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Estimating the Poynting flux of Alfv\'enic waves in polar coronal holes across Solar Cycle 24

T0 review · 3 major / 8 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Alfvénic wave energy flux into polar coronal holes is broadly constant across Solar Cycle 24, averaging about 99 W/m² at 20 Mm above the limb.

desk verdict A useful multi-epoch estimate of coronal-hole Alfvénic Poynting flux, but the cycle-invariance claim is softer than the abstract implies. read the letter →

arxiv 2501.13673 v1 pith:V4ACBQYT submitted 2025-01-23 astro-ph.SR

Richard J. Morton , Micah J. Weberg , N. Balodhi , James A. McLaughlin This is my paper · ORCID
classification astro-ph.SR
keywords AlfvénicwavesPoyntingfluxcoronalholessolarcycleSDO/AIAobservationsseismologywindenergybudget
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether the energy carried by Alfvénic waves into the Sun's polar coronal holes changed over Solar Cycle 24, and finds that its measured vertical Poynting flux stays broadly constant. The authors tracked fine-scale structures in SDO/AIA 171 Å images from eight southern coronal holes sampled roughly annually from 2010 to 2017, combining the wave measurements with electron densities from differential emission measure inversions and magnetic field strengths from potential-field extrapolations. They report an average vertical Poynting flux of 99 W/m² with a standard deviation of 28 W/m², and argue that the roughly 30% scatter between epochs reflects differences between individual coronal holes rather than the phase of the solar cycle. If correct, the Alfvénic wave energy input to the fast solar wind does not track solar magnetic activity, a useful constraint for models that tune wave energy to predict solar wind properties.

What carries the argument

The load-bearing identity is the time-averaged vertical Poynting flux for kink/Alfvénic waves, $\langle S_z\rangle \approx \sqrt{\rho/\mu_0}\, B\, v^2$, obtained from the MHD kink mode under the approximations that internal and external densities are nearly equal in coronal holes and that the flux-tube filling factor is close to one. Here $\rho$ is the mass density estimated from DEM-based electron density with the equivalent column depth formula, $B$ is the average magnetic field strength from potential-field source-surface extrapolations, and $v$ is the velocity amplitude of fine-scale coronal structures, derived by Fourier-transforming their tracked displacements in time-distance diagrams. This formula turns the observations of transverse motions, plasma density, and magnetic field into an energy flux per unit area, which is evaluated at 20 Mm above the limb for each coronal hole.

What would settle it

Compute the full-frequency integrated Poynting flux for the same eight coronal holes (or a denser time series across Cycle 24 and into Cycle 25) and compare it with 10.7 cm radio flux or sunspot number; a correlation between integrated flux and magnetic activity, or a disagreement between integrated and mean-amplitude trends, would refute the claim that the wave contribution to the solar wind energy budget is cycle-independent.

Watch

Extended reading notes

Core claim

The paper's central claim is that the vertical Poynting flux of Alfvénic waves in polar coronal holes shows no significant variation over Solar Cycle 24. At 20 Mm above the limb, the wave measurements give a mean vertical Poynting flux of $\bar{\langle S\rangle}=99\ \mathrm{W\,m^{-2}}$ with a standard deviation of $28\ \mathrm{W\,m^{-2}}$, and the fluxes show no evident correlation with the 10.7 cm radio flux or sunspot number. The authors are careful to call this a measure of Poynting flux rather than the total flux: it is based on the mean velocity amplitude, which effectively picks out a single frequency, and it likely underestimates the true value because of unknown wave polarization and unresolved wave modes. Their key assertion is that the constancy of this measure reflects a constant contribution from waves to the solar wind energy budget, with the year-to-year variation attributed to differences among individual coronal holes.

Load-bearing premise

The conclusion that wave energy input is independent of the solar cycle rests on the assumption that the variation in energy flux computed from the mean velocity amplitude is proportional to the variation in the total wave energy flux, even though the measurements sample only selected structures at effectively one frequency per epoch.

Editorial extensions

If this is right

  • If the constancy is real, Alfvén-wave-driven solar wind models should not need a cycle-dependent wave amplitude at the coronal base; any cycle modulation in their predicted wind properties would then come from the evolving magnetic field alone.
  • The roughly 30% variation between individual coronal holes sets a noise floor for single-epoch estimates, meaning one snapshot cannot reliably separate a solar-cycle trend from hole-to-hole differences.
  • The lack of correlation with the 10.7 cm flux suggests that the p-mode amplitude variations seen in sun-as-star measurements reflect conditions in the magnetic activity belt rather than in the polar regions where the fast wind originates.
  • Because the measured waves have periods mostly above about 100 s and are interpreted as energy-containing scales for turbulence, the flux values provide a useful constraint on the energy input used in Alfvénic turbulence models of the solar wind.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: repeating this analysis across Solar Cycle 25 would test whether the flatness is a general property of the driving mechanism rather than a coincidence of Cycle 24.
  • Editorial inference: integrating the velocity power spectra over all frequencies, instead of using the mean amplitude, would directly test whether the single-frequency measure tracks the total flux; the same datasets could support this calculation.
  • Editorial inference: if the cycle invariance holds for Sun-like stars, stellar wind models predicting mass and angular momentum loss should treat wave amplitude as roughly constant over magnetic activity cycles, which would change the predicted cycle modulation of stellar spin-down.
  • Editorial inference: adding polarization information or measuring at additional passbands could reveal whether the absolute flux is closer to the ~500 W/m² model-inferred values without changing the conclusion about cycle independence.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 8 minor

Summary. The paper uses SDO/AIA 171 Å imaging to measure transverse (Alfvénic) wave displacements of fine-scale structure in southern polar coronal holes at seven altitudes between 5 and 20 Mm, for eight epochs spanning 2010–2017. It combines these wave measurements with densities from AIA DEM inversions and magnetic field strengths from GONG-driven PFSS extrapolations to estimate the vertical Poynting flux at 20 Mm via Eq. (9). The reported mean vertical Poynting flux is 99 W/m² with a standard deviation of 28 W/m², which the authors interpret as 'broadly similar' over the solar cycle, with the residual scatter attributed to differences between individual coronal holes. The paper also compares these estimates with the Poynting fluxes inferred by Huang et al. (2023, 2024) from AWSoM model runs, and concludes that both datasets point to a lack of correlation between coronal Alfvénic-wave Poynting flux and the solar cycle.

Significance. If the central claim holds, the paper provides an important multi-epoch observational constraint on the Alfvénic wave energy input into polar coronal holes, with direct implications for wave-driven solar wind models that currently treat the coronal wave amplitude (or Poynting flux) as a free parameter. The measurement approach is laudable for combining three independent observational ingredients—imaging-derived wave amplitudes, DEM-derived densities, and PFSS-derived magnetic fields—and for clearly flagging several caveats, including the polarization lower bound and the single-frequency-sampling issue. The authors also correctly avoid overstating the precision of the absolute flux and state openly which parts of the comparison rely on normalization. The significance is, however, moderated by two load-bearing limitations: the statistical case for cycle invariance is made by visual inspection rather than a quantitative correlation test, and the scaling of the mean-amplitude flux to the total wave energy flux is assumed rather than tested. The comparison to Huang et al. is also normalized by construction, so the abstract's word 'agreement' needs to be qualified.

major comments (3)
  1. [§4.3 and Figure 11] The central claim of cycle-invariant Poynting flux rests on a visual impression: the text says 'the wave fluxes do not visually show any correlation with the 10.7 cm flux (any numerical estimates of correlation would be highly uncertain)' and 'there is no apparent correlation'. With only n = 8 epochs and a 30% scatter, a quantitative test is both feasible and necessary. A Spearman rank correlation of the eight Poynting-flux estimates against the 10.7 cm flux or sunspot number, with p-value and a statement of the statistical power of an n = 8 test, should be reported. Without such a test, the statement 'broadly similar over the solar cycle' and the conclusion 'no apparent correlation to magnetic activity' are not quantitatively supported.
  2. [§4.3, paragraph beginning 'There is also an unresolved issue around picking values of velocity amplitude'] The load-bearing assumption that 'the variations in wave energy flux calculated from the mean value of velocity amplitude reflect the variation in total wave energy flux' is admitted but not tested. Because Eq. (9) is evaluated with a single statistic (the mean velocity amplitude) that effectively samples wave energy at approximately one frequency per measurement, a stable marginal period distribution does not guarantee a stable joint amplitude–frequency distribution or a stable power-spectral shape. This matters because the abstract's conclusion about a 'consistent contribution from waves to the energy budget of the solar wind' concerns the total wave energy input, not merely the mean-amplitude measure. The authors explicitly decline to construct a PSD-based integrated flux ('We do not tackle this challenge here'); this is the one analysis that would resolve the concern, and the manuscript should either provide it, or explicitly restrict the conclusion to the mean-amplitude proxy and soften the energy-budget claim accordingly.
  3. [Abstract, §4.3, and Figure 11 caption] The abstract states that 'Our direct estimates are in agreement with recent studies by Huang_2023,Huang2024', but this agreement is engineered by multiplying the Huang et al. fluxes by a constant so that their mean matches the observational mean. The text states 'we multiply the results from Huang et al. (2023, 2024) by a constant such that the mean of the simulation results matches the observational value', and Figure 11 shows the Huang 2023 points 'reduced from true value by a factor of 0.2'. After this normalization, only the relative trends (not the absolute flux levels) can be compared. The abstract should be revised to state that the cycle-invariance of the two datasets are qualitatively consistent in trend after matching the mean, or the normalization constant and its uncertainty should be presented explicitly so the reader can see what the comparison does and does not establish.
minor comments (8)
  1. [Title page / affiliation] The author affiliation reads 'US Navel Research Laboratory'; this should be 'US Naval Research Laboratory'.
  2. [§4.1 heading] The heading 'Distributions of wave proprieties' contains a typo; it should be 'wave properties'.
  3. [Introduction, first paragraph] The sentence 'examining if there are is any evidence for variation' contains a grammatical error; it should be 'if there is any evidence'.
  4. [Conclusion, first paragraph] 'a continuos energy flux' should be 'a continuous energy flux'.
  5. [§4.2, paragraph following Eq. (7)] The text says the flow terms 'scale as v0/cph2'; this should be written as (v0/cph)² to avoid ambiguity.
  6. [Figure 11 caption] The caption states that Huang et al. (2023) points are 'reduced from true value by a factor of 0.2' but does not say whether the same factor applies to the Huang et al. (2024) points or how the factor was determined; specify the normalization constant and its provenance (including which of the two correction factors—the factor of 10 or the mean-matching factor—is being displayed).
  7. [Section 1 and §4.3 footnotes] The factor-of-10 correction to the Huang et al. values is attributed to private confirmation with the authors; since this correction directly affects the quoted absolute fluxes (470–520 W/m²), a published erratum, a reproducibility note, or a statement of the basis for the correction should be included so readers can verify the numbers.
  8. [§4.3, Eqs. (7)–(8) and following text] The symbol α is used both for the radius fraction in Eq. (8) and for the inverse filling factor in the Goossens et al. inequality; the notation should be disambiguated to avoid confusion about the physical meaning of α in each place.

Circularity Check

1 steps flagged · score 3.0 of 10

The direct Poynting-flux measurement is independent, but the claimed agreement with Huang et al. is constructed by mean-matching normalization; the cycle-invariance conclusion also rests on an explicitly untested single-frequency sampling assumption.

  1. fitted input called prediction [Abstract; Section 4.3 (Poynting fluxes), Figure 11 caption]
    "Our direct estimates are in agreement with recent studies by Huang et al. (2023, 2024) ... Hence in order to contrast the vertical Poynting flux in the simulations to our results, we multiply the results from Huang et al. (2023, 2024) by a constant such that the mean of the simulation results matches the observational value. ... Also shown are the wave energy flux estimates from Huang et al. (2023) (squares - reduced from true value by a factor of 0.2, see text)."

    The mean of the Huang series is forced to equal the observed mean by selecting the multiplicative constant (0.2), so the absolute numerical agreement asserted in the abstract is not an independent confirmation but a definitional consequence of the normalization. After the fit, only the relative pattern (scatter and absence of trend) can be compared; that weaker comparison may support the no-cycle-correlation conclusion, but it is not the same as the 'agreement' claimed. Hence the agreement claim reduces, by construction, to the fitted scaling. The underlying direct flux estimate and its own cycle scatter are not affected.

full rationale

The central observational estimate is not circular: the vertical Poynting-flux measure, Eq. 9, is evaluated from independent ingredients — AIA 171 Å wave tracking, DEM-derived density, and potential-field-source-surface magnetic field — so the 99 ± 28 W/m² figure and its cycle-to-cycle scatter are a direct measurement rather than a restatement of inputs. The load-bearing assumption in Section 4.3 that mean-velocity-amplitude flux variations track total wave-energy-flux variations is explicitly acknowledged ('We do not tackle this challenge here') and is an untested proportionality, not a definitional identity; it weakens the inference to total wave energy but does not make the derivation circular. Same-author methodological citations (Weberg et al. 2018, 2020; Morton & Cunningham 2023) are code-released or empirical and do not smuggle in the target result; the DEM neural-network reference to Balodhi & Morton (2024, in prep) is a reproducibility gap, but the resulting densities are benchmarked against external coronal-hole measurements. The one genuinely circular element is the comparison to Huang et al.: the abstract claims agreement, while Section 4.3 states that the Huang values were multiplied by a constant chosen so that the simulation mean matches the observed mean, so the absolute agreement is enforced by the fit rather than independently established. This does not infect the main cycle-invariance conclusion, which stands on the direct measurements, but it does make the abstract's 'agreement' claim partially constructed.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central estimate rests on established MHD formulas and measured quantities, so the free-parameter burden is modest. The main fitted element is the rescaling factor used to align Huang et al. fluxes with the observed mean. The density and magnetic field inputs carry several domain assumptions (DEM inversion, PFSS, column depth) that are standard but not bias-free. No new entities are introduced.

free parameters (3)
  • Multiplicative rescaling factor for Huang et al. (2023, 2024) fluxes = 0.2
    Applied in Section 4.3 and Figure 11 so that the mean of the model-inferred Poynting fluxes equals the observed mean of 99 W/m²; this normalization creates the apparent agreement between the two datasets.
  • Equivalent column depth z_eq = 1.4E10 to 2.3E10 cm
    Section 4.3: computed from Eq. 4 using the DEM-weighted temperature at 20 Mm; the multi-thermal temperature choice is non-unique and directly scales the electron density, hence the Poynting flux.
  • Mean wave velocity amplitude (per year) = not tabulated; varies approximately 20-30% between years
    Section 3.1 and 4.3: the average of the measured velocity amplitude distribution is used in Eq. 9 as a single representative frequency; this is a modeling choice that sets the flux magnitude and is not a full spectral integral.
assumptions (6)
  • domain assumption The observed fine-scale transverse motions are MHD kink/Alfvénic modes, so the linearized Poynting flux formulas (Eqs. 7-9) apply.
    Section 1 and 4.3 interpret the motions via Spruit (1982) and Goossens et al. (2013); this underpins the conversion of measured displacements into energy flux.
  • domain assumption The overdensity of coronal hole fine structure is small, so rho_i/rho_e is approximately 1 and the kink flux reduces to Eq. 9.
    Section 4.3: intensity overdensity of 2-3% and no observed damping; this approximation sets the normalization of the flux estimate.
  • domain assumption Potential field source surface models (pfsspy, source surface at 2.5 R_sun) give the coronal magnetic field strength.
    Section 3.3 uses GONG synoptic maps and PFSS to obtain B at 20 Mm; the Poynting flux scales linearly with B.
  • domain assumption The DEM inversion and the Aschwanden and Acton (2001) column depth model give an unbiased electron density.
    Section 3.2 derives density from EM divided by z_eq, with z_eq from Eq. 4; a non-unique temperature choice enters and systematic biases are not propagated.
  • ad hoc to paper Variations in the mean wave amplitude track variations in the total broadband wave energy flux.
    Section 4.3 explicitly assumes this because period distributions are stable across the cycle; it is the load-bearing assumption for the cycle-independence conclusion.
  • standard math The solar wind outflow contribution to the Poynting flux is negligible at the observed heights.
    Section 4.3 shows the flow term scales as v0/c_ph^2, with v0 about 10 km/s versus 300-500 km/s propagation speeds, so it is dropped.

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Cite this review

Pith. "Pith review of Estimating the Poynting flux of Alfv\'enic waves in polar coronal holes across Solar Cycle 24." pith.science (2026). https://pith.science/paper/V4ACBQYT

@misc{pith2026250113673,
  author       = {Pith},
  title        = {Pith review of: Estimating the Poynting flux of Alfv\'enic waves in polar coronal holes across Solar Cycle 24},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V4ACBQYT}},
  note         = {Machine review of arXiv:2501.13673}
}
read the original abstract

Alfv\'enic waves are known to be prevalent throughout the corona and solar wind. Determining the Poynting flux supplied by the waves is required for constraining their role in plasma heating and acceleration, as well as providing a constraint for Alfv\'en wave driven models that aim to predict coronal and solar wind properties. Previous studies of the Alfv\'enic waves in polar coronal holes have been able to provide a measure of energy flux for arbitrary case studies. Here we build upon previous work and take a more systematic approach, examining if there is evidence for any variation in vertical Poynting flux over the course of the solar cycle. We use imaging data from SDO/AIA to measure the displacements of the fine-scale structure present in coronal holes. It is found that the measure for vertical Poynting flux is broadly similar over the solar cycle, implying a consistent contribution from waves to the energy budget of the solar wind. There is variation in energy flux across the measurements (around 30\%), but this is suggested to be due to differences in the individual coronal holes rather than a feature of the solar cycle. Our direct estimates are in agreement with recent studies by \cite{Huang_2023,Huang2024} who constrain the vertical Poynting flux through comparison of predicted wind properties from Alfv\'enic wave driven turbulence models to those observed with OMNI at 1~AU. Taken together, both sets of results points towards a lack of correlation between the coronal Poynting flux from waves and the solar cycle.

Figures

Figures reproduced from arXiv: 2501.13673 by the authors.

Figure 1
Figure 1. Comparison of solar activity and dates of data sets used. The top panel shows the total (blue), Northern [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Same as Figure 2 but for coronal holes observed between 2014 and 2017. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Box plots for wave observations in southern coronal holes taken at 5 Mm above the limb during the different [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Same as Figure 4 but for wave observations in southern coronal holes taken at 20 Mm above the limb during [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Displacement amplitude as function of height for all coronal holes. The data points and error bars correspond [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Results of Differential Emission Measure (DEM) analysis. The figure shows the DEM results for the 2017 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Magnetic field extrapolations. Panel a) shows GONG magnetogram from 2017 during Carrington rotation [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: Estimated magnetic and plasma properties for the coronal holes. Panels a) and b) show the average temperature [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: Example power spectral densities for displacement amplitude (top) and velocity amplitude (bottom) for the [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: A measure of the Poynting flux in the coronal holes calculated at 20 Mm above the limb. Note this value [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Co-existence of longitudinal and transverse oscillations in polar plumes observed with Solar Orbiter/EUI

    astro-ph.SR 2025-09 conditional novelty 6.0 of 10

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Pith tools

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