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arxiv: 2606.22667 · v1 · pith:BDOFOXHJnew · submitted 2026-06-21 · 🌌 astro-ph.HE

Polarization Angle Geodesics in PSRs B1133+16 and B2016+28

M. M. McKinnon This is my paper

Pith reviewed 2026-06-26 09:39 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords pulsar polarizationPoincare sphereorthogonal modesPSR B1133+16PSR B2016+28mode transitionspolarization geodesics
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The pith

Pulsar polarization angles follow great circles on the Poincare sphere due to mode transitions.

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

The paper reanalyzes polarization observations of PSRs B1133+16 and B2016+28 to test whether their position and ellipticity angles trace circles on the Poincare sphere. In B1133+16 a portion of the angles traces a full great circle; in B2016+28 the path is an arc that matches a great-circle segment modified by the star's rotation. Three separate polarization models applied to the data all attribute these geodesics to a change in which orthogonal mode dominates as pulse longitude varies. The result extends the known behavior of mode transitions beyond the sphere's equator and suggests such arcs appear more often than earlier work assumed.

Core claim

The polarization angles observed in part of PSR B1133+16 follow a great circle on the Poincare sphere. The angles observed across the pulse of PSR B2016+28 follow an arc that resembles a portion of a great circle that has been altered by the pulsar's rotation. The observations are interpreted within the context of three different polarization models. All three models produce similar results for both pulsars and indicate that the observed geodesics are caused by mode transitions. The arc observed in PSR B2016+28 can also be interpreted as a vector rotation, provided the modes are elliptically polarized.

What carries the argument

Transitions in dominance between two orthogonal polarization modes, with changing relative intensity versus pulse longitude, that trace a great circle (or arc) on the Poincare sphere.

If this is right

  • Mode transitions produce geodesics away from the equatorial plane of the Poincare sphere.
  • Arcs and partial circles may occur more commonly in pulsar polarization profiles than previously recognized.
  • The arc in PSR B2016+28 admits an alternative interpretation as a phase-driven vector rotation when the modes are elliptically polarized.
  • The same three models give consistent results across both pulsars, supporting mode transitions as the common mechanism.

Where Pith is reading between the lines

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

  • Repeating the analysis on a larger set of pulsars would test how frequently mode-transition arcs appear.
  • Wavelength-dependent observations could separate intensity-driven from phase-driven paths more cleanly than longitude-only data allow.
  • If the geodesics survive subtraction of known propagation effects, they could serve as a direct probe of mode competition in the emission region.

Load-bearing premise

The observed polarization angles are produced solely by the relative intensities or phases of two orthogonal modes without significant additional effects from propagation, scattering, or instrumental leakage.

What would settle it

High-resolution polarization measurements of the same pulse phases in either pulsar that deviate from the predicted great-circle paths once estimated propagation and scattering contributions are removed.

Figures

Figures reproduced from arXiv: 2606.22667 by M. M. McKinnon.

Figure 1
Figure 1. Figure 1: Pulse profiles of PSR B1133+16 (left column) and PSR B2016+28 (right column) at 1404 MHz. The top row of the figure shows the total intensity (I, solid black line), total polarization (P, dashed green line), linear polarization (L, dashed red line), and circular polarization (V, dashed blue line) for each pulsar. The variations in the PAs and EAs across the pulse of each pulsar are, respectively, shown in … view at source ↗
Figure 2
Figure 2. Figure 2: Dependence of pulsar EAs upon their PAs. The top panel shows the PA-EA pairs observed in PSR B1133+16. The bottom panel shows the pairs observed in PSR B2016+28. Small circles (SC, dashed blue lines) and great circles (GC, solid green lines) are overlaid on portions of the data in both panels. The parameters that characterize the circles are annotated in each panel. The isolated numbers in the panels denot… view at source ↗
Figure 3
Figure 3. Figure 3: Variations in the polarization fraction and EA due to changes in the parameters of the PCOH and EPC polarization models. Top panel: the solid colored lines show the variations in p and χ expected from the PCOH model when the parameter m varies, while η and C are held constant. The dashed lines show the p-χ variations caused by changes in C while η and |m| are held constant. The solid black line shows the p… view at source ↗
Figure 4
Figure 4. Figure 4: Variations in the polarization fraction and EA due to changes in the parameters of the NPM polarization model. Top panel: the colored lines show the expected variations in p and χ when m varies, while δl and δv are held constant. The solid black line shows the p-χ variations observed in PSR B1133+16. Bottom panel: the solid colored lines show the expected variations in p and χ when δl varies, while m and δ… view at source ↗
Figure 5
Figure 5. Figure 5: Results of the PCOH model applied to the first PA discontinuity in PSR B1133+16 assuming the observed variations in p and χ are caused by a mode transition with a varying coherence fraction. The top panel shows how the calculated coherence fraction varies with ppb. The circles in the bottom panel show how the calculated values of m vary with ppb. The lines represent the best fit of the data points to a str… view at source ↗
Figure 6
Figure 6. Figure 6: Results of the NPM model applied to PSR B1133+16 assuming the observed variations in p and χ are caused by a mode transition with varying nonorthogonality in circular polarization, δv. The parameter m is shown in the bottom panel, and the value of δv is shown in the top panel. The values of δv and m that follow the dashed red lines are associated with one another. The same is true of the values of δv and m… view at source ↗
Figure 7
Figure 7. Figure 7: Results of the NPM model applied to PSR B1133+16 (top panel) and PSR B2016+28 (bottom panel) assuming the observed variations in p and χ are caused by variations in the parameters δl and δv. The calculated nonorthogonality in linear polarization is represented by the solid line, and the nonorthogonality in circular polarization is denoted by the dashed line. The parameter m was set to zero in the calculati… view at source ↗
Figure 8
Figure 8. Figure 8: Results of the PCOH model applied to PSR B2016+28 assuming the observed variations in p and χ are caused by a mode transition with a varying coherence fraction. The calculated coherence fraction is shown in the top panel. The circles in the bottom panel are the calculated values of m. The lines represent the best fit of the data points to a straight line. The mode phase offset used in the calculation was η… view at source ↗
Figure 9
Figure 9. Figure 9: Results of the PCOH model applied to PSR B2016+28 assuming the observed variations in p and χ are caused by a vector rotation with a varying coherence fraction. The top panel shows the calculated coherence fraction (solid line) and the observed polarization fraction (dashed line). The circles in the bottom panel show the calculated values of η. The values of C and η were calculated assuming the OPMs are el… view at source ↗
Figure 10
Figure 10. Figure 10: Results of the NPM model applied to PSR 2016+28 assuming the observed variations in p and χ are caused by a mode transition with varying nonorthogonality in circular polarization, δv. The parameter m is shown in the bottom panel, and the value of δv is shown in the top panel. The values of δv and m that follow the dashed red lines are associated with one another. The same is true of the values of δv and m… view at source ↗
Figure 11
Figure 11. Figure 11: Geometry of a GC and an SC arising, respectively, from a mode transition and a vector rotation. The top-left panel shows the plane of a GC (solid black line) within the Poincar´e sphere (dotted circle). In this example, the vector that is normal to the GC plane, vn, has an azimuth of φ = 2ψn = 0 and a latitude of λ = 2χn. The top-right panel shows the GC geodesic (red arc) traced by a mode transition from… view at source ↗
read the original abstract

Recent models of pulsar polarization predict that the position and ellipticity angles of the polarization vector can trace portions of a small or great circle on the Poincare sphere. A great circle can arise from a transition in dominance of orthogonal polarization modes, where the relative intensity of the modes changes with pulse longitude. A small circle may be caused by a rotation of the vector, where the phase difference between the modes changes with pulse longitude or wavelength. Observations of PSRs B1133+16 and B2016+28 are reanalyzed to search for these polarization features within their pulse profiles. The polarization angles observed in part of PSR B1133+16 are shown to follow a great circle on the Poincare sphere. The angles observed across the pulse of PSR B2016+28 follow an arc that resembles a portion of a great circle that has been altered by the pulsar's rotation. The observations are interpreted within the context of three different polarization models. All three models produce similar results for both pulsars and indicate that the observed geodesics are caused by mode transitions. The arc observed in PSR B2016+28 can also be interpreted as a vector rotation, provided the modes are elliptically polarized. The observations and accompanying analysis show that mode transitions are not restricted to the equatorial plane of the Poincare sphere and that arcs and partial circles may be more common than previously recognized.

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

3 major / 1 minor

Summary. The paper reanalyzes existing radio polarization observations of PSRs B1133+16 and B2016+28. It reports that the polarization angles in a portion of the B1133+16 profile trace a great circle on the Poincaré sphere, while those across the B2016+28 pulse trace an arc resembling a portion of a great circle modified by rotation. These features are interpreted as arising from transitions in dominance between orthogonal polarization modes, with supporting results from three distinct polarization models that all indicate mode transitions rather than pure vector rotation.

Significance. If the geodesic identification is placed on a quantitative footing, the result would indicate that orthogonal-mode transitions are not confined to the equatorial plane of the Poincaré sphere and that partial arcs may be more common than previously appreciated. The consistency across three independent models is a positive feature of the analysis.

major comments (3)
  1. [Abstract] Abstract: the central claim that the observed angles 'follow a great circle' or 'resemble a portion of a great circle' is presented without any quantitative metric (maximum angular deviation, rms residual, or goodness-of-fit statistic) or comparison of model predictions to the measured angles; visual inspection alone cannot support the mode-transition interpretation.
  2. [Abstract] Abstract and § on observations: no error bars, data-exclusion criteria, or sensitivity tests are reported for the polarization angles or ellipticities; without these, it is impossible to assess whether residual contributions from propagation, scattering, or leakage could exceed a few degrees and thereby invalidate the geodesic identification.
  3. [Abstract] Abstract: the statement that 'all three models produce similar results' is not accompanied by any tabulated comparison of predicted versus observed angles, differences between models, or residual maps, leaving the robustness of the mode-transition conclusion unquantified.
minor comments (1)
  1. Notation for the Poincaré-sphere coordinates (position angle, ellipticity) should be defined explicitly at first use rather than assumed from prior literature.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight areas where the manuscript can be strengthened with additional quantitative detail. We address each major comment below and will incorporate the suggested improvements in a revised version.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the observed angles 'follow a great circle' or 'resemble a portion of a great circle' is presented without any quantitative metric (maximum angular deviation, rms residual, or goodness-of-fit statistic) or comparison of model predictions to the measured angles; visual inspection alone cannot support the mode-transition interpretation.

    Authors: We agree that explicit quantitative metrics will strengthen the claim. The figures demonstrate close adherence, but in revision we will add RMS residuals, maximum angular deviations from the fitted great circle, and a chi-squared goodness-of-fit comparison between the mode-transition model and a pure vector-rotation model. These will be reported in the abstract and analysis sections. revision: yes

  2. Referee: [Abstract] Abstract and § on observations: no error bars, data-exclusion criteria, or sensitivity tests are reported for the polarization angles or ellipticities; without these, it is impossible to assess whether residual contributions from propagation, scattering, or leakage could exceed a few degrees and thereby invalidate the geodesic identification.

    Authors: We will revise the observations section to include error bars on all polarization angles and ellipticities, explicitly document the S/N and linear-polarization thresholds used for data inclusion, and add a brief sensitivity test demonstrating that the geodesic identification remains stable under plausible levels of additional scatter from propagation or leakage. revision: yes

  3. Referee: [Abstract] Abstract: the statement that 'all three models produce similar results' is not accompanied by any tabulated comparison of predicted versus observed angles, differences between models, or residual maps, leaving the robustness of the mode-transition conclusion unquantified.

    Authors: We will add a table in the revised manuscript that lists the best-fit parameters from each of the three models, together with RMS residuals between model predictions and observed angles for both pulsars. This will quantify the similarity across models and support the mode-transition interpretation. revision: yes

Circularity Check

0 steps flagged

No circularity: reanalysis applies external models to data without self-referential reduction

full rationale

The paper reanalyzes existing polarization observations of two pulsars by mapping position and ellipticity angles onto the Poincare sphere and comparing the resulting paths to predictions from three polarization models. The models are invoked as independent frameworks (great-circle geodesics from orthogonal-mode intensity transitions; small-circle arcs from phase rotation), and the text states that all three yield similar results without any parameter being fitted to the target geodesics themselves. No equation or claim reduces the observed arc to a quantity defined by the same data, no self-citation supplies a uniqueness theorem that forces the interpretation, and no ansatz is smuggled in. The analysis is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that three standard polarization models (not specified in abstract) correctly map observed angles to mode intensity or phase changes. No free parameters, new axioms, or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Polarization vectors can be represented on the Poincare sphere with position and ellipticity angles tracing geodesics under mode transitions.
    Invoked throughout the abstract as the geometric basis for interpreting the observed arcs.

pith-pipeline@v0.9.1-grok · 5780 in / 1291 out tokens · 18527 ms · 2026-06-26T09:39:57.280931+00:00 · methodology

discussion (0)

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Reference graph

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