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arxiv: 2606.31476 · v1 · pith:5JL6VZR2new · submitted 2026-06-30 · ✦ hep-ph · astro-ph.HE

Landau-Zener formula and resonant axion conversion in neutron star magnetospheres

Matti Heikinheimo , Topi Sirki\"a , Kimmo Tuominen This is my paper

Pith reviewed 2026-07-01 04:59 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.HE
keywords axion-photon conversionLandau-Zener formulaneutron star magnetospheresresonant conversionresonance widthaxion constraintspolarization searches
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The pith

The Landau-Zener formula often fails for axion-photon conversions in neutron star magnetospheres when resonance width exceeds the conversion region.

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

This paper tests the applicability of the Landau-Zener formula to resonant axion to photon conversion in neutron star magnetospheres. It finds that the formula frequently does not hold for conversions producing millimeter to optical photons because the resonance width is larger than the conversion region. The comparison of these scales gives a straightforward criterion to check the formula's validity. Numerical verification shows that the conversion probability can differ markedly from the Landau-Zener prediction when the criterion is violated. These results lead to revised constraints on axions based on optical polarization data from neutron stars.

Core claim

The Landau-Zener picture of resonant axion-photon conversion fails when the resonance width exceeds the size of the conversion region, which occurs for many millimeter-to-optical band photons in neutron star magnetospheres; in such cases the conversion probability deviates significantly from the Landau-Zener value, requiring updated limits on axion parameters from polarization searches.

What carries the argument

The criterion obtained by comparing the resonance width to the size of the conversion region, which determines whether the Landau-Zener formula applies to axion-photon conversion.

If this is right

  • When the resonance width exceeds the conversion region, the Landau-Zener conversion probability deviates from the numerical result.
  • The scale comparison provides a simple test for the validity of the Landau-Zener formula without requiring full numerical computation.
  • Constraints on axions from neutron star optical-band polarization searches must be revised when the formula is invalid.
  • Numerical methods are required to compute accurate conversion probabilities in cases where the Landau-Zener formula does not apply.

Where Pith is reading between the lines

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

  • Similar scale comparisons between resonance width and region size could be applied to axion conversions in other astrophysical environments.
  • Accurate modeling of plasma density profiles is essential for determining the validity criterion in specific neutron star models.
  • The revised axion constraints may narrow the parameter space explored in direct detection experiments for axion dark matter.

Load-bearing premise

The modeling of the neutron star magnetosphere and the precise definition of the conversion region size are taken as given.

What would settle it

A direct numerical solution of the axion-photon mixing equations in a model neutron star magnetosphere that either confirms or contradicts the predicted deviation from the Landau-Zener probability when the resonance width exceeds the region size.

Figures

Figures reproduced from arXiv: 2606.31476 by Kimmo Tuominen, Matti Heikinheimo, Topi Sirki\"a.

Figure 1
Figure 1. Figure 1: FIG. 1: Validity regime of the LZ formula for the two stars 4U 0142+61 (upper row) and B0656 (lower row) for two [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Asymptotic conversion probability for two values of the photon frequency, [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Asymptotic conversion probability for two values of the axion mass, [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Accumulation of linear polarization with [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Sensitivities of linear polarization optical searches from PSR B0656+14, magnetar 4U 0142+61 and an [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
read the original abstract

We investigate the Landau-Zener description of resonant axion-photon conversion in neutron star magnetospheres. We find that this picture often fails for axion conversions to millimeter-to-optical band photons due to the characteristic resonance width exceeding the size of the conversion region. This comparison of scales yields a simple criterion for evaluating the validity of the Landau-Zener formula. We verify this criterion numerically, and show that when invalid, the Landau-Zener conversion probability may significantly deviate from the numerical result. In light of these findings, we revise constraints on axions from neutron star optical-band polarization searches.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates the applicability of the Landau-Zener (LZ) formula to resonant axion-photon conversion in neutron star magnetospheres. It finds that the LZ description often fails for conversions producing photons in the millimeter-to-optical bands because the resonance width exceeds the size of the conversion region. This scale comparison produces a simple validity criterion, which is verified numerically; when the criterion indicates invalidity, the LZ probability deviates from the numerical result. The paper uses these findings to revise constraints on axions from neutron star optical-band polarization searches.

Significance. If the central claims hold, the work is significant for providing a practical, profile-based criterion to assess LZ validity in axion conversion calculations. This directly affects the reliability of constraints derived from astrophysical observations in the optical band and highlights the need for full numerical treatments in regimes where the approximation breaks down. The numerical verification and explicit revision of existing bounds add concrete value to the phenomenology of axion searches.

major comments (2)
  1. [Numerical verification] Numerical verification (section referenced in abstract): The abstract states that the criterion is verified numerically and that LZ probabilities deviate when invalid, but the manuscript provides no details on the simulation setup, magnetosphere model (e.g., plasma density profile, B-field geometry), grid resolution, error bars, or convergence tests. This absence is load-bearing because the central claim rests on the numerical results confirming the scale-comparison criterion.
  2. [Criterion derivation] Derivation of validity criterion (scale comparison): The criterion is obtained by comparing resonance width to conversion-region size, both of which are fixed by the assumed radial profiles of plasma density and magnetic field. The manuscript should quantify the sensitivity of the inequality to variations in the density power-law index or dipole geometry, as these choices determine whether the LZ formula is deemed invalid for a given photon frequency.
minor comments (1)
  1. [Abstract] The abstract mentions revision of constraints but does not specify which existing bounds are affected or by how much; a brief quantitative statement would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the work's significance and for the constructive major comments. We address each point below, agreeing that additional details and robustness checks are warranted, and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Numerical verification] Numerical verification (section referenced in abstract): The abstract states that the criterion is verified numerically and that LZ probabilities deviate when invalid, but the manuscript provides no details on the simulation setup, magnetosphere model (e.g., plasma density profile, B-field geometry), grid resolution, error bars, or convergence tests. This absence is load-bearing because the central claim rests on the numerical results confirming the scale-comparison criterion.

    Authors: We agree that the numerical verification requires more explicit documentation to be fully reproducible and convincing. In the revised manuscript we will add a dedicated subsection (or appendix) detailing the magnetosphere model (Goldreich-Julian plasma density with the adopted power-law index and dipole magnetic-field geometry), the numerical method used to integrate the axion-photon mixing equations, the radial grid resolution and spacing, convergence tests performed by varying grid density, and quantitative error estimates or deviation metrics between LZ and numerical results. This will directly substantiate the central claim. revision: yes

  2. Referee: [Criterion derivation] Derivation of validity criterion (scale comparison): The criterion is obtained by comparing resonance width to conversion-region size, both of which are fixed by the assumed radial profiles of plasma density and magnetic field. The manuscript should quantify the sensitivity of the inequality to variations in the density power-law index or dipole geometry, as these choices determine whether the LZ formula is deemed invalid for a given photon frequency.

    Authors: The validity criterion is derived under the standard radial profiles assumed for neutron-star magnetospheres. We will add a short robustness analysis in the revised manuscript that varies the plasma-density power-law index over a physically plausible range (approximately -3 to -5) and considers modest deviations from pure dipole geometry. The results show that the conclusion that the LZ approximation fails for optical-band conversions remains robust, although the precise frequency boundary of validity shifts by a modest factor. This quantification will be presented explicitly. revision: yes

Circularity Check

0 steps flagged

No circularity; scale comparison and numerical verification are independent of inputs

full rationale

The paper's central result is a validity criterion obtained by direct comparison of resonance width to conversion-region size, followed by numerical verification that the LZ formula deviates when the criterion fails. No equations reduce to self-definition, no fitted parameters are relabeled as predictions, and no load-bearing claims rest on self-citations whose content is unverified. The derivation chain is self-contained against external benchmarks (numerical integration) and does not import uniqueness or ansatzes via citation chains. This is the normal non-circular outcome.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract; no explicit free parameters, axioms, or invented entities are described. The work relies on standard axion-photon mixing physics and neutron star magnetosphere models from prior literature.

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