arxiv: 2605.15112 · v1 · submitted 2026-05-14 · 🌌 astro-ph.SR

Recognition: no theorem link

Analysing the highly irregular boundaries of solar pores

T. J. Duckenfield , D. B. Jess , S. Jafarzadeh , L. A. C. A. Schiavo , S. S. A. Silva , S. D. T. Grant

Authors on Pith no claims yet

Pith reviewed 2026-05-15 02:50 UTC · model grok-4.3

classification 🌌 astro-ph.SR

keywords solar poresMHD wavesboundary irregularitysausage modeskink modesconvex hullProper Orthogonal Decompositionwave propagation

0 comments

The pith

Convex hulls of irregular solar pore boundaries allow reliable detection of sausage and kink wave modes while degrading higher fluting modes.

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

The paper develops a consistent way to analyze magnetohydrodynamic waves in solar pores whose boundaries are far from circular. It defines the analysis domain as the convex hull obtained from intensity minimum error thresholding and validates the approximation with the modal assurance criterion. Proper Orthogonal Decomposition applied to multi-height observations then extracts the dominant modes. Sausage-like modes account for most of the variance at every height and show a systematic frequency increase that matches freely propagating compressive waves. Kink-like motions stay weak and confined to low frequencies, appearing instead as a forced response to granular buffeting.

Core claim

The convex hull derived from intensity minimum error thresholding supplies a usable domain for wave-mode extraction in real solar pores. Within this domain the fundamental sausage (m=1) and kink (m=2) modes remain identifiable, while higher-order fluting modes (m≥3) are strongly suppressed by small-scale boundary irregularity. Sausage-like motions dominate the variance at all observed heights and exhibit an upward frequency shift consistent with freely propagating compressive waves; kink-like motions remain weak, persist at low frequencies, and are interpreted as a forced response to granular buffeting rather than a propagating mode.

What carries the argument

The convex hull of the pore boundary obtained from intensity minimum error thresholding, used as the spatial domain for Proper Orthogonal Decomposition of intensity time series.

If this is right

Sausage modes can be tracked as propagating waves across multiple atmospheric heights using the same hull boundary.
Kink motions extracted this way are unlikely to carry significant energy upward and are better viewed as driven oscillations.
Higher-order fluting modes become unreliable indicators once pore boundaries depart from smooth ellipses.
The framework supplies a repeatable procedure for comparing wave properties between pores of different evolutionary stages.

Where Pith is reading between the lines

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

The same hull-based decomposition could be applied to time series of magnetic field strength or Doppler velocity to test whether the mode dominance persists in vector data.
If the observed frequency up-shift scales with height in a manner predicted by tube-wave theory, the result would constrain the internal density and magnetic-field gradients inside pores.
Granular buffeting as the driver of the low-frequency kink peak implies that pore oscillations may be continuously forced rather than freely excited, altering estimates of wave energy input.

Load-bearing premise

The convex hull derived from intensity thresholding accurately represents the effective magnetic flux domain across the range of observed pore shapes.

What would settle it

Detection of persistent, high-amplitude fluting modes (m≥3) inside pores whose boundaries deviate strongly from the convex hull would falsify the claim that small-scale irregularity degrades those modes.

Figures

Figures reproduced from arXiv: 2605.15112 by D. B. Jess, L. A. C. A. Schiavo, S. D. T. Grant, S. Jafarzadeh, S. S. A. Silva, T. J. Duckenfield.

**Figure 1.** Figure 1: G-band context image of the pore, with the boundary extracted via Minimum Error Thresholding overplotted in yellow. mately 3.60 Mm and remains largely isolated from nearby magnetic activity throughout the sequence. 3. Methodology 3.1. Boundary extraction Given the inherent complexity of solar observations, including the effects of variable seeing conditions and the evolving, non-trivial shape of the pore… view at source ↗

**Figure 2.** Figure 2: Modal Assurance Criterion matrix between the first 5 eigenmodes of a pore boundary calculated in the G-band, and the first 5 eigenmodes of the pore boundaries convex hull. modifications to the boundary geometry would alter the set of supported deformation modes. We compare corresponding eigenmodes using the Modal Assurance Criterion (MAC), defined as the normalised inner product between two mode shapes (l… view at source ↗

**Figure 3.** Figure 3: Leading Proper Orthogonal Decomposition (POD) modes of the convexified pore boundary across the four atmospheric heights sampled by the continuum, G-band, Na i, and Ca ii K filters respectively Rows correspond to the first three POD modes, ordered by decreasing energy content. In the first four columns, the spatial deformation patterns for each POD mode is shown, with blue and red curves denoting the extre… view at source ↗

**Figure 4.** Figure 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

read the original abstract

Solar pores possess irregular and evolving boundaries that are often far from the ideal circular flux tubes assumed in many magnetohydrodynamic (MHD) oscillation models. To tackle this irregularity in a consistent way for wave analysis, we introduce a framework that employs the convex hull of the pore boundary - derived from intensity minimum error thresholding - as the domain to perform further analysis. Using the modal assurance criterion, we find the range of pore shapes for which this approximation is valid. We demonstrate the usefulness of this framework by applying it to multi-height, high-cadence observations (4170 angstrom continuum, G-band, Na~\textsc{i}, and Ca~\textsc{ii}~K) of a solar pore, and apply Proper Orthogonal Decomposition of the convex hull to determine wave modes. The fundamental sausage ($m=1$) and kink ($m=2$) mode is found to remain reliable, while higher-order fluting modes ($m\ge3$) are strongly degraded by small-scale boundary irregularity. As expected, sausage-like modes dominate the variance at all heights and exhibit a systematic upward shift in frequency, consistent with freely propagating compressive waves. In contrast, the kink-like motions appear weak, confined to a persistent low-frequency peak, and most plausibly interpreted as a forced response to granular buffeting rather than a propagating mode. Together, these results establish a practical methodology for boundary-mode analysis in real, highly structured pores and provide new constraints on the nature and height evolution of MHD waves in the lower solar atmosphere.

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

The paper gives a workable convex-hull method for extracting wave modes from irregular solar pores via POD on multi-height data, showing sausage and kink modes hold while higher fluting modes degrade, but the intensity hull as magnetic proxy is only lightly checked.

read the letter

The main point is that this work supplies a concrete way to handle the messy, evolving boundaries of solar pores when doing wave analysis. They define the analysis domain as the convex hull of the pore edge found by minimum-error intensity thresholding, then run Proper Orthogonal Decomposition inside that domain on simultaneous observations at four heights (4170 Å continuum through Ca II K). The result is that the lowest-order sausage (m=1) and kink (m=2) modes stay reliable across the observed shapes, while m≥3 fluting modes are washed out by the small-scale boundary wiggles. Sausage-like power dominates the variance at every height and shows a clear upward frequency shift, which they read as evidence for freely propagating compressive waves; the kink signal stays weak and pinned at low frequency, which they attribute to granular forcing rather than a trapped mode.

Referee Report

2 major / 1 minor

Summary. The paper introduces a framework using the convex hull of solar pore boundaries (derived from intensity minimum-error thresholding) as the analysis domain for MHD wave modes in irregular pores. Applying Proper Orthogonal Decomposition to multi-height observations (4170 Å continuum, G-band, Na I, Ca II K), it reports that fundamental sausage (m=1) and kink (m=2) modes remain reliable while higher-order fluting modes (m≥3) are strongly degraded by small-scale boundary irregularity. Sausage-like modes dominate variance at all heights with a systematic upward frequency shift (consistent with freely propagating compressive waves), whereas kink-like motions are weak, low-frequency, and interpreted as forced responses to granular buffeting rather than propagating modes. The modal assurance criterion is used to identify the valid range of pore shapes for the convex-hull approximation.

Significance. If the central results hold, the work supplies a practical, observationally grounded methodology for wave-mode analysis in highly structured solar pores and yields new constraints on the height evolution of MHD waves in the lower atmosphere. Strengths include the multi-height dataset, explicit use of the modal assurance criterion for shape validation, and the distinction between propagating sausage modes and forced kink motions.

major comments (2)

[Abstract / methodology] Abstract and implied methodology: the central claim that sausage and kink modes remain reliable (while fluting modes degrade) rests on performing POD inside the convex hull derived from intensity minimum-error thresholding. This hull is treated as the effective domain for wave propagation, yet intensity boundaries can decouple from the true magnetic flux surface due to line-of-sight integration, temperature structuring, and small-scale features; the paper provides no quantitative overlap metric (e.g., with simultaneous magnetograms or simulated B-field contours) confirming that the hull encloses the same flux across the observed irregular shapes.
[Results / abstract] Results (mode reliability and frequency analysis): the abstract reports that sausage-like modes dominate variance and exhibit an upward frequency shift, but supplies no quantitative error bars, exact modal-assurance thresholds, or full validation statistics on the POD decomposition. This limits assessment of whether the data robustly support the stated mode-reliability claims and the interpretation of kink motions as forced rather than propagating.

minor comments (1)

[Abstract] The mode indexing (m=1 for sausage, m=2 for kink) follows standard cylindrical-wave convention but should be stated explicitly in the text to avoid ambiguity for readers unfamiliar with the azimuthal-order convention used here.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their constructive and detailed review. We address each major comment below and indicate the revisions planned for the manuscript.

read point-by-point responses

Referee: [Abstract / methodology] Abstract and implied methodology: the central claim that sausage and kink modes remain reliable (while fluting modes degrade) rests on performing POD inside the convex hull derived from intensity minimum-error thresholding. This hull is treated as the effective domain for wave propagation, yet intensity boundaries can decouple from the true magnetic flux surface due to line-of-sight integration, temperature structuring, and small-scale features; the paper provides no quantitative overlap metric (e.g., with simultaneous magnetograms or simulated B-field contours) confirming that the hull encloses the same flux across the observed irregular shapes.

Authors: We acknowledge that intensity boundaries can decouple from magnetic flux surfaces owing to line-of-sight integration and temperature effects. Our analysis targets the observable intensity domain in the multi-height data, with the convex hull providing a reproducible boundary for irregular pores. The modal assurance criterion supplies a quantitative shape-validation metric for the observed pore morphologies. The dataset consists of intensity observations without simultaneous magnetograms, so direct overlap metrics with B-field contours cannot be computed. We will revise the text to expand the justification for intensity thresholding, reference prior work on intensity-based pore proxies, and explicitly discuss this dataset limitation. revision: partial
Referee: [Results / abstract] Results (mode reliability and frequency analysis): the abstract reports that sausage-like modes dominate variance and exhibit an upward frequency shift, but supplies no quantitative error bars, exact modal-assurance thresholds, or full validation statistics on the POD decomposition. This limits assessment of whether the data robustly support the stated mode-reliability claims and the interpretation of kink motions as forced rather than propagating.

Authors: We agree that quantitative details are needed for robust evaluation. The revised manuscript will include error bars on variance fractions and frequency shifts, state the exact MAC thresholds applied (e.g., MAC > 0.85 for reliable modes), and add a table summarizing POD validation statistics across heights. These changes will strengthen support for the sausage-mode propagation interpretation and the forced-response characterization of the kink motions. revision: yes

standing simulated objections not resolved

Absence of simultaneous magnetogram data prevents supplying the requested quantitative overlap metrics between the intensity-derived convex hull and magnetic flux surfaces.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper defines its analysis domain via convex hull of intensity-thresholded boundaries from observational data, validates applicability with the modal assurance criterion (MAC) across shape ranges, and extracts modes via proper orthogonal decomposition (POD) within that domain. The reported mode reliability, variance dominance, and frequency shifts are direct empirical outputs from this pipeline applied to multi-height observations; no step reduces by the paper's own equations or citations to a fitted input renamed as prediction, self-definitional loop, or load-bearing self-citation. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on standard image-processing assumptions and observational interpretation rather than new physical postulates.

free parameters (1)

intensity threshold parameter
Chosen via minimum error method to define pore boundary before convex hull computation

axioms (1)

domain assumption Convex hull of intensity-thresholded boundary approximates the magnetic domain for wave analysis within a quantifiable shape range
Invoked when applying modal assurance criterion to validate the approximation

pith-pipeline@v0.9.0 · 5604 in / 1302 out tokens · 50820 ms · 2026-05-15T02:50:14.673677+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages

[1]

S., Silva, S

Alanezy, A. S., Silva, S. S. A., Ballai, I., et al. 2026, Solar Physics, 301, 61, doi:10.1007/s11207-026-02652-y

work page doi:10.1007/s11207-026-02652-y 2026
[2]

B., Fedun, V., Aldhafeeri, A

Albidah, A. B., Fedun, V., Aldhafeeri, A. A., et al. 2022, The Astro- physical Journal, 927, 201, doi:10.3847/1538-4357/ac51d9 —. 2023, The Astrophysical Journal, 954, 30, doi:10.3847/ 1538-4357/acd7eb Aldhafeeri,A.A.,Verth,G.,Brevis,W.,etal.2021,TheAstrophysical Journal, 912, 50, doi:10.3847/1538-4357/abec7a

work page doi:10.3847/1538-4357/ac51d9 2022
[3]

Mbarek and D

Aldhafeeri, A. A., Verth, G., Fedun, V., Lennard, M., & Ballai, I. 2022, The Astrophysical Journal, 938, 32, doi:10.3847/1538-4357/ ac912b

work page doi:10.3847/1538-4357/ 2022
[4]

P., Uitenbroek, H., et al

Cauzzi, G., Reardon, K. P., Uitenbroek, H., et al. 2008, Astronomy & Astrophysics, 480, 515, doi:10.1051/0004-6361:20078642

work page doi:10.1051/0004-6361:20078642 2008
[5]

Aghanim, et al., Astron

Dumbadze, G., Shergelashvili, B. M., Kukhianidze, V., et al. 2017, Astronomy and Astrophysics, 597, doi:10.1051/0004-6361/ 201628213

work page doi:10.1051/0004-6361/ 2017
[6]

J., et al

Freij, N., Dorotovič, I., Morton, R. J., et al. 2016, The Astrophysical Journal, 817, 44, doi:10.3847/0004-637X/817/1/44

work page doi:10.3847/0004-637x/817/1/44 2016
[7]

A., Jess, D

Gilchrist-Millar, C. A., Jess, D. B., Grant, S. D. T., et al. 2021, Philo- sophical Transactions of the Royal Society A: Mathematical, Phys- ical and Engineering Sciences, 379, rsta.2020.0172, doi:10.1098/ rsta.2020.0172

work page arXiv 2021
[8]

Grant, S. D. T., Jess, D. B., Moreels, M. G., et al. 2015, The Astro- physical Journal, 806, 132, doi:10.1088/0004-637X/806/1/132

work page doi:10.1088/0004-637x/806/1/132 2015
[9]

Grant, S. D. T., Jess, D. B., Stangalini, M., et al. 2022, The Astro- physical Journal, 938, 143, doi:10.3847/1538-4357/ac91ca Gómez, J. C. G., Jafarzadeh, S., Wedemeyer, S., et al. 2023, Astron- omy & Astrophysics, 671, A69, doi:10.1051/0004-6361/202244228

work page doi:10.3847/1538-4357/ac91ca 2022
[10]

2024, Astronomy & As- trophysics, doi:10.1051/0004-6361/202449685

Jafarzadeh, S., Schiavo, L., Fedun, V., et al. 2024, Astronomy & As- trophysics, doi:10.1051/0004-6361/202449685

work page doi:10.1051/0004-6361/202449685 2024
[11]

B., Stangalini, M., et al

Jafarzadeh, S., Jess, D. B., Stangalini, M., et al. 2025, Nature Reviews Methods Primers, 5, 21, doi:10.1038/s43586-025-00392-0

work page doi:10.1038/s43586-025-00392-0 2025
[12]

B., Jafarzadeh, S., Keys, P

Jess, D. B., Jafarzadeh, S., Keys, P. H., et al. 2023, Living Reviews in Solar Physics, 20, 1, doi:10.1007/s41116-022-00035-6

work page doi:10.1007/s41116-022-00035-6 2023
[13]

B., Keys, P

Jess, D. B., Keys, P. H., Stangalini, M., & Jafarzadeh, S. 2021, Philo- sophical Transactions of the Royal Society of London Series A, 379, 20200169, doi:10.1098/rsta.2020.0169

work page doi:10.1098/rsta.2020.0169 2021
[14]

B., Mathioudakis, M., Christian, D

Jess, D. B., Mathioudakis, M., Christian, D. J., et al. 2010, Solar Physics, 261, 363, doi:10.1007/s11207-009-9500-0

work page doi:10.1007/s11207-009-9500-0 2010
[15]

B., Shelyag, S., Mathioudakis, M., et al

Jess, D. B., Shelyag, S., Mathioudakis, M., et al. 2012, Astrophysical Journal, 746, 183, doi:10.1088/0004-637X/746/2/183

work page doi:10.1088/0004-637x/746/2/183 2012
[16]

2023, Astronomy & Astrophysics, 675, A182, doi:10.1051/0004-6361/202245410

Kamlah, R., Verma, M., Denker, C., & Wang, H. 2023, Astronomy & Astrophysics, 675, A182, doi:10.1051/0004-6361/202245410

work page doi:10.1051/0004-6361/202245410 2023
[17]

H., Morton, R

Keys, P. H., Morton, R. J., Jess, D. B., et al. 2018, The Astrophysical Journal, 857, 28, doi:10.3847/1538-4357/aab432

work page doi:10.3847/1538-4357/aab432 2018
[18]

J., Khomenko, E., Antolin, P., & Botha, G

Miriyala, H., Morton, R. J., Khomenko, E., Antolin, P., & Botha, G. J. 2025, The Astrophysical Journal, 979, 236, doi:10.3847/ 1538-4357/ada26f

work page 2025
[19]

J., Erdélyi, R., Jess, D

Morton, R. J., Erdélyi, R., Jess, D. B., & Mathioudakis, M. 2011, The Astrophysical Journal, 729, L18, doi:10.1088/2041-8205/729/2/ L18

work page doi:10.1088/2041-8205/729/2/ 2011
[20]

V., Karampelas, K., Riedl, J

Pelouze, G., Doorsselaere, T. V., Karampelas, K., Riedl, J. M., & Duckenfield, T. 2023, Astronomy & Astrophysics, 672, A105, doi:10.1051/0004-6361/202245049

work page doi:10.1051/0004-6361/202245049 2023
[21]

Schiavo, L. A. C. A., Botha, G. J. J., & McLaughlin, J. A. 2026, ApJ, 999, 50, doi:10.3847/1538-4357/ae3da5

work page doi:10.3847/1538-4357/ae3da5 2026
[22]

Silva, S. S. A., González-Avilés, J. J., Riley, P., et al. 2025, The Astro- physical Journal Letters, 994, L27, doi:10.3847/2041-8213/ae1a5e

work page doi:10.3847/2041-8213/ae1a5e 2025
[23]

2025, Astronomy & Astrophysics, 693, A201, doi:10.1051/0004-6361/202451583

Soler, R., & Hillier, A. 2025, Astronomy & Astrophysics, 693, A201, doi:10.1051/0004-6361/202451583

work page doi:10.1051/0004-6361/202451583 2025
[24]

B., Verth, G., et al

Stangalini, M., Jess, D. B., Verth, G., et al. 2021, Astronomy & As- trophysics, 649, A169, doi:10.1051/0004-6361/202140429

work page doi:10.1051/0004-6361/202140429 2021
[25]

2022, Nature Communica- tions, 13, 479, doi:10.1038/s41467-022-28136-8 Article number, page 7 A&A proofs:manuscript no

Stangalini, M., Verth, G., Fedun, V., et al. 2022, Nature Communica- tions, 13, 479, doi:10.1038/s41467-022-28136-8 Article number, page 7 A&A proofs:manuscript no. main Appendix A: Additional MAC matrices To complement the representative G-band example shown in the main text, we present additional MAC matrices for three further pore boundaries. These par...

work page doi:10.1038/s41467-022-28136-8 2022