toroidal field, so the magnetic field's shape, not just its strength, controls the wavelike response.
  • Strong fields can move tidal dissipation outside the inertial frequency range because fast magneto-inertial or Alfvénic waves are resonantly excited when the forcing frequency matches weakly damped eigenmodes.
  • With turbulent diffusivities (Ek≈1e-5, Pm≈1), viscous dissipation remains comparable to Ohmic dissipation for strong fields, so convective turbulence contributes to tidal damping even in magnetised regimes.
  • Frequency-averaged tidal power stays close to the standard hydrodynamic prediction for most field configurations, so long-term spin and orbital evolution may be relatively insensitive to magnetic geometry; strong free-decay poloidal fields are the exception, with deviations up to about 37%.
  • Tilted dipoles break axisymmetry and produce a time-periodic linear response, including oscillatory zonal flows, so magnetic-field and rotation-axis misalignment can qualitatively change tidal dynamics even in linear theory.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If real convective envelopes have effective magnetic Prandtl numbers much lower than unity, the paper's own Pm scans suggest Ohmic dissipation would peak at intermediate Pm and then fall, so the conclusion of comparable viscous and Ohmic dissipation may not extrapolate to microscopic-Pm bodies; the geometry-dependent resonance structure, however, could persist with stronger Ohmic damping of high-f
  • The linear oscillatory zonal flows generated by tilted fields suggest a route to magnetic-field-driven differential rotation that does not require nonlinear Reynolds stresses; a testable extension is whether these flows survive in nonlinear simulations with finite tidal amplitude.
  • The breakdown of frequency-averaged dissipation for non-current-free poloidal fields implies that the standard impulsive-formalism formula should carry a magnetic correction term proportional to the work done by the background Lorentz force; deriving such a term for a poloidal field of given energy would be a direct follow-up.
  • The same spherical-shell linear machinery could be applied to other low-frequency forcings—such as free inner-core nutation or obliquity tides—to see whether the poloidal-versus-toroidal hierarchy and high-frequency Alfvénic resonances generalise.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 10 minor

Summary. This paper studies linear tidal forcing of magneto-inertial waves in a rotating, incompressible spherical shell, covering seven background magnetic field configurations (aligned and tilted dipoles, Malkus torque-free field, Prendergast field, and free-decay poloidal dipole/quadrupole fields) at fixed diffusivity Ek=1e-5 and Pm=1 in the baseline (§3.1). The authors use Dedalus boundary-value solves for axisymmetric fields and MagIC initial-value solves for tilted dipoles, verify energy balance, and examine the response versus Lehnert number, frequency, shell thickness α, Ek, and Pm. The main claims are: (i) field geometry—not just strength—controls the linear tidal response, with poloidal components more effective and toroidal Malkus fields weak; (ii) misaligned dipoles produce linear oscillatory zonal flows; (iii) high-frequency Alfvénic resonances outside the inertial range appear for strong fields and are identified with least-damped magneto-inertial eigenmodes; (iv) with turbulent Pm=O(1), viscous dissipation remains comparable to Ohmic dissipation for strong fields, in contrast to Lin & Ogilvie (2018); and (v) frequency-averaged tidal power is mostly insensitive to magnetic fields, except for free-decay poloidal fields where the background Lorentz work breaks the Ogilvie (2013) prediction.

Significance. If the results hold, the paper provides the broadest numerical survey to date of magnetic geometries in linear tidal calculations and identifies several physically interesting effects: a geometry-dependent hierarchy of magnetic sensitivity, linear zonal-flow generation for tilted fields, and a caveat to the Lin & Ogilvie (2018) conclusion that Ohmic dissipation dominates at strong fields. The computational work is carefully cross-checked (Dedalus vs MagIC, energy balance to <1%, eigenmode validation of resonances) and the paper is largely reproducible in structure. However, the headline contrast with previous work on viscous-versus-Ohmic dissipation rests on the Pm=O(1) turbulent-viscosity assumption, which the paper itself acknowledges (§2.1) to be uncertain for real convective envelopes; the paper's own Pm-scan (§3.4) shows maximum Ohmic dissipation at Pm≈1e-3–1e-2, precisely the microscopic/Pm range most relevant to stars and giant planets. The central geometric claims and the frequency-averaged insensitivity are more robust than the Pm=1 dissipation-balance claim. The paper would be a useful contribution if the Pm-dependence of the D_ohm/D_vis ratio is quantified and the dissip

major comments (4)
  1. [§3.1, Fig. 2; §3.4, Fig. 12; §2.1, Eq. (5)–(6)] The abstract's central quantitative claim—'viscous dissipation remains comparable to Ohmic dissipation for strong fields, in contrast to previous studies'—is established only for Pm=1, Ek=1e-5 (§3.1). Yet the paper itself quotes (§2.1) solar convective-envelope Pm≈8e-3 (density-weighted) and planetary Pm≈1e-6–1e-5, and Fig. 12(a,b) shows D_ohm peaking near Pm≈1e-2 (Le=1e-2) and Pm≈1e-3 (Le=5e-2). Since Fig. 12 plots D_ohm but not D_vis, the 'comparable' statement is not verified for Pm≈1e-2–1e-3. Please add a direct D_ohm/D_vis ratio scan over Pm (e.g., at the Fig. 12 maxima and at Pm=8e-3), or soften the abstract/conclusions to state that the result holds for Pm=O(1) and that for Pm≈1e-2 the ratio may differ. Without this, the contrast with Lin & Ogilvie (2018) appears to be a consequence of the chosen effective Pm rather than a robust physical finding.
  2. [§3.4, Fig. 12] The interpretation of the Pm-scan is incomplete: Fig. 12 shows D_ohm and P_t, but not D_vis, so one cannot determine whether the decrease of D_ohm at large Pm (e.g., Pm=10) is compensated by increased viscous dissipation. The text states that at large Pm 'the tidal flow becomes insensitive to further increases in Pm' and that the reduction in D_ohm is due to smaller Em. This is plausible, but the claimed 'comparable' balance requires D_vis, which is absent. Please show D_vis (or D_ohm/D_vis) in a Pm-scan figure, even for one representative field configuration (e.g., aligned dipole), to support the central dissipation-balance claim across Pm.
  3. [§3.5, Table 1, Eq. (37)] The frequency-averaged values are reported without error estimates. The paper states frequency resolutions were 'sufficient' but also notes that tilted-dipole cases at α=0.5, Pm=1, Ek=1e-5 deviate from the predicted value by a few percent 'almost certainly' due to lower resolution (§3.5). For a quantitative comparison of the free-decay-field discrepancies (up to 37%) to the W_lf-based explanation, the numerical integration error should be estimated (e.g., varying Δω, or comparing with higher-resolution runs for at least one case). The discussion of integrals ∫ W_lf/ω² dω would also benefit from reporting the integrand's convergence with the same frequency range used in Table 1.
  4. [§3.4, Fig. 14] The Ek-scan is limited to three values (1e-4, 1e-5, 1e-6) and two field configurations. The conclusion that 'reducing Ek has little effect on inertial-wave dynamics but enhances high-frequency Alfvénic resonances' is consistent with the presented results, but the associated claim in the conclusions that 'turbulent viscosity continues to contribute significantly' relies on Ek=1e-5 and Pm=1. Since the paper explicitly acknowledges that microscopic Ek is orders of magnitude smaller (Ek≈1e-15 in stars), the extrapolation to astrophysical parameters should be more clearly flagged as an assumption. I do not require additional calculations, but the current wording in §3.1 and the abstract could be read as a general statement rather than a parameter-choice conditional.
minor comments (10)
  1. [Abstract] The phrase 'viscous dissipation remains comparable to Ohmic dissipation for strong fields' should be qualified with 'for Pm=O(1) and Ek=1e-5' to avoid overgeneralization, especially given the Pm values quoted in §2.1.
  2. [§2.1, Eq. (7)] The forcing expression (7) would benefit from a brief note on the derivation of the pre-factor and the sign convention; the footnote about the corrected pre-factor compared to AB22/AB23 is helpful, but the equation itself is introduced without a derivation reference aside from Ogilvie (2013).
  3. [§2.2.3, Eq. (12)–(14)] The Prendergast field is described as confined to the outer boundary, but the shell also has an inner boundary at r=α. Clarify whether the field is confined to the entire shell (vanishing at r=1) and how it behaves at the inner boundary (is it singular or nonzero?).
  4. [§3.1, Figs. 2–4] The tilted-dipole results are presented with time-averaged quantities (presumably time-averaged over the periodic steady state), but this averaging is not explicitly defined in the text or figure captions. Please state the averaging interval and that the quoted P_t and D_ohm/D_vis are time-averaged over one oscillation period.
  5. [§3.2, Fig. 8] The figure shows Ohmic dissipation and tidal power, but the reader must infer the viscous dissipation from the difference (since P_t≈D_vis+D_ohm+W_lf in some cases). For the cases where W_lf is significant (Malkus, Prendergast, free-decay), the total dissipation is not equal to P_t, so the 'Ohmic dissipation comparable to viscous dissipation' statement in §3.2 should at least note the W_lf contribution in the caption or text.
  6. [§3.3, Fig. 10] Fig. 10 omits tilted dipole at Le=5e-2 due to computational cost, which is fine, but the text could explicitly note that the comparison at large Le does not include the strongly tilted cases.
  7. [§3.5, Eq. (38)] The order-of-magnitude estimate for W_lf/P_t uses several assumptions (ℓ~R, u~C_t Rω, b~ω_A/ω u). The final point about the Ek-dependent amplification factor is interesting but should be referenced in the conclusions, since it is a potentially important caveat to the 'magnetic field unlikely to be dominant energy source' statement.
  8. [References] The reference list contains some entries with no page numbers (e.g., Sethi et al. 2026, Spejcher et al. 2025). If this is a preprint, this is fine; but if it is submitted to MNRAS, the journal style requires full publication data where available.
  9. [Table 1] The table caption states 'Predicted' from Eq. (37), but the columns for Malkus, Prendergast, etc. are missing for some rows (e.g., tilted dipoles at Le=1e-2, Ek=1e-4). The dashes should be spelled out or replaced with '—' and a note explaining why those cases were not run.
  10. [§4 Conclusions] The conclusions repeat the abstract's unqualified claim about viscous dissipation remaining comparable to Ohmic dissipation. Please add the Pm and Ek dependence in this summary, consistent with the suggested major revision.

Circularity Check

0 steps flagged

No significant circularity: the paper solves a forced linear system, benchmarks against external analytic results, and its main caveats are parameter sensitivities, not fitted predictions.

full rationale

The paper solves the linearised MHD system (Eqs. 1–4) with imposed background fields and tidal forcing (Eq. 7), then reports dissipation rates (Eqs. 29–30) and compares frequency-averaged power to the external analytic prediction of Ogilvie (2013) (Eqs. 34–37). No output quantity is used to set an input parameter: C_t is set to 1 with explicit rescaling; field-normalisation factors S_m, S_d, S_qd equalize volume-integrated magnetic energy for fair comparison, not to match dissipation; and Pm and Ek are chosen a priori from mixing-length arguments and then varied in §3.4. Thus the 'viscous vs Ohmic' result is a parameter-sensitivity statement, not a fitted prediction. The resonant interpretation in Fig. 9 is checked by solving the eigenvalue problem of the same linear operator, which is a genuine internal consistency test rather than a circular derivation. Self-citations (Astoul & Barker 2022, 2023, 2025) are contextual (forcing decomposition, prior nonlinear simulations) and are not used to justify the central claims; the frequency-averaged benchmark is an external analytic result. The main caveats — uncertain effective Pm and the steady-background-field assumption — are explicitly acknowledged in §2.1 and affect applicability, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 7 axioms · 0 invented entities

The paper does not fit free parameters to its output. The scaling factors S_m, S_d, S_qd are fixed by equalizing volume-integrated magnetic energy, not by matching results. The load-bearing assumptions are the incompressible-shell model, the imposed steady background field, linearity, and the turbulent values of Ek and Pm.

axioms (7)
  • domain assumption The convective envelope is modeled as an incompressible, constant-density fluid in a spherical shell.
    Section 2.1 sets density to 1; this is a standard idealization but omits stratification and compressibility, which can alter wave propagation in real stars.
  • domain assumption The background magnetic field is steady, imposed, and perfectly maintained by an unmodeled dynamo.
    Section 2.1 states the field is 'assumed to be perfectly maintained by a turbulent convective dynamo... we do not explicitly model.' This ignores back-reaction and field evolution.
  • domain assumption The tidal response is linear: C_t is small and nonlinear terms are neglected.
    Section 2.1: 'The assumption of linear tides is formally appropriate if C_t << 1'; the paper notes nonlinear effects could matter even for small C_t.
  • domain assumption The wavelike tide is driven only by the Coriolis acceleration acting on the equilibrium tide, with impenetrable boundary conditions.
    Section 2.1, Eq. (7); this is the standard construction from Ogilvie (2013) and Lin & Ogilvie (2018), and excludes other forcing contributions such as the Lorentz force on the equilibrium tide (acknowledged in Section 3.5).
  • domain assumption Stress-free velocity and insulating magnetic boundary conditions are applicable at both boundaries.
    Section 2.1, Eqs. (8)-(9): the conditions minimize coupling; the insulating condition is an approximation for stars with radiative cores and for the external vacuum.
  • domain assumption Ek ≈ 10^-5 and Pm = O(1) represent turbulent viscosity and magnetic diffusivity in convective envelopes.
    Sections 2.1 and 3.1: the paper adopts mixing-length based values; if actual effective Pm is much smaller, the central result on comparable viscous/Ohmic dissipation would not hold.
  • domain assumption Free-decay and Prendergast fields are stable enough over the simulation timescale.
    Section 2.2.3: the Prendergast field is resistively unstable on long timescales but stable within 10^4 Ω^-1 in the authors' tests.

pith-pipeline@v1.3.0-daily-deepseek · 26525 in / 11805 out tokens · 116500 ms · 2026-08-03T12:52:54.406031+00:00 · methodology

0 comments
read the original abstract

We study tidal flows in the convective envelopes of rotating, magnetised fluid bodies, such as low-mass stars and giant planets. In well-mixed convective regions, (magneto-)inertial waves are linearly excited by tidal forcing, and their dissipation can dominantly drive spin and orbital evolution in many close star-planet and binary star systems. We perform linear magnetohydrodynamic calculations of wavelike tides in spherical-shell geometry of a tidally-forced, rotating, incompressible, viscous and non-ideal magnetised fluid. Our calculations consider the widest range of magnetic field configurations to date (including both aligned and misaligned dipole fields, free-decay dipole and quadrupole fields, azimuthal "Malkus fields" and mixed poloidal-toroidal "Prendergast fields") to analyse the effects of magnetic fields on the wavelike response and dissipation. We find that the tidal response at a given frequency depends strongly on both magnetic field strength and geometry. Magnetic fields with strong poloidal components modify the flow more efficiently and introduce high-frequency Alfv\'enic resonances associated with weakly damped eigenmodes. When an enhanced (turbulent) viscosity is adopted, we find that viscous dissipation remains comparable to Ohmic dissipation for strong fields, in contrast to previous studies in which Ohmic dissipation was argued to dominate. We also explore the variation in magnetic effects as the shell thickness, magnetic Prandtl and Ekman numbers are varied. Finally, the frequency-averaged tidal power is found to be largely insensitive to the magnetic field in most cases, though significant deviations are found for free-decay fields. Our results have important implications for the tidal evolution of magnetised, rotating stars and planets.

Figures

Figures reproduced from arXiv: 2607.29141 by Adrian J. Barker, Aur\'elie Astoul, Rainer Hollerbach, Shijun Chu, Zhao Guo.

Figure 1
Figure 1. Figure 1: Illustration of the three-dimensional magnetic field lines for each of the background magnetic fields we consider. (𝑎) Malkus field; (𝑏) Prendergast field; (𝑐) Aligned dipolar field; (𝑑) tilted dipolar field with 𝜃0 = 𝜋/4; (𝑒) tilted dipolar field with 𝜃0 = 𝜋/2. ( 𝑓 ) Axisymmetric free-decay poloidal dipole field. (𝑔) Axisymmetric free-decay quadrupole field. Colours denote the strength of the magnetic fie… view at source ↗
Figure 3
Figure 3. Figure 3: (𝑎) Time evolution of tidal power for the periodic steady-state tidal flow for the case of a tilted dipolar field (𝜃0 = 𝜋/4) at various Le. (𝑏) Time evolution of kinetic energy (𝐸𝑢 = [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: (𝑎) Ohmic dissipation 𝐷ohm (solid lines), viscous dissipation 𝐷vis (dotted lines) and (𝑏) tidal power 𝑃t as a function of Le considering various background magnetic fields at 𝛼 = 0.5, 𝜔 = 1.1, Pm = 1 , Ek = 10−5 . The lines with 𝜃0 = 0, 𝜋/4, 𝜋/2 indicate the aligned dipolar field, and tilted dipolar fields with an angle of 𝜋/4 and 𝜋/2, respectively. (𝑐) Tidal power 𝑃t and the associated energy balance acco… view at source ↗
Figure 4
Figure 4. Figure 4: Azimuthally-averaged azimuthal velocity and azimuthal magnetic field in the meridional plane. ⟨·⟩𝜙 indicates the azimuthal average operation on the final periodic (but otherwise steady) tidal flow in the presence of a tilted dipolar field (𝜃0 = 𝜋/4) at various Le and 𝜔 = 1.1 , Ek = 10−5 , 𝛼 = 0.5 , Pm = 1. (𝑎, 𝑑) Le = 10−3 ; (𝑏, 𝑒) Le = 10−2 ;(𝑐, 𝑓 ) Le = 5 × 10−2 . in other cases (as indicated by the colo… view at source ↗
Figure 5
Figure 5. Figure 5: Pseudo-colour maps in the meridional plane and iso-surfaces in the shell for (𝑎) velocity perturbation |𝒖| and (𝑏 − ℎ) magnetic perturbations |𝑩| when considering different background magnetic fields 𝑩0 at Le = 10−3 and 𝜔 = 1.1 , Ek = 10−5 , 𝛼 = 0.5 , Pm = 1. As the velocity perturbation is almost unchanged for different 𝑩0 for this Le, only one case is shown. (𝑏 − ℎ) represents the magnetic perturbations … view at source ↗
Figure 6
Figure 6. Figure 6: Pseudo-colour maps in the meridional plane and iso-surfaces in the shell for velocity |𝒖| (upper) and magnetic perturbations |𝑩| (bottom) when considering different background magnetic fields 𝑩0 at Le = 10−2 and 𝜔 = 1.1 , Ek = 10−5 , 𝛼 = 0.5 , Pm = 1. (𝑎 − 𝑔) represent the velocity perturbations 𝒖 with the Malkus field, Prendergast field, aligned dipolar field, tilted dipolar (𝜃0 = 𝜋/4), tilted dipolar (𝜃0… view at source ↗
Figure 7
Figure 7. Figure 7: Pseudo-colour maps in the meridional plane and iso-surfaces in the shell for velocity |𝒖| (upper) and magnetic perturbations |𝑩| (bottom) when considering different background magnetic fields 𝑩0 at Le = 5 × 10−2 and 𝜔 = 1.1 , Ek = 10−5 , 𝛼 = 0.5 , Pm = 1. (𝑎 − 𝑔) represent the velocity perturbations 𝒖 with the Malkus field, Prendergast field, aligned dipolar field, tilted dipolar (𝜃0 = 𝜋/4), tilted dipolar… view at source ↗
Figure 8
Figure 8. Figure 8: Ohmic dissipation 𝐷ohm (left) and tidal power 𝑃t (right) versus tidal frequency considering different background magnetic fields at 𝛼 = 0.5, Pm = 1, Ek = 10−5 . (𝑎) Le = 10−3 . (𝑏) Le = 10−2 . (𝑐) Le = 5 × 10−2 for −3 < 𝜔 < 3. (𝑑) Le = 5 × 10−2 for −6 < 𝜔 < 6. Le = 5×10−2 . Similar trends are found for other magnetic field con￾figurations. This confirms that magnetic diffusivity primarily damps high-freque… view at source ↗
Figure 9
Figure 9. Figure 9: Tidal power versus tidal frequency together with the damping rates (imaginary parts of the frequency) and frequencies of the least-damped eigenmodes at Le = 5 × 10−2 when a free-decay poloidal dipole field (𝑙 = 1) is adopted as the background magnetic field. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Tidal power 𝑃t versus tidal frequency considering different back￾ground magnetic field strengths and configurations for 𝛼 = 0.8, Pm = 1 , Ek = 10−5 ; (𝑎) Le = 10−2 . (𝑏, 𝑐) Le = 5 × 10−2 with −3 < 𝜔 < 3 and −6 < 𝜔 < 6. parameter survey. Instead, they are intended to illustrate the most important changes in the roles of viscous and magnetic diffusion in shaping the tidal response. In particular, the trends… view at source ↗
Figure 12
Figure 12. Figure 12: Ohmic dissipation 𝐷ohm versus Pm considering various background magnetic fields at (𝑎) Le = 10−2 and (𝑏) Le = 5 × 10−2 . Tidal power 𝑃t versus Pm considering various background magnetic fields at (𝑐) Le = 10−2 and (𝑑) Le = 5 × 10−2 . The parameters are 𝜔 = 1.1, 𝛼 = 0.5, Ek = 10−5 . The tilted dipolar field is only considered at Le = 10−2 due to the greater computational costs of performing the initial val… view at source ↗
Figure 14
Figure 14. Figure 14: Tidal power 𝑃t versus tidal frequency considering different back￾ground magnetic fields at 𝛼 = 0.5 and different Ek; (𝑎) Le = 10−2 and (𝑏) Le = 5 × 10−2 . Solid lines represent cases with a (radially decaying) dipolar field, while dotted lines represent cases with a free-decay poloidal dipole field. MNRAS 000, 1–19 (2026) [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Ratio of work done by background Lorentz forces 𝑊lf to the tidal power 𝑃t for cases with Ek = 10−5 , 𝛼 = 0.5, Ek = 10−5 . (a) Le = 10−2 ;(b) Le = 5 × 10−2 . the lengthscale of the field is 𝑑 ∼ 2 × 108 m, then 𝑊lf/𝑃t ∼ 0.03, and the magnetic energy would exceed the energy in the tidal flow or convection. Furthermore, it is possible that 𝑊lf/𝑃t could be very large on small scales, so the work done by Lorent… view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

78 extracted references · 6 canonical work pages

  1. [1]

    Monthly Notices of the Royal Astronomical Society , volume=

    The effects of non-linearities on tidal flows in the convective envelopes of rotating stars and planets in exoplanetary systems , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2022 , publisher=

    2022

  2. [2]

    , keywords =

    Tidally Driven Inertial Waves Enhance Eccentricity Damping and Spin Evolution in Planets and Stars. , keywords =. doi:10.3847/1538-4357/ae18ca , archivePrefix =. 2510.25812 , primaryClass =

    arXiv

  3. [3]

    Celestial Mechanics and Dynamical Astronomy , keywords =

    Effect of the rotation and tidal dissipation history of stars on the evolution of close-in planets. Celestial Mechanics and Dynamical Astronomy , keywords =. doi:10.1007/s10569-016-9690-3 , archivePrefix =. 1603.06268 , primaryClass =

    Pith/arXiv arXiv

  4. [4]

    , keywords =

    Tidal dissipation in evolving low-mass and solar-type stars with predictions for planetary orbital decay. , keywords =. doi:10.1093/mnras/staa2405 , archivePrefix =. 2008.03262 , primaryClass =

    Pith/arXiv arXiv 2008

  5. [5]

    , keywords =

    Tidal interactions in spin-orbit misaligned systems. , keywords =. doi:10.1093/mnras/stx540 , archivePrefix =. 1702.08805 , primaryClass =

    Pith/arXiv arXiv

  6. [6]

    , keywords =

    Tidal Dissipation in Rotating Solar-Type Stars. , keywords =. doi:10.1086/515435 , archivePrefix =. astro-ph/0702492 , primaryClass =

    Pith/arXiv arXiv

  7. [7]

    , keywords =

    Theory of solar oscillations in the inertial frequency range: Linear modes of the convection zone. , keywords =. doi:10.1051/0004-6361/202243164 , archivePrefix =. 2203.04442 , primaryClass =

    Pith/arXiv arXiv

  8. [8]

    , keywords =

    Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity. , keywords =. doi:10.1093/mnras/staa2216 , archivePrefix =. 2007.12624 , primaryClass =

    Pith/arXiv arXiv 2007

  9. [9]

    , keywords =

    Tidal dissipation due to the elliptical instability and turbulent viscosity in convection zones in rotating giant planets and stars. , keywords =. doi:10.1093/mnras/stad1990 , archivePrefix =. 2306.17622 , primaryClass =

    Pith/arXiv arXiv

  10. [10]

    , keywords =

    Tidal dissipation and spin─orbit alignment due to the precessional instability in convection zones in rotating giant planets and stars. , keywords =. doi:10.1093/mnras/staf1882 , archivePrefix =. 2510.25624 , primaryClass =

    arXiv

  11. [11]

    , keywords =

    Tidal Erasure of Stellar Obliquities Constrains the Timing of Hot Jupiter Formation. , keywords =. doi:10.3847/1538-4357/ac4993 , archivePrefix =. 2201.03653 , primaryClass =

    Pith/arXiv arXiv

  12. [12]

    , keywords =

    Influence of stellar structure, evolution, and rotation on the tidal damping of exoplanetary spin-orbit angles. , keywords =. doi:10.1051/0004-6361/201732538 , archivePrefix =. 1803.09661 , primaryClass =

    Pith/arXiv arXiv

  13. [13]

    , keywords =

    On turbulence driven by axial precession and tidal evolution of the spin-orbit angle of close-in giant planets. , keywords =. doi:10.1093/mnras/stw1172 , archivePrefix =. 1605.03867 , primaryClass =

    Pith/arXiv arXiv

  14. [14]

    , keywords =

    Tidal dissipation in planet-hosting stars: damping of spin-orbit misalignment and survival of hot Jupiters. , keywords =. doi:10.1111/j.1365-2966.2012.20893.x , archivePrefix =. 1109.4703 , primaryClass =

    arXiv 2012

  15. [15]

    Influence of secular evolution on their population

    Magnetic and tidal migration of close-in planets. Influence of secular evolution on their population. , keywords =. doi:10.1051/0004-6361/202040173 , archivePrefix =. 2104.01004 , primaryClass =

    Pith/arXiv arXiv

  16. [16]

    , keywords =

    Tidal migration of hot Jupiters: introducing the impact of gravity wave dissipation. , keywords =. doi:10.1093/mnras/stab2768 , archivePrefix =. 2109.09257 , primaryClass =

    Pith/arXiv arXiv

  17. [17]

    3D Obliquities of Five Low-Mass Eclipsing Binaries

    The EBLM Project XVIII. 3D Obliquities of Five Low-Mass Eclipsing Binaries. arXiv e-prints , keywords =. doi:10.48550/arXiv.2511.23430 , archivePrefix =. 2511.23430 , primaryClass =

    doi:10.48550/arxiv.2511.23430

  18. [18]

    , keywords =

    Measuring tidal dissipation in giant planets from tidal circularization. , keywords =. doi:10.1093/mnras/stad2298 , archivePrefix =. 2308.06324 , primaryClass =

    Pith/arXiv arXiv

  19. [19]

    Axisymmetric shear Alfv \'e n modes of a spherical shell in a dipolar magnetic field

    Oscillations of magnetic stars: I. Axisymmetric shear Alfv \'e n modes of a spherical shell in a dipolar magnetic field. , keywords =. doi:10.1051/0004-6361:20021671 , adsurl =

    work page doi:10.1051/0004-6361:20021671

  20. [20]

    Magnetic fields and stellar oscillations

  21. [21]

    , keywords =

    Zonal Wind Driven by Inertial Modes. , keywords =. doi:10.1103/PhysRevLett.99.194501 , adsurl =

    work page doi:10.1103/physrevlett.99.194501

  22. [22]

    , keywords =

    Comprehensive Bayesian modelling of tidal circularization in open cluster binaries part I: M 35, NGC 6819, and NGC 188. , keywords =. doi:10.1093/mnras/stac2618 , archivePrefix =. 2209.08109 , primaryClass =

    Pith/arXiv arXiv

  23. [23]

    , keywords =

    EBLM XVII - Tidal Synchronization and Circularization in Tight Stellar Binaries. , keywords =. doi:10.1093/mnras/stag454 , archivePrefix =. 2603.04554 , primaryClass =

    arXiv

  24. [24]

    , keywords =

    Magnetic Fields of Nondegenerate Stars. , keywords =. doi:10.1146/annurev-astro-082708-101833 , archivePrefix =. 0904.1938 , primaryClass =

    Pith/arXiv arXiv 1938

  25. [25]

    Annual Review of Fluid Mechanics , year = 2011, month = jan, volume =

    Planetary Magnetic Fields and Fluid Dynamos. Annual Review of Fluid Mechanics , year = 2011, month = jan, volume =. doi:10.1146/annurev-fluid-122109-160727 , adsurl =

    work page doi:10.1146/annurev-fluid-122109-160727 2011

  26. [26]

    The Astrophysical Journal Letters , volume=

    Tidally excited inertial waves in stars and planets: Exploring the frequency-dependent and averaged dissipation with nonlinear simulations , author=. The Astrophysical Journal Letters , volume=. 2023 , publisher=

    2023

  27. [27]

    Monthly Notices of the Royal Astronomical Society , pages=

    Interplay between tidal flows and magnetic fields in nonlinear simulations of stellar and planetary convective envelopes , author=. Monthly Notices of the Royal Astronomical Society , pages=. 2025 , publisher=

    2025

  28. [28]

    Annual Review of Astronomy and Astrophysics , volume=

    Tidal dissipation in stars and giant planets , author=. Annual Review of Astronomy and Astrophysics , volume=. 2014 , publisher=

    2014

  29. [29]

    Monthly Notices of the Royal Astronomical Society , volume=

    Tides in rotating barotropic fluid bodies: the contribution of inertial waves and the role of internal structure , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2013 , publisher=

    2013

  30. [30]

    Monthly Notices of the Royal Astronomical Society , volume=

    Tidal dissipation in rotating fluid bodies: the presence of a magnetic field , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2018 , publisher=

    2018

  31. [31]

    The Equilibrium of a Self-Gravitating Incompressible Fluid Sphere with a Magnetic Field. I. , author=. Astrophysical Journal, vol. 123, p. 498 , volume=

  32. [32]

    Physics of the Earth and Planetary Interiors , volume=

    Planetary magnetic fields: Observations and models , author=. Physics of the Earth and Planetary Interiors , volume=. 2011 , publisher=

    2011

  33. [33]

    Monthly Notices of the Royal Astronomical Society , volume=

    The stability of prendergast magnetic fields , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2022 , publisher=

    2022

  34. [34]

    , keywords =

    Evolutionary state of magnetic chemically peculiar stars. , keywords =. doi:10.1051/0004-6361:20054596 , archivePrefix =. astro-ph/0601461 , primaryClass =

    Pith/arXiv arXiv

  35. [35]

    Physical Review Research , volume=

    Dedalus: A flexible framework for numerical simulations with spectral methods , author=. Physical Review Research , volume=. 2020 , publisher=

    2020

  36. [36]

    , keywords =

    The Magnetic Effect on Dynamical Tide in Rapidly Rotating Astronomical Objects. , keywords =. doi:10.3847/1538-4357/aaa54d , archivePrefix =. 1801.05552 , primaryClass =

    Pith/arXiv arXiv

  37. [37]

    , keywords =

    Does magnetic field impact tidal dynamics inside the convective zone of low-mass stars along their evolution?. , keywords =. doi:10.1051/0004-6361/201936477 , archivePrefix =. 1909.10490 , primaryClass =

    Pith/arXiv arXiv 1909

  38. [38]

    , keywords =

    Tidal dissipation in rotating and evolving giant planets with application to exoplanet systems. , keywords =. doi:10.1093/mnras/stad3689 , archivePrefix =. 2311.15815 , primaryClass =

    Pith/arXiv arXiv

  39. [39]

    , keywords =

    Tidal Dissipation Due to Inertial Waves Can Explain the Circularization Periods of Solar-type Binaries. , keywords =. doi:10.3847/2041-8213/ac5b63 , archivePrefix =. 2203.03950 , primaryClass =

    Pith/arXiv arXiv 2041

  40. [40]

    Encyclopedia of Astrophysics , year = 2026, volume =

    Tidal interactions in stellar and planetary systems. Encyclopedia of Astrophysics , year = 2026, volume =. doi:10.1016/B978-0-443-21439-4.00075-4 , adsurl =

    work page doi:10.1016/b978-0-443-21439-4.00075-4 2026

  41. [41]

    Science , keywords =

    Asteroseismology can reveal strong internal magnetic fields in red giant stars. Science , keywords =. doi:10.1126/science.aac6933 , archivePrefix =. 1510.06960 , primaryClass =

    Pith/arXiv arXiv

  42. [42]

    Physics of Fluids , keywords =

    Solar convective velocities: Updated helioseismic constraints. Physics of Fluids , keywords =. doi:10.1063/5.0216728 , adsurl =

    doi:10.1063/5.0216728

  43. [43]

    , keywords =

    Ab Initio Simulations for Material Properties along the Jupiter Adiabat. , keywords =. doi:10.1088/0067-0049/202/1/5 , adsurl =

    doi:10.1088/0067-0049/202/1/5

  44. [44]

    The interior of Jupiter. Jupiter. The Planet, Satellites and Magnetosphere , year = 2004, editor =

    2004

  45. [45]

    The Solar Tachocline , year = 2007, editor =

    An introduction to the solar tachocline. The Solar Tachocline , year = 2007, editor =

    2007

  46. [46]

    , keywords =

    Rossby and Magnetic Prandtl Number Scaling of Stellar Dynamos. , keywords =. doi:10.3847/1538-4357/ab14ea , archivePrefix =. 1904.00225 , primaryClass =

    Pith/arXiv arXiv 1904

  47. [47]

    Science , year = 1996, month = may, volume =

    The Current State of Solar Modeling. Science , year = 1996, month = may, volume =. doi:10.1126/science.272.5266.1286 , adsurl =

    arXiv 1996

  48. [48]

    , keywords =

    A prevalence of dynamo-generated magnetic fields in the cores of intermediate-mass stars. , keywords =. doi:10.1038/nature16171 , archivePrefix =. 1601.00004 , primaryClass =

    Pith/arXiv arXiv

  49. [49]

    Earth and Planetary Science Letters , keywords =

    Planetary magnetic fields. Earth and Planetary Science Letters , keywords =. doi:10.1016/S0012-821X(02)01126-3 , adsurl =

    doi:10.1016/s0012-821x(02)01126-3

  50. [50]

    , keywords =

    Magnetic fields of 30 to 100 kG in the cores of red giant stars. , keywords =. doi:10.1038/s41586-022-05176-0 , archivePrefix =. 2208.09487 , primaryClass =

    Pith/arXiv arXiv

  51. [51]

    EAS Publications Series , year = 2019, series =

    Tidal dissipation in stars and giant planets: Jean-Paul Zahn's pioneering work and legacy. EAS Publications Series , year = 2019, series =. doi:10.1051/eas/1982002 , adsurl =

    arXiv 2019

  52. [52]

    , keywords =

    Non-linear evolution of tidally forced inertial waves in rotating fluid bodies. , keywords =. doi:10.1093/mnras/stu003 , archivePrefix =. 1401.0643 , primaryClass =

    Pith/arXiv arXiv

  53. [53]

    , keywords =

    On Obliquely Magnetized and Differentially Rotating Stars. , keywords =. doi:10.1088/0004-637X/806/1/50 , archivePrefix =. 1501.04211 , primaryClass =

    Pith/arXiv arXiv

  54. [54]

    Journal of Fluid Mechanics , year = 1967, month = jan, volume =

    Hydromagnetic planetary waves. Journal of Fluid Mechanics , year = 1967, month = jan, volume =. doi:10.1017/S0022112067002447 , adsurl =

    work page doi:10.1017/s0022112067002447 1967

  55. [55]

    from the pms to the rgb at solar metallicity , author=

    Tidal dissipation in rotating low-mass stars and implications for the orbital evolution of close-in planets-i. from the pms to the rgb at solar metallicity , author=. Astronomy & Astrophysics , volume=. 2017 , publisher=

    2017

  56. [56]

    Monthly Notices of the Royal Astronomical Society , volume=

    Water loss from terrestrial planets orbiting ultracool dwarfs: implications for the planets of TRAPPIST-1 , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2017 , publisher=

    2017

  57. [57]

    Les houches , volume=

    Course 8 Waves in the presence of magnetic fields, rotation and convection , author=. Les houches , volume=. 2008 , publisher=

    2008

  58. [58]

    Astronomy & Astrophysics , volume=

    Turbulent viscosity and magnetic Prandtl number from simulations of isotropically forced turbulence , author=. Astronomy & Astrophysics , volume=. 2020 , publisher=

    2020

  59. [59]

    Astronomy & Astrophysics , volume=

    Stable magnetic fields in stellar interiors , author=. Astronomy & Astrophysics , volume=. 2006 , publisher=

    2006

  60. [60]

    , keywords =

    The magnetic properties of the star Kepler-78. , keywords =. doi:10.1093/mnras/stw809 , archivePrefix =. 1605.03255 , primaryClass =

    Pith/arXiv arXiv

  61. [61]

    , keywords =

    A hot Jupiter around the very active weak-line T Tauri star TAP 26. , keywords =. doi:10.1093/mnras/stx009 , archivePrefix =. 1701.01512 , primaryClass =

    Pith/arXiv arXiv

  62. [62]

    , keywords =

    Large-scale magnetic topologies of late M dwarfs*. , keywords =. doi:10.1111/j.1365-2966.2010.17101.x , archivePrefix =. 1005.5552 , primaryClass =

    arXiv 2010

  63. [63]

    Reports on Progress in Physics , keywords =

    The magnetic fields of forming solar-like stars. Reports on Progress in Physics , keywords =. doi:10.1088/0034-4885/73/12/126901 , archivePrefix =. 1008.1883 , primaryClass =

    Pith/arXiv arXiv

  64. [64]

    Astronomische Nachrichten , keywords =

    Analytic and numerical models of the 3D multipolar magnetospheres of pre-main sequence stars. Astronomische Nachrichten , keywords =. doi:10.1002/asna.201111621 , archivePrefix =. 1110.5901 , primaryClass =

    Pith/arXiv arXiv

  65. [65]

    , keywords =

    Can We Predict the Global Magnetic Topology of a Pre-main-sequence Star from Its Position in the Hertzsprung-Russell Diagram?. , keywords =. doi:10.1088/0004-637X/755/2/97 , archivePrefix =. 1206.5238 , primaryClass =

    Pith/arXiv arXiv

  66. [67]

    , keywords =

    Magnetic fields and accretion flows on the classical T Tauri star V2129 Oph. , keywords =. doi:10.1111/j.1365-2966.2007.12194.x , archivePrefix =. 0709.1414 , primaryClass =

    arXiv 2007

  67. [68]

    , keywords =

    The surprising magnetic topology of Sco: fossil remnant or dynamo output?. , keywords =. doi:10.1111/j.1365-2966.2006.10558.x , archivePrefix =. astro-ph/0606156 , primaryClass =

    arXiv 2006

  68. [69]

    , keywords =

    On the Stability of Non-force-free Magnetic Equilibria in Stars. , keywords =. doi:10.1088/2041-8205/724/1/L34 , archivePrefix =. 1009.5384 , primaryClass =

    Pith/arXiv arXiv 2041

  69. [70]

    Relaxed equilibrium configurations to model fossil fields . I. A first family. , keywords =. doi:10.1051/0004-6361/200913496 , adsurl =

    doi:10.1051/0004-6361/200913496

  70. [71]

    , keywords =

    Effect of a fossil magnetic field on the structure of a young Sun. , keywords =. doi:10.1111/j.1365-2966.2009.15955.x , archivePrefix =. 0911.0788 , primaryClass =

    arXiv 2009

  71. [72]

    Magnetic field generation in electrically conducting fluids

  72. [73]

    Handbook of Mathematical Functions

  73. [74]

    Earth and Planetary Science Letters , keywords =

    Ohmic dissipation in the Earth's outer core resulting from the free inner core nutation. Earth and Planetary Science Letters , keywords =. doi:10.1016/j.epsl.2019.115888 , archivePrefix =. 1910.02210 , primaryClass =

    arXiv 2019

  74. [75]

    Journal of Physics Conference Series , year = 2013, series =

    Where is the solar dynamo?. Journal of Physics Conference Series , year = 2013, series =. doi:10.1088/1742-6596/440/1/012014 , adsurl =

    work page doi:10.1088/1742-6596/440/1/012014 2013

  75. [77]

    Characterisation of the large-scale magnetic field with Zeeman-Doppler imaging

    Evolving magnetic lives of Sun-like stars: I. Characterisation of the large-scale magnetic field with Zeeman-Doppler imaging. , keywords =. doi:10.1051/0004-6361/202555502 , archivePrefix =. 2507.14861 , primaryClass =

    Pith/arXiv arXiv

  76. [79]

    Astronomische Nachrichten , keywords =

    Surface magnetism of cool stars. Astronomische Nachrichten , keywords =. doi:10.1002/asna.201713310 , archivePrefix =. 1612.03388 , primaryClass =

    Pith/arXiv arXiv

  77. [80]

    , keywords =

    Large-scale magnetic topologies of mid M dwarfs. , keywords =. doi:10.1111/j.1365-2966.2008.13809.x , archivePrefix =. 0808.1423 , primaryClass =

    arXiv 2008

  78. [81]

    , keywords =

    Stable stratification promotes multiple zonal jets in a turbulent Jovian dynamo model. , keywords =. doi:10.1016/j.icarus.2021.114514 , archivePrefix =. 2012.06438 , primaryClass =

    arXiv 2021