PIMMS: Pulsation-Informed Magnetic Mapping of Stars with Zeeman-Doppler Imaging I. Formalism and numerical tests

C. Catala; C. Gutteridge; C. Neiner; C. P. Folsom

arxiv: 2509.02152 · v2 · submitted 2025-09-02 · 🌌 astro-ph.SR

PIMMS: Pulsation-Informed Magnetic Mapping of Stars with Zeeman-Doppler Imaging I. Formalism and numerical tests

C. Gutteridge , C. Neiner , C. Catala , C. P. Folsom This is my paper

Pith reviewed 2026-05-18 20:10 UTC · model grok-4.3

classification 🌌 astro-ph.SR

keywords pulsating starsZeeman-Doppler imagingmagnetic mappingpulsationsspectropolarimetrystellar magnetismsurface velocity fieldshot stars

0 comments

The pith

PIMMS extends Zeeman-Doppler Imaging to pulsating stars by adding a pulsation velocity map to the reconstruction.

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

The paper presents PIMMS as a modified form of Zeeman-Doppler Imaging that builds an extra surface velocity map to handle the time-varying Doppler shifts caused by stellar pulsations. Standard ZDI cannot separate these shifts from brightness and magnetic signals, so the new code fits a surface-integrated line profile model directly to spectropolarimetric data. Numerical experiments on realistic hot-star models recover the input magnetic fields and brightness distributions with good fidelity once enough observations are supplied. The approach therefore supplies the surface magnetic characterization that magneto-asteroseismology needs for pulsating magnetic stars.

Core claim

PIMMS reconstructs simultaneous maps of surface brightness, magnetic field, and the velocity field arising from both rotation and pulsations by fitting a surface-integrated line profile model that includes the additional Doppler shifts of local lines produced by pulsations. Tests on synthetic data demonstrate that the code accurately reproduces the magnetic fields and brightness distributions of realistic models of pulsating hot stars, although the required number of observations exceeds that for non-pulsating targets because the velocity map must be disentangled from brightness variations.

What carries the argument

The surface-integrated line profile model that adds pulsation-induced Doppler shifts to the local line profiles before disk integration.

If this is right

PIMMS recovers input magnetic and brightness maps from realistic pulsating-star models when supplied with sufficient data.
The number of required observations increases compared with ordinary ZDI because an additional velocity map must be separated from brightness variations.
The code is ready for direct application to observed spectropolarimetric time series of real pulsating magnetic stars.

Where Pith is reading between the lines

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

Improved surface magnetic maps from PIMMS would feed directly into magneto-asteroseismology inversions for internal structure.
The same framework could be extended to stars whose pulsation modes are already well characterized by photometry or spectroscopy.

Load-bearing premise

The line profile model fully accounts for all Doppler shifts from pulsations without unmodeled effects or degeneracies that would prevent separating the velocity map from brightness changes.

What would settle it

Running PIMMS on a set of simulated observations generated from a known input magnetic field and pulsation velocity field and finding that the recovered magnetic map deviates substantially from the input would show the method does not work as claimed.

Figures

Figures reproduced from arXiv: 2509.02152 by C. Catala, C. Gutteridge, C. Neiner, C. P. Folsom.

**Figure 1.** Figure 1: Examples of line profiles for stars with three different pulsation modes, all with inclination angles of 75◦ . pulsation modes and play an important role in the dynamics of the stellar interior, e.g. by decreasing or suppressing internal differential rotation. These effects can be inferred if a surface magnetic field is detected and then taken into account in the modelling. Due to a lack of targets with… view at source ↗

**Figure 2.** Figure 2: Model Stokes V signatures for stars at rotation phases 0, 0.5, and 1. The solid black line is for a star with a single ℓ = 2, m = −2 pulsation mode, while the dashed grey line is for a non-pulsating star. The stars have a uniform surface brightness, and identical rotation periods and magnetic fields. The model Stokes V signatures deviate strongly from each other, even at equivalent rotation phases i.e. 0 a… view at source ↗

**Figure 3.** Figure 3: Test for a dipolar star with uniform brightness. The left-hand plot is the brightness map used to generate the model line profiles we test the codes on, the middle is the best fit brightness map produced by ZDIpy, and the final plot is the best fit brightness map produced by PIMMS [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Test for a dipolar star with uniform brightness. The left-hand plot is the magnetic map used to generate the model line profiles we test the codes on, the middle is the outputted magnetic field map from ZDIpy assuming the input surface brightness map, and the final plot is the magnetic field map from PIMMS using the fitted brightness map [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Same as [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: A comparison between the line profiles of a ℓ = 5, m = −5 mode generated for three different resolutions. The solid black line is the higher resolution model using 10000 equally sized cells on the stellar surface, while the green dashed line is the 1000 cell moderate resolution model, and the red dotted line is the lower resolution model using only 100. The agreement between the 10000 and 1000 cell model… view at source ↗

read the original abstract

Context. Magneto-asteroseismology is a novel technique allowing for more precise determinations of internal properties of magnetic pulsating stars, but requires an accurate characterisation of the surface magnetic field, not previously possible with Zeeman-Doppler Imaging (ZDI) due to the time-dependent surface velocity of pulsating stars. Aims. We aim to develop a new version of ZDI, which creates an additional surface velocity map, that includes the time-dependent velocities of surface elements due to pulsations. Methods. We present a new code, PIMMS: Pulsation-Informed Magnetic Mapping of Stars, which uses a surface-integrated line profile model that accounts for the additional Doppler shifts of local lines caused by pulsations. It is then possible to fit this model to spectropolarimetric observations, reconstructing maps of the surface brightness, magnetic field, and the velocity field due to the combination of pulsation and rotation. In this paper, we present and test PIMMS extensively, to understand its limitations and data requirements. Results. We find that PIMMS can accurately reproduce the magnetic fields and brightness distributions of realistic models of pulsating hot stars. The required number of observations is higher than that required for ZDI of a non-pulsating star due to the additional velocity map that must be disentangled from surface brightness variations. PIMMS is now ready to be applied to real stars.

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.

Desk Editor's Note private letter to a colleague

PIMMS extends ZDI to pulsating stars via a velocity map, with synthetic tests showing good recovery but potential degeneracy issues in real data.

read the letter

The one or two things to know are that this paper presents PIMMS as a new code for Zeeman-Doppler Imaging that incorporates pulsation effects through an extra velocity map, and that the numerical tests on synthetic data indicate successful recovery of the underlying magnetic and brightness maps for pulsating hot stars. What is actually new is the modification to the line profile modeling to include the additional Doppler shifts from the time-dependent pulsation velocities on the stellar surface. Previous ZDI approaches did not account for this, limiting their use on pulsating stars for magneto-asteroseismology. The authors test the code extensively with realistic models and find that it reproduces the inputs accurately, which is a useful validation step. They also note the higher number of observations needed, which shows they have thought through the practical implications. The paper does well in being upfront about the data requirements and in focusing on the formalism first before the tests. This makes the contribution clear without overclaiming. Where the soft spots are is in the nature of the numerical tests. They appear to use ideal conditions generated from the model itself, so while they support the method in controlled settings, they may not expose issues like degeneracies when pulsation velocity fields partially overlap with brightness-induced profile changes under noisy or sparsely sampled data. The stress-test note correctly flags this as the least secure link, and it would be good to see more varied test cases in future work or revisions. This paper is primarily for specialists in stellar magnetic fields and asteroseismology. Readers who are already familiar with ZDI and looking for ways to extend it to pulsating stars will find the most value, as it provides a ready-to-use approach with initial benchmarks. The work shows clear thinking on the problem and honest engagement with the limitations, so it deserves a serious referee even if some revisions are needed for broader applicability. My recommendation is to send it to peer review rather than desk reject.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces PIMMS, an extension of Zeeman-Doppler Imaging that adds a surface velocity map to account for time-dependent pulsation velocities in hot stars. It describes a surface-integrated line-profile forward model incorporating pulsation-induced Doppler shifts, then fits this model to synthetic spectropolarimetric data to reconstruct simultaneous maps of brightness, magnetic field, and the combined pulsation-plus-rotation velocity field. Numerical tests on data generated from realistic pulsating-star models are presented to show that the input magnetic fields and brightness distributions can be recovered accurately, albeit with a higher observational requirement than standard ZDI owing to the extra map.

Significance. If the numerical tests prove robust, PIMMS would remove a long-standing barrier to magneto-asteroseismology by enabling reliable surface magnetic mapping of pulsating stars. The explicit treatment of the additional velocity map and the provision of self-consistent synthetic tests constitute clear technical advances over prior ZDI implementations.

major comments (1)

Numerical tests section: the reported tests use synthetic data generated from the identical forward operator under (apparently) ideal sampling and noise-free conditions. This setup demonstrates internal consistency but does not directly test whether the pulsation velocity map remains separable from brightness variations when realistic SNR, incomplete rotational-phase coverage, or pulsation modes whose velocity fields partially mimic brightness-induced profile changes are introduced. Because the abstract itself states that more observations are required precisely to disentangle the extra map, these tests are load-bearing for the central claim of accurate reproduction and should be extended or supplemented with such regimes.

minor comments (2)

Abstract: quantitative recovery metrics (e.g., typical RMS errors on the recovered B-field or brightness maps) would strengthen the results statement.
Notation: ensure that the definition of the local line profile and the surface integration operator are introduced with consistent symbols before their first use in the formalism.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript's significance and for the constructive major comment on the numerical tests. We respond to this point below.

read point-by-point responses

Referee: Numerical tests section: the reported tests use synthetic data generated from the identical forward operator under (apparently) ideal sampling and noise-free conditions. This setup demonstrates internal consistency but does not directly test whether the pulsation velocity map remains separable from brightness variations when realistic SNR, incomplete rotational-phase coverage, or pulsation modes whose velocity fields partially mimic brightness-induced profile changes are introduced. Because the abstract itself states that more observations are required precisely to disentangle the extra map, these tests are load-bearing for the central claim of accurate reproduction and should be extended or supplemented with such regimes.

Authors: We agree that the numerical tests employ synthetic data generated from the same forward operator under ideal, noise-free conditions with full phase coverage. This choice establishes the internal consistency of the PIMMS formalism and confirms that the brightness, magnetic field, and combined pulsation-plus-rotation velocity maps can be recovered accurately when the data are fully consistent with the model, as reported in the results. The accurate reproduction of input maps in these tests supports separability of the velocity field from brightness variations within the controlled regime examined. We acknowledge, however, that the tests do not yet address realistic SNR, incomplete rotational-phase coverage, or pulsation modes with velocity fields that could partially mimic brightness-induced profile changes. To strengthen the manuscript, we will revise the Numerical tests section to include additional experiments with moderate added noise and partial phase coverage, along with expanded discussion quantifying the impact on map recovery and the increased observational requirements already noted in the abstract. This will be implemented as a partial revision, as exhaustive coverage of all possible degenerate modes lies beyond the scope of this first paper on the formalism but will be flagged for future investigation. revision: partial

Circularity Check

0 steps flagged

PIMMS formalism and numerical tests are self-contained with no circular reduction

full rationale

The paper introduces an explicit new forward model for surface-integrated line profiles that incorporates time-dependent pulsation velocities in addition to rotation and magnetic effects. It then performs numerical tests by generating synthetic spectropolarimetric data from known input maps of brightness, magnetic field, and pulsation velocity, followed by recovery using the same model. This constitutes standard self-consistency validation for an inversion method rather than any reduction of the claimed accuracy to a fitted parameter, self-definition, or self-citation chain. The abstract explicitly notes the increased observational requirements due to the extra velocity map, confirming the separation is treated as an independent modeling choice rather than assumed by construction. No load-bearing steps reduce to prior author results or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim depends on standard assumptions about line profile formation in stellar atmospheres and the separability of pulsation velocities from other effects, with no free parameters explicitly fitted in the abstract summary.

axioms (1)

domain assumption Pulsations produce time-dependent surface velocities that cause additional Doppler shifts in local spectral lines beyond rotation.
This premise is invoked to justify extending the ZDI model to include a velocity map.

invented entities (1)

pulsation velocity map no independent evidence
purpose: To represent the combined effects of pulsation and rotation on surface velocities for disentangling from brightness and magnetic maps.
New component introduced in the reconstruction process, tested numerically but without independent evidence outside the simulations.

pith-pipeline@v0.9.0 · 5800 in / 1261 out tokens · 59415 ms · 2026-05-18T20:10:38.481827+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

surface-integrated line profile model that accounts for the additional Doppler shifts of local lines caused by pulsations (Eq. 12)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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F., Wade, G

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& Donati, J

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