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arxiv: 2604.12731 · v1 · submitted 2026-04-14 · 🌌 astro-ph.SR

Solar Orbiter observations of solar energetic electron events associated with hard microflares

Diane Mittaine , Andrea Francesco Battaglia , Laura Rodr\'iguez-Garc\'ia , Nils Janitzek , Ra\'ul G\'omez-Herrero , Francisco Espinosa Lara , Louise Harra This is my paper

Pith reviewed 2026-05-10 14:24 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords hard microflaressolar energetic electronshard X-ray spectraelectron accelerationSolar Orbitermagnetic connectivitySTIXEPD
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The pith

Hard microflares accelerate electrons efficiently and launch them as solar energetic electrons on open sunspot field lines.

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

Hard microflares show unusually flat hard X-ray spectra, indicating they accelerate electrons to high energies despite releasing little total energy compared with large flares. This study matches Solar Orbiter STIX hard X-ray observations of eight such events with EPD measurements of the associated in-situ electrons. Timing from velocity dispersion and magnetic connectivity estimates confirm the Sun-to-spacecraft link in seven cases, and the electron spectra remain hard, extending the known HXR-to-electron index correlation to the small-event regime. The results indicate that these microflares can inject energetic particles into interplanetary space without needing the energy scale of major flares.

Core claim

HMFs produce prompt SEEs with hard spectra, demonstrating efficient electron acceleration without requiring large flare energy release. Their magnetic configuration, involving open field lines from the sunspot, suggests they may be an important contributor to filling the heliosphere with energetic particles.

What carries the argument

Joint HXR spectroscopy of HMFs with STIX and in-situ electron spectral analysis with EPD, tied together by timing coincidence and magnetic connectivity estimates.

Load-bearing premise

The eight events are correctly paired with their in-situ electrons through timing and connectivity, and interplanetary transport does not substantially soften the observed electron spectra relative to the flare-accelerated population.

What would settle it

An HMF with clear magnetic connectivity whose velocity-dispersion injection time misses the hard X-ray peak or whose in-situ electron spectrum is much softer than the HXR photon index predicts.

Figures

Figures reproduced from arXiv: 2604.12731 by Andrea Francesco Battaglia, Diane Mittaine, Francisco Espinosa Lara, Laura Rodr\'iguez-Garc\'ia, Louise Harra, Nils Janitzek, Ra\'ul G\'omez-Herrero.

Figure 1
Figure 1. Figure 1: Solar Orbiter/STIX images of the four hard microflares not present in Battaglia et al. (2024) and representing flares in lines 1, 2, 7, and 8 of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: VDA fitting of the EPT-South electrons for the event on [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Background-subtracted peak flux spectrum of the EPT [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Pre-flare background subtracted STIX count spectrum [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Background-subtracted EPD peak flux spectra for four selected events. The fainter, lower-intensity points indicate the pre [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Correlation plots of the in-situ electron spectral index [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Electron spectral index δHXR as a function of the background-subtracted GOES flux of different studies. Events with general statistical studies of flares and microflares have been represented in gray, and the reference sample of hard mi￾croflares of Battaglia et al. (2024) in black. Studies comparing electron spectra in-situ and in HXRs have been represented in blue (Krucker et al. 2007) and green (Dresing… view at source ↗
Figure 8
Figure 8. Figure 8: HXR RHESSI images of two events from previous studies. [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
read the original abstract

Generally, large solar flares accelerate electrons to high energies more efficiently than microflares. However, some microflares, known as hard microflares (HMFs), also produce high-energy electrons, as indicated by their flat hard X-ray (HXR) spectra. These events are typically associated with footpoints located in or at the edge of sunspots. The mechanisms behind this efficient acceleration, and their connection to solar energetic electrons (SEEs), remain unclear. We compare, for the first time, HXR spectra of HMFs with in-situ electron spectra of associated SEEs using Solar Orbiter STIX and EPD observations. This provides insight into acceleration processes and the transport of high-energy electrons into interplanetary space. We identify eight HMFs observed jointly by Solar Orbiter and Earth-based instruments that are associated with SEEs, confirmed through timing and magnetic connectivity analysis. Each event is studied using HXR spectroscopy, SEE velocity-dispersion analysis, and in-situ electron spectral analysis. Seven of eight events show consistent timing between flare HXR emission and inferred electron injection, as well as good agreement with magnetic connectivity estimates. The known correlation between HXR photon and in-situ electron spectral indices extends to HMFs, which occupy the hard end of the distribution, even compared to larger flares. We conclude that HMFs produce prompt SEEs with hard spectra, demonstrating efficient electron acceleration without requiring large flare energy release. Their magnetic configuration, involving open field lines from the sunspot, suggests they may be an important contributor to filling the heliosphere with energetic particles.

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 / 2 minor

Summary. The manuscript reports Solar Orbiter STIX and EPD observations of eight hard microflares (HMFs) jointly detected with Earth-based instruments and associated with solar energetic electron events (SEEs). It finds that seven of the eight events exhibit consistent timing between HXR peaks and velocity-dispersion-derived injection times, plus good agreement with magnetic connectivity estimates. The known correlation between HXR photon and in-situ electron spectral indices is shown to extend to these HMFs, which occupy the hard end of the distribution. The authors conclude that HMFs produce prompt SEEs with hard spectra via efficient acceleration, without needing large flare energy release, and that their sunspot-associated open field lines may make them important contributors to heliospheric energetic particles.

Significance. If the event associations and spectral results hold after uncertainty quantification, the work provides the first direct comparison of HMF HXR spectra with associated in-situ SEE spectra. It strengthens evidence that small-scale events can accelerate electrons to high energies efficiently and extends the spectral-index correlation into a harder regime, with potential implications for models of particle escape along open fields from sunspots and the overall contribution of microflares to heliospheric particle populations.

major comments (2)
  1. [Event identification and association] Event identification section: The claim of seven-of-eight events showing 'consistent timing' and 'good agreement' with connectivity rests on timing coincidence and magnetic connectivity estimates, but the manuscript provides no quantified uncertainties (e.g., 1-sigma widths on EPD velocity-dispersion injection times, footpoint uncertainties from PFSS source-surface height or active-region extrapolations). Without these or a control test against random coincidences, the robustness of the association rate cannot be evaluated and directly affects the 'prompt SEEs' and 'hard spectra' conclusions.
  2. [Spectral analysis] Spectral analysis and results: The extension of the HXR-electron spectral index correlation to HMFs is a central result, yet details on spectral fitting procedures, error propagation, and any selection biases (e.g., restricting to events with clear SEE detections) are not reported. This leaves open whether the placement of HMFs at the hard end of the distribution is representative or influenced by the association criteria.
minor comments (2)
  1. [Abstract] Abstract: Specify the energy ranges over which the HXR and electron spectral indices are measured to allow direct comparison with prior flare studies.
  2. [Figures] Figures: Include explicit statements in figure captions about the fitting methods, energy ranges, and how uncertainties are displayed in the spectral plots and timing diagrams.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We have carefully considered the major comments and provide point-by-point responses below. Where appropriate, we have revised the manuscript to incorporate additional details on uncertainties and analysis methods to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Event identification and association] Event identification section: The claim of seven-of-eight events showing 'consistent timing' and 'good agreement' with connectivity rests on timing coincidence and magnetic connectivity estimates, but the manuscript provides no quantified uncertainties (e.g., 1-sigma widths on EPD velocity-dispersion injection times, footpoint uncertainties from PFSS source-surface height or active-region extrapolations). Without these or a control test against random coincidences, the robustness of the association rate cannot be evaluated and directly affects the 'prompt SEEs' and 'hard spectra' conclusions.

    Authors: We agree that providing quantified uncertainties would improve the evaluation of the event associations. In the revised version, we have included 1-sigma error bars on the velocity dispersion analysis for the injection times from the EPD data. For magnetic connectivity, we have added estimates of uncertainties arising from the choice of source surface height in the PFSS model and variations in active region extrapolations. While a formal control test for random coincidences was not included originally, the specific timing matches (within minutes of expected delays) and connectivity to the observed active regions make chance associations unlikely. We have added a brief discussion quantifying the expected number of random matches based on the timing window and event rate. These revisions support our conclusion of prompt SEEs associated with the HMFs. revision: yes

  2. Referee: [Spectral analysis] Spectral analysis and results: The extension of the HXR-electron spectral index correlation to HMFs is a central result, yet details on spectral fitting procedures, error propagation, and any selection biases (e.g., restricting to events with clear SEE detections) are not reported. This leaves open whether the placement of HMFs at the hard end of the distribution is representative or influenced by the association criteria.

    Authors: We acknowledge the need for more transparency in the spectral analysis. The revised manuscript now includes a dedicated subsection detailing the spectral fitting procedures for both STIX HXR spectra (using thermal plus non-thermal power-law models) and EPD in-situ electron spectra (power-law fits in the relevant energy range). Error propagation is described, accounting for Poisson statistics, background subtraction, and instrumental uncertainties. Regarding selection biases, the events were identified based on joint observations by Solar Orbiter and Earth-based instruments with SEE detections, but the spectral hardness was not a selection criterion; all detected HMFs were included. We have clarified that the sample is representative of HMFs with associated SEEs, and their position at the hard end extends the known correlation without bias from the association. This addresses the concern and reinforces the central result. revision: yes

Circularity Check

0 steps flagged

No circularity: purely observational analysis with standard techniques

full rationale

The paper reports direct Solar Orbiter STIX and EPD measurements of eight hard microflares and associated in-situ electrons. Event identification uses timing coincidence between HXR peaks and velocity-dispersion injection times plus magnetic connectivity estimates; spectral indices are compared via standard HXR and electron spectroscopy. These steps apply established methods to new data without any mathematical derivation, parameter fitting that defines the target quantity, or load-bearing self-citation. The extension of the known HXR-electron index correlation is an empirical observation, not a constructed prediction. The analysis chain is therefore self-contained and externally falsifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

This is a purely observational study using established solar physics analysis methods on public instrument data; no new free parameters, ad-hoc axioms, or invented physical entities are introduced.

axioms (1)
  • domain assumption Standard assumptions of solar flare electron acceleration and interplanetary transport physics
    The timing, connectivity, and spectral comparisons rest on established models of electron propagation from the Sun to the spacecraft.

pith-pipeline@v0.9.0 · 5620 in / 1266 out tokens · 32870 ms · 2026-05-10T14:24:33.016796+00:00 · methodology

discussion (0)

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Works this paper leans on

58 extracted references · 58 canonical work pages

  1. [1]

    F., Swisdak, M., et al

    Arnold, H., Drake, J. F., Swisdak, M., et al. 2021, Phys. Rev. Lett., 126, 135101

    work page 2021

  2. [2]

    P., van Driel-Gesztelyi, L., et al

    Baker, D., Rouillard, A. P., van Driel-Gesztelyi, L., et al. 2009, Annales Geo- physicae, 27, 3883

    work page 2009

  3. [3]

    S., Benz, A

    Bastian, T. S., Benz, A. O., & Gary, D. E. 1998, ARA&A, 36, 131

    work page 1998

  4. [4]

    Battaglia, A. F. & Krucker, S. 2025, A&A, 694, A58

    work page 2025

  5. [5]

    F., Krucker, S., Veronig, A

    Battaglia, A. F., Krucker, S., Veronig, A. M., et al. 2024, A&A, 691, A172

    work page 2024

  6. [6]

    F., Saqri, J., Massa, P., et al

    Battaglia, A. F., Saqri, J., Massa, P., et al. 2021, A&A, 656, A4

    work page 2021

  7. [7]

    C., & Benz, A

    Battaglia, M., Grigis, P. C., & Benz, A. O. 2005, A&A, 439, 737

    work page 2005

  8. [8]

    Benz, A. O. 2017, Living Reviews in Solar Physics, 14, 59

    work page 2017

  9. [9]

    Brown, J. C. 1971, Solar Physics, 18, 489–502

    work page 1971

  10. [10]

    Domingo, V ., Fleck, B., & Poland, A. I. 1995, Solar Physics, 162, 1

    work page 1995

  11. [11]

    2020, ApJ, 889, 143

    Dresing, N., Effenberger, F., Gómez-Herrero, R., et al. 2020, ApJ, 889, 143

    work page 2020

  12. [12]

    2021, A&A, 654, A92

    Dresing, N., Warmuth, A., Effenberger, F., et al. 2021, A&A, 654, A92

    work page 2021

  13. [13]

    2026, A&A, 706, A107

    Fedeli, A., Dresing, N., Gieseler, J., et al. 2026, A&A, 706, A107

    work page 2026

  14. [14]

    R., Hudson, H

    Fletcher, L., Dennis, B. R., Hudson, H. S., et al. 2011, Space Sci. Rev., 159, 19

    work page 2011

  15. [15]

    Freeland, S. L. & Handy, B. N. 1998, Solar Physics, 182, 497

    work page 1998

  16. [16]

    E., Chen, B., Dennis, B

    Gary, D. E., Chen, B., Dennis, B. R., et al. 2018, ApJ, 863, 83 Article number, page 13 A&A proofs:manuscript no. main

    work page 2018

  17. [17]

    2023, Frontiers in Astronomy and Space Sciences, 9, 384 Gómez-Herrero, R., Pacheco, D., Kollhoff, A., et al

    Gieseler, J., Dresing, N., Palmroos, C., et al. 2023, Frontiers in Astronomy and Space Sciences, 9, 384 Gómez-Herrero, R., Pacheco, D., Kollhoff, A., et al. 2021, A&A, 656, L3

    work page 2023

  18. [18]

    G., Christe, S., Krucker, S., et al

    Hannah, I. G., Christe, S., Krucker, S., et al. 2008, ApJ, 677, 704

    work page 2008

  19. [19]

    D., Aschwanden, M

    Holman, G. D., Aschwanden, M. J., Aurass, H., et al. 2011, A&A, 136, 107

    work page 2011

  20. [20]

    S., O’Brien, H., Carrasco Blazquez, I., et al

    Horbury, T. S., O’Brien, H., Carrasco Blazquez, I., et al. 2020, A&A, 642, 11

    work page 2020

  21. [21]

    J., Krucker, S., Lin, R

    Hurford, G. J., Krucker, S., Lin, R. P., et al. 2006, ApJ, 644, L93 Högbom, J. A. 1974, Astronomy and Astrophysics Supplement, 15, 417

    work page 2006

  22. [22]

    L., Kucera, T

    Kaiser, M. L., Kucera, T. A., Davila, J. M., et al. 2008, Space Sci. Rev., 136, 5

    work page 2008

  23. [23]

    P., Bischof, L., et al

    Kistler, F., Janitzek, N. P., Bischof, L., et al. 2025, Solar Orbiter Flare Link - Au- tomated Linkage between Solar Flares and Energetic Particle Events,https: //flaretool.pmodwrc.ch/#so-flink-solar-orbiter-flare-link

    work page 2025

  24. [24]

    Kontar, E. P. & Reid, H. A. 2009, The Astrophysical Journal Letters, 695, 4

    work page 2009

  25. [25]

    J., Grimm, O., et al

    Krucker, S., Hurford, G. J., Grimm, O., et al. 2020, A&A, 642, A15

    work page 2020

  26. [26]

    P., Christe, S., Glesener, L., & Lin, R

    Krucker, S., Kontar, E. P., Christe, S., Glesener, L., & Lin, R. P. 2011, ApJ, 742, 82

    work page 2011

  27. [27]

    P., Christe, S., & Lin, R

    Krucker, S., Kontar, E. P., Christe, S., & Lin, R. P. 2007, ApJ, 663, L109

    work page 2007

  28. [28]

    H., & Lin, R

    Krucker, S., Oakley, P. H., & Lin, R. P. 2009, ApJ, 691, 806

    work page 2009

  29. [29]

    S., et al

    Krucker, S., Saint-Hilaire, P., Hudson, H. S., et al. 2015, ApJ, 802, 19

    work page 2015

  30. [30]

    A., Gómez-Herrero, R., et al

    Lario, D., Balmaceda, L. A., Gómez-Herrero, R., et al. 2024, ApJ, 975, 84

    work page 2024

  31. [31]

    1985, Solar Physics, 100, 537

    Lin, R., P. 1985, Solar Physics, 100, 537

    work page 1985

  32. [32]

    P., Anderson, K

    Lin, R. P., Anderson, K. A., Ashford, S., et al. 1995, Space Sci. Rev., 71, 125

    work page 1995

  33. [33]

    P., Dennis, B

    Lin, R. P., Dennis, B. R., Hurford, G. J., et al. 2002, Sol. Phys., 210, 3

    work page 2002

  34. [34]

    P., Dennis, B

    Lin, R. P., Dennis, B. R., Hurford, G. J., et al. 2002, Solar Physics, 210, 3

    work page 2002

  35. [35]

    Y ., Reid, H

    Lorfing, C. Y ., Reid, H. A. S., Gómez-Herrero, R., et al. 2023, A&A, 959, 11

    work page 2023

  36. [36]

    M., Kouloumvakos, A., Ho, G

    Mason, G. M., Kouloumvakos, A., Ho, G. C., et al. 2025, ApJ, 992, 24

    work page 2025

  37. [37]

    1994, Nature, 371, 495 Müller, D., St

    Masuda, S., Kosugi, T., Hara, H., Tsuneta, S., & Ogawara, Y . 1994, Nature, 371, 495 Müller, D., St. Cyr, O. C., Zouganelis, I., et al. 2020, A&A, 642, A1 Müller-Mellin, R., Böttcher, S., Falenski, J., et al. 2008, Space Sci. Rev., 136, 363

    work page 1994

  38. [38]

    Ogilvie, K. W. & Desch, M. D. 1997, Advances in Space Research, 20, 559

    work page 1997

  39. [39]

    J., Bruno, R., Livi, S., et al

    Owen, C. J., Bruno, R., Livi, S., et al. 2020, A&A, 642, 36

    work page 2020

  40. [40]

    2018, Solar Physics, 293, 53

    Paassilta, M., Papaioannou, A., Dresing, N., et al. 2018, Solar Physics, 293, 53

    work page 2018

  41. [41]

    2022, Frontiers in Astronomy and Space Sciences, 9, id.395

    Palmroos, C., Gieseler, J., Dresing, N., et al. 2022, Frontiers in Astronomy and Space Sciences, 9, id.395

    work page 2022

  42. [42]

    Parker, E. N. 1973, ApJ, 180, 247

    work page 1973

  43. [43]

    Reid, H. A. & Kontar, E. P. 2010, A&A, 721, 864

    work page 2010

  44. [44]

    Reid, H. A. & Kontar, E. P. 2013, Solar Physics, 285, 217 Rodríguez-García, L., Gómez-Herrero, R., Dresing, N., et al. 2025, A&A, 694, A64 Rodríguez-García, L., Gómez-Herrero, R., Dresing, N., et al. 2023, A&A, 670, A51 Rodríguez-García, L., Gómez-Herrero, R., Zouganelis, I., et al. 2021, A&A, 653, A137 Rodríguez-Pacheco, J., Wimmer-Schweingruber, R. F., ...

    work page 2013

  45. [45]

    P., Pinto, R

    Rouillard, A. P., Pinto, R. F., V ourlidas, A., et al. 2020, A&A, 642, 32

    work page 2020

  46. [46]

    M., Battaglia, A

    Saqri, J., Veronig, A. M., Battaglia, A. F., et al. 2024, A&A, 683, A41

    work page 2024

  47. [47]

    H., Bogart, R

    Scherrer, P. H., Bogart, R. S., Bush, R. I., et al. 1995, Sol. Phys., 162, 129

    work page 1995

  48. [48]

    A., Csillaghy, A., Tolbert, A

    Schwartz, R. A., Csillaghy, A., Tolbert, A. K., et al. 2002, Solar Physics, 210, 165–191

    work page 2002

  49. [49]

    W., et al

    Shibata, K., Ishido, Y ., Acton, L. W., et al. 1992, PASJ, 44, L173

    work page 1992

  50. [50]

    D., Dresing, N., Kollhoff, A., & Brüdern, M

    Strauss, R. D., Dresing, N., Kollhoff, A., & Brüdern, M. 2020, ApJ, 897, 24

    work page 2020

  51. [51]

    2013, Journal of Space Weather and Space Climate, 3, A12

    Vainio, R., Valtonen, E., Heber, B., et al. 2013, Journal of Space Weather and Space Climate, 3, A12

    work page 2013

  52. [52]

    P., Krucker, S., & Mason, G

    Wang, L., Lin, R. P., Krucker, S., & Mason, G. M. 2012, ApJ, 759, 69

    work page 2012

  53. [53]

    F., Krucker, S., & Wang, L

    Wang, W., Battaglia, A. F., Krucker, S., & Wang, L. 2023, ApJ, 950, 118

    work page 2023

  54. [54]

    & Mann, G

    Warmuth, A. & Mann, G. 2016, A&A, 588, 16

    work page 2016

  55. [55]

    & Mann, G

    Warmuth, A. & Mann, G. 2020, A&A, 644, A172

    work page 2020

  56. [56]

    2025, A&A, 701, 27

    Warmuth, A., Schuller, F., Gómez-Herrero, R., et al. 2025, A&A, 701, 27

    work page 2025

  57. [57]

    F., Berger, L., Kollhoff, A., et al

    Wimmer-Schweingruber, R. F., Berger, L., Kollhoff, A., et al. 2023, A&A, 678, 11

    work page 2023

  58. [58]

    F., Janitzek, N

    Wimmer-Schweingruber, R. F., Janitzek, N. P., Pacheco, D., et al. 2021, A&A, 656, 17 Article number, page 14 D. Mittaine et al.: Solar Orbiter observations of SEE events associated with HMFs Appendix A: VDA analysis: SERPENTINE tool and EPT-viewing selection A.1. VDA method Under the standard VDA assumptions described in Section 3.2, electrons of differen...

    work page 2021