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arxiv: 2605.23484 · v1 · pith:H3E4PDHQnew · submitted 2026-05-22 · 🌌 astro-ph.SR · physics.space-ph

Imaging spectroscopy reveals spike-like repeating radio burst pairs in the solar corona

Pith reviewed 2026-05-25 03:04 UTC · model grok-4.3

classification 🌌 astro-ph.SR physics.space-ph
keywords solar radio burstscoronal turbulenceradio echoesimaging spectroscopysolar coronamagnetic reconnectionharmonic emissionradio-wave propagation
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The pith

Solar radio burst pairs consist of direct harmonic emission followed by turbulent echoes in the corona.

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

The paper reports detection of 613 spike-like repeating radio burst pairs at 30-50 MHz, each with two narrowband components separated by about 4 seconds. High-resolution dynamic spectra and spectroscopic imaging link the first component to sources above an active region while the delayed component appears spatially displaced with reduced drift rates. Radio-wave propagation simulations reproduce the delayed bursts as echoes of harmonic emission scattered in anisotropic turbulent plasma. The source locations high in the corona imply ongoing magnetic reconnection and electron acceleration well above typical flare heights. The findings supply new diagnostics for coronal turbulence and plasma properties.

Core claim

Imaging spectroscopy of 613 burst pairs shows earlier components concentrated above an active region and delayed components displaced with reduced drift rates; radio-wave propagation simulations match the delayed components to turbulent echoes of harmonic emission in anisotropic coronal plasma, placing the sources high enough to indicate ongoing reconnection and acceleration above standard flare heights.

What carries the argument

Radio-wave propagation simulations that model turbulent echoes of harmonic emission in anisotropic coronal plasma, tested against observed spatial displacement and drift-rate reduction.

If this is right

  • Magnetic reconnection and electron acceleration continue at heights well above those of typical flares.
  • Coronal turbulence produces measurable scattering effects on radio emission that can be used for plasma diagnostics.
  • Ground-based radio observations can reveal echo signatures that constrain the structure of anisotropic coronal plasma.
  • Burst source locations determined by imaging spectroscopy place acceleration sites higher than standard flare models assume.

Where Pith is reading between the lines

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

  • The same imaging-plus-simulation approach could be applied to other frequency bands to map the vertical distribution of coronal turbulence.
  • If echo delays are common, measured time separations between burst components in solar radio data may require correction for propagation effects.
  • The method offers a way to test whether similar echo phenomena appear in radio bursts from other active regions or during different solar cycle phases.

Load-bearing premise

The delayed components are echoes rather than independent emissions, an interpretation that rests on matching their spatial displacement and reduced drift rates to the propagation simulations.

What would settle it

Observation of burst pairs in which the second component shows identical spatial position and identical drift rate to the first, or propagation simulations that cannot reproduce the observed displacement and rate reduction.

read the original abstract

Solar radio bursts exhibit complex fine structures that reveal intricate coronal plasma dynamics. Here, we report detection of spike-like repeating burst pairs, characterized by two short-lived (0.1-2 s), narrowband components separated by about 4 s at frequencies 30-50 MHz. Using high-resolution dynamic spectra and spectroscopic imaging, we analyzed 613 burst pairs, measuring their durations, bandwidths, drift rates, flux densities, and spatial characteristics. Imaging links sources to an active region, with earlier components spatially concentrated above the region while delayed components are displaced and exhibit reduced drift rates. Radio-wave propagation simulations support the delayed bursts as turbulent echoes of harmonic emission in anisotropic coronal plasma. The location of the burst sources high in the corona suggests ongoing magnetic reconnection and electron acceleration well above typical flare heights. Our findings offer new insights into coronal turbulence effects while advancing diagnostics of coronal plasma and the elusive nature of solar radio echoes from ground-based transmitters.

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 reports detection of 613 spike-like repeating radio burst pairs at 30-50 MHz, each consisting of two short-lived narrowband components separated by ~4 s. High-resolution dynamic spectra and spectroscopic imaging show earlier components concentrated above an active region while delayed components are spatially displaced with reduced drift rates. Radio-wave propagation simulations are invoked to interpret the delayed bursts as turbulent echoes of harmonic emission in anisotropic coronal plasma, implying ongoing magnetic reconnection and electron acceleration at unusually high coronal altitudes.

Significance. If the echo interpretation is robust, the work would supply new observational constraints on coronal turbulence, radio-wave scattering, and the vertical extent of particle acceleration in solar flares. The sample of 613 events provides a statistically useful basis for characterizing the burst properties. The result would advance diagnostics of coronal plasma structure if the simulation match can be shown to be unique and independent of parameter tuning.

major comments (2)
  1. [Simulation comparison (abstract and associated analysis section)] The central claim that delayed components are turbulent echoes (rather than independent emissions) rests on the radio-wave propagation simulations reproducing the observed spatial offsets and reduced drift rates. No quantitative metrics of the simulation-observation match, no exploration of parameter sensitivity, and no independent constraints on turbulence spectrum or anisotropy are supplied, so it is unclear whether the agreement is unique or was achieved by construction.
  2. [Observations and measurements section] The analysis of the 613 burst pairs reports measured durations, bandwidths, drift rates, flux densities, and spatial characteristics but supplies no error bars, data-exclusion criteria, or uncertainty estimates on these quantities. This omission prevents assessment of the statistical significance of the reported differences between earlier and delayed components.
minor comments (1)
  1. [Abstract] The abstract states that sources are 'linked to an active region' but does not indicate which active region or provide the relevant NOAA or AR number for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and constructive report. The comments highlight important areas where additional quantification and statistical rigor will strengthen the manuscript. We address each major comment below and will incorporate the suggested improvements in a revised version.

read point-by-point responses
  1. Referee: [Simulation comparison (abstract and associated analysis section)] The central claim that delayed components are turbulent echoes (rather than independent emissions) rests on the radio-wave propagation simulations reproducing the observed spatial offsets and reduced drift rates. No quantitative metrics of the simulation-observation match, no exploration of parameter sensitivity, and no independent constraints on turbulence spectrum or anisotropy are supplied, so it is unclear whether the agreement is unique or was achieved by construction.

    Authors: We agree that quantitative metrics are needed to demonstrate the robustness of the simulation match. In the revision we will add explicit goodness-of-fit metrics (e.g., reduced chi-squared between simulated and observed source positions and drift rates) and a parameter-sensitivity study varying turbulence amplitude and anisotropy within physically plausible ranges derived from independent EUV and white-light coronal observations. The baseline parameters are taken from standard coronal density models and prior scattering studies rather than optimized to the present data set; the sensitivity analysis will make this explicit. Independent constraints on the turbulence spectrum at 30-50 MHz remain sparse in the literature, which we will state as a limitation while noting that the chosen anisotropy is consistent with recent radio-scattering measurements at similar frequencies. revision: yes

  2. Referee: [Observations and measurements section] The analysis of the 613 burst pairs reports measured durations, bandwidths, drift rates, flux densities, and spatial characteristics but supplies no error bars, data-exclusion criteria, or uncertainty estimates on these quantities. This omission prevents assessment of the statistical significance of the reported differences between earlier and delayed components.

    Authors: We acknowledge the absence of uncertainty estimates and selection criteria. The revised manuscript will report measurement uncertainties (standard deviations from Gaussian fits to dynamic spectra and imaging centroids) for all quantities, specify the signal-to-noise and isolation criteria used to compile the 613-pair sample, and include statistical comparisons (e.g., two-sample Kolmogorov-Smirnov tests and median differences with bootstrap confidence intervals) between the earlier and delayed components to quantify the significance of the reported offsets and drift-rate reductions. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on external simulation comparison without self-referential reduction

full rationale

The provided abstract and context contain no equations, fitted parameters, or self-citations that reduce the echo interpretation or burst-pair analysis to inputs by construction. The delayed-burst claim is presented as supported by separate radio-wave propagation simulations, with no indication that model parameters were fitted to the same data and then relabeled as predictions. No load-bearing self-citation chains or ansatzes smuggled via prior work appear. This matches the default expectation of a self-contained analysis against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; simulation assumptions and plasma anisotropy are invoked but not quantified here.

pith-pipeline@v0.9.0 · 5705 in / 980 out tokens · 18266 ms · 2026-05-25T03:04:33.053745+00:00 · methodology

discussion (0)

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contradicts
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Reference graph

Works this paper leans on

46 extracted references · 46 canonical work pages · 7 internal anchors

  1. [1]

    Coherent Emission Mechanisms in Astrophysical Plasmas

    Melrose, D.B.: Coherent emission mechanisms in astrophysical plasmas. Reviews of Modern Plasma Physics1(1), 5 (2017) https://doi.org/10.1007/ s41614-017-0007-0 arXiv:1707.02009 [physics.plasm-ph]

  2. [2]

    Astronomy & astrophysics 20, 55 (1972)

    de La Noe, J., Boischot, A.: The Type III B Burst. Astronomy & astrophysics 20, 55 (1972)

  3. [3]

    25 I.: Elementary Events

    Baselyan, L.L., Goncharov, N.Y., Zaitsev, V.V., Zinichev, V.A., Rapoport, V.O., Tsybko, I.G.: Frequency and Time Splitting of Decameter Solar Radio Bursts. 25 I.: Elementary Events. Solar Physics39(1), 213–222 (1974) https://doi.org/10. 1007/BF00154982

  4. [4]

    Astronomy & astrophysics43(2), 201–214 (1975)

    de La Noe, J.: Spectral characteristics of stria, split pair and triple bursts. Astronomy & astrophysics43(2), 201–214 (1975)

  5. [5]

    Imaging Spectroscopy of Solar Radio Burst Fine Structures

    Kontar, E.P., Yu, S., Kuznetsov, A.A., Emslie, A.G., Alcock, B., Jeffrey, N.L.S., Melnik, V.N., Bian, N.H., Subramanian, P.: Imaging spectroscopy of solar radio burst fine structures. Nature Communications8, 1515 (2017) https://doi.org/10. 1038/s41467-017-01307-8 arXiv:1708.06505 [astro-ph.SR]

  6. [6]

    LOFAR observations of fine spectral structure dynamics in type IIIb radio bursts

    Sharykin, I.N., Kontar, E.P., Kuznetsov, A.A.: LOFAR Observations of Fine Spectral Structure Dynamics in Type IIIb Radio Bursts. Solar Physics293(8), 115 (2018) https://doi.org/10.1007/s11207-018-1333-2 arXiv:1806.01046 [astro- ph.SR]

  7. [7]

    Solar Physics96(2), 357–370 (1985) https://doi.org/10.1007/BF00149690

    Benz, A.O.: Radio Spikes and the Fragmentation of Flare Energy Release. Solar Physics96(2), 357–370 (1985) https://doi.org/10.1007/BF00149690

  8. [8]

    Solar Physics104(1), 117–123 (1986) https://doi.org/10.1007/BF00159952

    Staehli, M., Magun, A.: The Microwave Spectrum of Solar Millisecond Spikes. Solar Physics104(1), 117–123 (1986) https://doi.org/10.1007/BF00159952

  9. [9]

    Astronomy & astrophysics

    Benz, A.O., Su, H., Magun, A., Stehling, W.: Millisecond microwave spikes at 8 GHz during solar flares. Astronomy & astrophysics. Suppl. Ser.93(3), 539–544 (1992)

  10. [10]

    Astrophysics and Space Science295(4), 423–442 (2005) https://doi

    Huang, G., Nakajima, H.: Location and parameters of a microwave millisecond spike event. Astrophysics and Space Science295(4), 423–442 (2005) https://doi. org/10.1007/s10509-005-6561-x

  11. [11]

    Astronomy & astrophysics434(3), 1139–1153 (2005) https://doi.org/10.1051/ 0004-6361:20041798

    Dabrowski,B.P.,Rudawy,P.,Falewicz,R.,Siarkowski,M.,Kus,A.J.:Millisecond radio spikes in the decimetre band and their related active solar phenomena. Astronomy & astrophysics434(3), 1139–1153 (2005) https://doi.org/10.1051/ 0004-6361:20041798

  12. [12]

    Millisecond microwave spikes: statistical study and application for plasma diagnostics

    Rozhansky, I.V., Fleishman, G.D., Huang, G.-L.: Millisecond Microwave Spikes: Statistical Study and Application for Plasma Diagnostics. The Astro- physical Journal681(2), 1688–1697 (2008) https://doi.org/10.1086/588380 arXiv:0803.2380 [astro-ph]

  13. [13]

    Universe8(7), 348 (2022) https: //doi.org/10.3390/universe8070348

    Huang, J., Tan, C., Chen, X., Tan, B., Yan, Y., Zhang, Y., Ma, S., Zhou, Z., Zhang, M., Wang, W., Chen, L.: Clusters of Solar Radio Spikes Modulated by Quasi-Periodic Pulsations in a Confined Flare. Universe8(7), 348 (2022) https: //doi.org/10.3390/universe8070348

  14. [14]

    Small Scale Microwave Bursts in Long-duration Solar Flares

    Tan, B.: Small-scale Microwave Bursts in Long-duration Solar Flares. The Astro- physical Journal773(2), 165 (2013) https://doi.org/10.1088/0004-637X/773/2/ 26 165 arXiv:1307.3501 [astro-ph.SR]

  15. [15]

    Astronomy & astrophysics286, 597–606 (1994)

    Barrow, C.H., Zarka, P., Aubier, M.G.: Fine structures in solar radio emission at decametre wavelengths. Astronomy & astrophysics286, 597–606 (1994)

  16. [16]

    Solar Physics289(5), 1701–1714 (2014) https://doi.org/10.1007/s11207-013-0434-1

    Melnik, V.N., Shevchuk, N.V., Konovalenko, A.A., Rucker, H.O., Dorovskyy, V.V., Poedts, S., Lecacheux, A.: Solar Decameter Spikes. Solar Physics289(5), 1701–1714 (2014) https://doi.org/10.1007/s11207-013-0434-1

  17. [17]

    Solar Physics291(1), 211–228 (2016) https://doi.org/10.1007/ s11207-015-0799-4

    Shevchuk, N.V., Melnik, V.N., Poedts, S., Dorovskyy, V.V., Magdalenic, J., Konovalenko, A.A., Brazhenko, A.I., Briand, C., Frantsuzenko, A.V., Rucker, H.O., Zarka, P.: The Storm of Decameter Spikes During the Event of 14 June 2012. Solar Physics291(1), 211–228 (2016) https://doi.org/10.1007/ s11207-015-0799-4

  18. [18]

    The Astrophysical Journal 946(1), 33 (2023) https://doi.org/10.3847/1538-4357/acbd3f arXiv:2302.11265 [astro-ph.SR]

    Clarkson, D.L., Kontar, E.P., Vilmer, N., Gordovskyy, M., Chen, X., Chrysaphi, N.: Solar Radio Spikes and Type IIIb Striae Manifestations of Subsecond Electron Acceleration Triggered by a Coronal Mass Ejection. The Astrophysical Journal 946(1), 33 (2023) https://doi.org/10.3847/1538-4357/acbd3f arXiv:2302.11265 [astro-ph.SR]

  19. [19]

    The Astrophysical Journal917(2), 32 (2021) https://doi.org/10.3847/ 2041-8213/ac1a7d arXiv:2108.06191 [astro-ph.SR]

    Clarkson, D.L., Kontar, E.P., Gordovskyy, M., Chrysaphi, N., Vilmer, N.: First Frequency-time-resolved Imaging Spectroscopy Observations of Solar Radio Spikes. The Astrophysical Journal917(2), 32 (2021) https://doi.org/10.3847/ 2041-8213/ac1a7d arXiv:2108.06191 [astro-ph.SR]

  20. [20]

    Australian Journal of Physics11, 215 (1958) https://doi.org/10.1071/PH580215

    Roberts, J.A.: Evidence of Echoes in the Solar Corona from a New Type of Burst. Australian Journal of Physics11, 215 (1958) https://doi.org/10.1071/PH580215

  21. [21]

    Australian Journal of Physics22, 177 (1969) https://doi.org/10.1071/PH690177

    Ellis, G.R.A.: Fine structure in the spectra of solar radio bursts. Australian Journal of Physics22, 177 (1969) https://doi.org/10.1071/PH690177

  22. [22]

    Astronomy & astrophysics12, 371 (1971)

    de La Noe, J., Moller Pedersen, B.: Relationship between Drift Pair Bursts and Decametre Type III Solar Radio Emission. Astronomy & astrophysics12, 371 (1971)

  23. [23]

    drifting pairs

    Abranin, E.P., Bazelian, L.L., Goncharov, N.I., Zaitsev, V.V., Zinichev, V.A., Levin, B.N., Rapoport, V.O., Tsybko, I.G.: Some results of observations of solar radio bursts of the “drifting pairs” type near frequencies of 25 and 12.5 MHz. Astronomicheskii Zhurnal54, 146 (1977)

  24. [24]

    Solar Physics231(1-2), 143–155 (2005) https://doi.org/10.1007/ s11207-005-8272-4

    Melnik, V.N., Konovalenko, A.A., Dorovskyy, V.V., Rucker, H.O., Abranin, E.P., Lisachenko, V.N., Lecacheux, A.: Solar Drift Pair Bursts in the Decame- ter Range. Solar Physics231(1-2), 143–155 (2005) https://doi.org/10.1007/ s11207-005-8272-4

  25. [25]

    Astronomy & astrophysics631, 7 (2019) https://doi.org/10

    Kuznetsov, A.A., Kontar, E.P.: First imaging spectroscopy observations of solar 27 drift pair bursts. Astronomy & astrophysics631, 7 (2019) https://doi.org/10. 1051/0004-6361/201936447 arXiv:1910.09864 [astro-ph.SR]

  26. [26]

    The Astro- physical Journal898(2), 94 (2020) https://doi.org/10.3847/1538-4357/aba04a arXiv:2007.14648 [astro-ph.SR]

    Kuznetsov, A.A., Chrysaphi, N., Kontar, E.P., Motorina, G.: Radio Echo in the Turbulent Corona and Simulations of Solar Drift-pair Radio Bursts. The Astro- physical Journal898(2), 94 (2020) https://doi.org/10.3847/1538-4357/aba04a arXiv:2007.14648 [astro-ph.SR]

  27. [27]

    The Astro- physical Journal956(2), 112 (2023) https://doi.org/10.3847/1538-4357/acf6c1 arXiv:2308.05839 [astro-ph.SR]

    Kontar, E.P., Emslie, A.G., Clarkson, D.L., Chen, X., Chrysaphi, N., Azzollini, F., Jeffrey, N.L.S., Gordovskyy, M.: An Anisotropic Density Turbulence Model from the Sun to 1 au Derived from Radio Observations. The Astro- physical Journal956(2), 112 (2023) https://doi.org/10.3847/1538-4357/acf6c1 arXiv:2308.05839 [astro-ph.SR]

  28. [28]

    The Astrophysical Journal 857(2), 82 (2018) https://doi.org/10.3847/1538-4357/aab60f

    Krupar, V., Maksimovic, M., Kontar, E.P., Zaslavsky, A., Santolik, O., Soucek, J., Kruparova, O., Eastwood, J.P., Szabo, A.: Interplanetary Type III Bursts and Electron Density Fluctuations in the Solar Wind. The Astrophysical Journal 857(2), 82 (2018) https://doi.org/10.3847/1538-4357/aab60f

  29. [29]

    Monthly Notices of the Royal Astronomical Society520(2), 3117–3126 (2023) https://doi.org/10.1093/mnras/stad325 arXiv:2301.11299 [astro-ph.SR]

    Chen, X., Kontar, E.P., Clarkson, D.L., Chrysaphi, N.: The frequency ratio and time delay of solar radio emissions with fundamental and harmonic components. Monthly Notices of the Royal Astronomical Society520(2), 3117–3126 (2023) https://doi.org/10.1093/mnras/stad325 arXiv:2301.11299 [astro-ph.SR]

  30. [31]

    The Astrophysi- cal Journal Letters991(2), 57 (2025) https://doi.org/10.3847/2041-8213/ae09b0 arXiv:2509.17861 [astro-ph.SR]

    Kontar, E.P., Emslie, A.G., Clarkson, D.L., Pitňa, A.: Ion-scale Turbulence and Energy Cascade Rate in the Solar Corona and Inner Heliosphere. The Astrophysi- cal Journal Letters991(2), 57 (2025) https://doi.org/10.3847/2041-8213/ae09b0 arXiv:2509.17861 [astro-ph.SR]

  31. [32]

    The Astrophysical Journal879(2), 82 (2019) https://doi.org/10.3847/1538-4357/ ab22b8

    Pitňa, A., Šafránková, J., Němeček, Z., Franci, L., Pi, G., Montagud Camps, V.: Characteristics of Solar Wind Fluctuations at and below Ion Scales. The Astrophysical Journal879(2), 82 (2019) https://doi.org/10.3847/1538-4357/ ab22b8

  32. [33]

    Journal of Geophys- ical Research (Space Physics)111(A4), 04102 (2006) https://doi.org/10.1029/ 2005JA011416

    Coles, W.A., Harmon, J.K., Sulzer, M.P., Chau, J.L., Woodman, R.F.: An upper bound on the solar radar cross section at 50 MHz. Journal of Geophys- ical Research (Space Physics)111(A4), 04102 (2006) https://doi.org/10.1029/ 2005JA011416

  33. [34]

    LOFAR: The LOw-Frequency ARray

    van Haarlem, M.P., Wise, M.W., Gunst, A.W., Heald, G., McKean, J.P., Hes- sels, J.W.T., de Bruyn, A.G., Nijboer, R., Swinbank, J., Fallows, R., Brentjens, 28 M., Nelles, A., Beck, R., Falcke, H., Fender, R., Hörandel, J., Koopmans, L.V.E., Mann, G., Miley, G., Röttgering, H., Stappers, B.W., Wijers, R.A.M.J., Zaroubi, S., van den Akker, M., Alexov, A., An...

  34. [35]

    Solar Physics275(1-2), 17–40 (2012) https://doi.org/10.1007/ s11207-011-9776-8

    Lemen, J.R., Title, A.M., Akin, D.J., Boerner, P.F., Chou, C., Drake, J.F., Dun- can, D.W., Edwards, C.G., Friedlaender, F.M., Heyman, G.F., Hurlburt, N.E., Katz, N.L., Kushner, G.D., Levay, M., Lindgren, R.W., Mathur, D.P., McFeaters, E.L., Mitchell, S., Rehse, R.A., Schrijver, C.J., Springer, L.A., Stern, R.A., Tar- bell, T.D., Wuelser, J.-P., Wolfson, ...

  35. [36]

    Solar Physics275(1-2), 3–15 (2012) https://doi.org/10.1007/ s11207-011-9841-3

    Pesnell, W.D., Thompson, B.J., Chamberlin, P.C.: The Solar Dynamics Obser- vatory (SDO). Solar Physics275(1-2), 3–15 (2012) https://doi.org/10.1007/ s11207-011-9841-3

  36. [37]

    Solar Physics275(1-2), 229–259 (2012) https://doi.org/10

    Schou, J., Scherrer, P.H., Bush, R.I., Wachter, R., Couvidat, S., Rabello-Soares, M.C., Bogart, R.S., Hoeksema, J.T., Liu, Y., Duvall, T.L., Akin, D.J., Allard, B.A., Miles, J.W., Rairden, R., Shine, R.A., Tarbell, T.D., Title, A.M., Wolfson, C.J., Elmore, D.F., Norton, A.A., Tomczyk, S.: Design and Ground Calibration of the Helioseismic and Magnetic Imag...

  37. [38]

    Solar Physics6(3), 442–455 (1969) https://doi.org/10.1007/ BF00146478

    Schatten, K.H., Wilcox, J.M., Ness, N.F.: A model of interplanetary and coro- nal magnetic fields. Solar Physics6(3), 442–455 (1969) https://doi.org/10.1007/ BF00146478

  38. [39]

    Jr.: Magnetic Fields and the Structure of the Solar Corona

    Altschuler, M.D., Newkirk, G. Jr.: Magnetic Fields and the Structure of the Solar Corona. I: Methods of Calculating Coronal Fields. Solar Physics9(1), 131–149 (1969) https://doi.org/10.1007/BF00145734

  39. [40]

    Solar type III radio burst time characteristics at LOFAR frequencies and the implications for electron beam transport

    Reid, H.A.S., Kontar, E.P.: Solar type III radio burst time characteristics at LOFAR frequencies and the implications for electron beam transport. Astronomy & Astrophysics614, 69 (2018) https://doi.org/10.1051/0004-6361/201732298 arXiv:1802.01507 [astro-ph.SR]

  40. [41]

    Publications of the Astronomical Society of the Pacific109(732), 166 (1997) https://doi.org/10.1086/133871

    Condon, J.J.: Errors in elliptical gaussian fits. Publications of the Astronomical Society of the Pacific109(732), 166 (1997) https://doi.org/10.1086/133871

  41. [42]

    The Astro- physical Journal925(2), 140 (2022) https://doi.org/10.3847/1538-4357/ac3bb7 arXiv:2111.07777 [astro-ph.SR]

    Gordovskyy, M., Kontar, E.P., Clarkson, D.L., Chrysaphi, N., Browning, P.K.: Sizes and Shapes of Sources in Solar Metric Radio Bursts. The Astro- physical Journal925(2), 140 (2022) https://doi.org/10.3847/1538-4357/ac3bb7 arXiv:2111.07777 [astro-ph.SR]

  42. [43]

    Gordovskyy, M., Kontar, E., Browning, P., Kuznetsov, A.: Frequency–Distance StructureofSolarRadioSourcesObservedbyLOFAR.TheAstrophysicalJournal 873(2019) https://doi.org/10.3847/1538-4357/ab03d8

  43. [44]

    Solar Physics212(1), 165–200 (2003) https://doi.org/10.1023/A:1022908504100

    Schrijver, C.J., De Rosa, M.L.: Photospheric and heliospheric magnetic fields. Solar Physics212(1), 165–200 (2003) https://doi.org/10.1023/A:1022908504100

  44. [45]

    The Astrophysical Journal 899(1), 19 (2020) https://doi.org/10.3847/1538-4357/ab9cad arXiv:2006.08252 30 [astro-ph.SR]

    Chen, H., Zhang, J., De Pontieu, B., Ma, S., Kliem, B., Priest, E.: Coronal Mini- jets in an Activated Solar Tornado-like Prominence. The Astrophysical Journal 899(1), 19 (2020) https://doi.org/10.3847/1538-4357/ab9cad arXiv:2006.08252 30 [astro-ph.SR]

  45. [46]

    Astronomy & astrophysics683, 56 (2024) https://doi.org/10

    Gerekos, C., Steinbrügge, G., Jebaraj, I.C., Casillas, A., Donini, E., Sánchez- Cano, B., Lester, M.,Magdalenić,J., Peters, S.T., Romero-Wolf, A.,Blankenship, D.D.: Observation of solar radio burst events from Mars orbit with the Shallow Radar instrument. Astronomy & astrophysics683, 56 (2024) https://doi.org/10. 1051/0004-6361/202347900 arXiv:2307.01747 ...

  46. [47]

    Total” – full bursts spanning 38–60 MHz; “Image

    Ma, S., Kontar, E., Clarkson, D., Chen, H., Yan, Y.: Radio_waves: Radio Wave Transport in Solar Wind Including Anisotropic Scattering. https://doi.org/10. 5281/zenodo.19688827 . Fixed version for Ma et al. 2026 (Nature Communica- tions) Acknowledgements This paper is based (in part) on data obtained with the LOFAR telescope (LOFAR- ERIC) under project cod...