Energy budget in the 2017-09-07 "cold" solar flare

Galina G. Motorina; Gelu M. Nita; Gregory D. Fleishman; Sijie Yu

REVIEW 3 major objections 5 minor 25 references

Energy budget in the 2017-09-07 "cold" solar flare

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read In the 2017-09-07 'cold' solar flare, nonthermal electron energy deposition alone explains the observed thermal emission.

desk verdict A careful, useful single-event energy budget that makes a reasonable case for another cold flare, but the 'no direct heating' conclusion outruns the evidence and the hot-plasma volume from the 3D model is the linchpin to check. read the letter →

arxiv 2506.15501 v1 pith:LIGZI7FR submitted 2025-06-18 astro-ph.SR

Gregory D. Fleishman , Galina G. Motorina , Sijie Yu , Gelu M. Nita This is my paper · ORCID

classification astro-ph.SR

keywords solarflarescoldenergybudgetnonthermalelectronscoronalmagneticfieldmicrowaveimagingspectroscopyEOVSAX-rays

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 studies the 2017 September 7 'cold' solar flare, a compact early impulsive event in which nearly all released magnetic energy is thought to go into accelerating electrons rather than directly heating plasma. The authors assemble X-ray, EUV, and microwave imaging spectroscopy observations, including the first Expanded Owens Valley Solar Array data for a cold flare, to compute the flare's thermal and nonthermal energy budgets. Their central claim is that the cumulative energy deposited by the accelerated electrons is sufficient to account for the entire observed thermal emission, so the thermal plasma is purely the response to nonthermal energy deposition and no direct heating is required. This matters because confirmed cold flares give the cleanest available test of how magnetic energy is converted into particle acceleration and then into heat in the solar corona.

What carries the argument

The argument rests on an energy-budget comparison between two independently derived quantities. The nonthermal energy deposition rate is obtained from thick-target hard X-ray fits as $dW_{\rm nth}/dt = F_0 E_c\,(\delta-1)/(\delta-2)$, integrated over time, with $F_0$ the total electron flux, $E_c$ the low-energy cutoff, and $\delta$ the electron spectral index. The thermal energy of the hot plasma is computed from the isothermal fit as $W_{\rm th} = 3k_B T \sqrt{EM\cdot V}$, where $V$ is taken from the hottest loop (Loop 2) of a 3D model built to reproduce the microwave, X-ray, and EUV data. The supporting measurement is the EOVSA spectral fitting, which yields maps of the coronal magnetic field, thermal density, and nonthermal electron density, revealing a soft-hard-soft evolution of the spectral index from about 15 to 3 and back while the magnetic field stays nearly constant.

What would settle it

Direct X-ray imaging of a cold flare that resolves the hot source volume would test the claim: if the thermal energy computed with the measured volume exceeds the cumulative nonthermal energy deposition, then nonthermal deposition alone cannot explain the flare's heat.

Watch

Extended reading notes

Core claim

The paper establishes that in the 2017 September 7 'cold' flare, the nonthermal energy deposition from the accelerated electrons is sufficient to drive the observed thermal response. The thermal energies derived from AIA differential emission measure maps and from the isothermal component of the Fermi/GBM fits evolve together with the cumulative nonthermal energy computed from the thick-target electron parameters, and the cumulative nonthermal input is sufficient to account for the peak thermal energy. A second result is the direct coronal magnetic field measurement from EOVSA microwave imaging spectroscopy: the field at the flare site stays near 500--600 G with no statistically significant variation, and its uncertainty is about an order of magnitude larger than both the thermal and nonthermal energies, leaving ample free energy to drive the flare. The paper concludes that the entire thermal emission is the plasma's response to nonthermal energy deposition, with no direct plasma heating, making this flare a clean case for the cold-flare scenario.

Load-bearing premise

The conclusion depends on the assumed volume of the hottest X-ray-emitting plasma, which is taken from one loop of a 3D model instead of from imaging; if the true volume differs by more than a factor of a few, the thermal energy estimate changes and could exceed the nonthermal energy available.

Editorial extensions

If this is right

If cold flares are always nonthermal-dominated, their thermal emission can be used as a calorimeter of the energy that accelerated electrons deposit in the corona, giving a direct constraint on acceleration efficiency.
The pronounced soft-hard-soft spectral evolution measured in microwaves, from index about 15 down to 3 and back within seconds, places a tight observational constraint on particle acceleration models.
The near-constancy of the coronal magnetic field during the flare, combined with the large uncertainty in magnetic energy, means that magnetic energy release cannot be directly detected in this event; larger datasets or higher sensitivity would be needed to confirm the magnetic free energy supply.
The consistency between the nonthermal energy computed from hard X-rays and that from the 3D model with sub-second escape time indicates that the single power-law thick-target model is sufficient to capture the energy budget in this compact flare.

Reading between the lines

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

If the hot-source volume were measured directly for a sample of cold flares, a similar budget analysis could determine whether nonthermal sufficiency holds universally or only when the hot loop is compact, and could sharpen the thermal-to-nonthermal ratio.
The apparent anti-correlation between the total electron density above 15 keV and the microwave flux at the peak suggests that the single power-law assumption may undercount or overcount the actual emitting electrons; testing a broken power-law or a kappa distribution might alter the inferred energy partition.
The same EOVSA plus X-ray methodology could be applied to 'early impulsive' flares that are not formally cold, to see whether the nonthermal-dominated energy budget is a property of the compactness of the flare rather than of the class itself.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper is worth reading. It is the first cold flare with EOVSA microwave imaging spectroscopy, and it uses that to measure the coronal magnetic field (a null result), to show a pronounced soft-hard-soft evolution of the microwave-emitting electrons, and to assemble a multi-instrument energy budget. The authors are honest about the main weakness: with no X-ray imaging, the volume of the hot X-ray source is taken from their 3D model, and they say so in Section 8.2. That alone puts it above much of the flare-energetics literature.

What is genuinely new is the EOVSA data applied to this subclass. The magnetic field stability during the flare is a clean measurement, and the SHS pattern in microwaves is a nice addition. The energy budget comparison between nonthermal deposition (from Fermi/GBM) and thermal energy (from AIA and Fermi/GBM) is plausible, and the 3D model is used as a cross-check rather than as the sole basis. I appreciate that they show the model thermal energies as diamonds on the same plot, so you can see the loop-by-loop breakdown.

The soft spots are real but not fatal. The quantitative linchpin is Equation (3): W_GBM_th scales as sqrt(V), with V = 1.49e26 cm3 taken from Loop 2 of the 3D model. A factor of 4 in volume doubles the thermal energy and would erode the sufficiency margin. The paper concedes the volume issue, but it still phrases the abstract as 'likely sufficient' and then in Section 9.1 goes further: 'no direct plasma heating.' Correlation and sufficiency cannot prove that. That sentence should be softened unless they can rule out direct heating independently. Also, the magnetic energy statement in the abstract is a bit loose: an uncertainty larger than the flare energy means you cannot detect a change, not that you have proven enough free energy exists. That is a minor point.

Figure 13 has no propagated uncertainties on the energy curves. Adding even rough error bars would help the reader see how close the sufficiency margin actually is. The ad hoc third flux tube in the 3D model only affects the nonthermal lower bound, not the central thermal-vs-nonthermal comparison, so I do not weight that heavily.

Who is this for? Flare modelers and observers working on energy budgets and the cold-flare scenario. It is a solid case study, not a paradigm shift. It deserves a serious referee, not a desk reject. I would recommend sending it to review with the request that the authors either quantify the volume uncertainty directly or pull back the no-direct-heating claim to match the evidence.

Referee Report

3 major / 5 minor

Summary. The paper presents a multi-instrument energy budget analysis of the 2017-09-07 C4.5 'cold' solar flare, the first such event observed with EOVSA microwave imaging spectroscopy. Using Fermi/GBM and Konus-Wind hard X-ray spectroscopy, SDO/AIA DEM analysis, GOES, and a 3D magnetic loop model built with the GX simulator, the authors derive the thermal energy of the hot plasma, the cumulative nonthermal electron energy deposition, and the model-based nonthermal energy of three flux tubes. They report that the nonthermal energy deposition is sufficient to account for the observed thermal response, infer a soft-hard-soft spectral evolution of microwave-emitting electrons, find no statistically significant coronal magnetic field variations, and conclude that 'there was no direct plasma heating in this flare.'

Significance. If the central energy-budget claim holds, this event provides a clean observational case in which the entire thermal output of a flare can be attributed to the collisional deposition of accelerated electrons, which is an important test for flare acceleration and heating models. The paper's strengths include the first EOVSA-based study of a cold flare, the derivation of evolving magnetic field and density maps in the flaring corona, the construction of a data-constrained 3D model, and a generally transparent presentation of the data and fitting procedures. The authors are also candid in Section 8.2 about the lack of X-ray imaging and the resulting uncertainty in the hot-loop volume. However, the strongest conclusion, the absence of direct plasma heating, is not fully supported by the evidence presented, because the quantitative comparison in Figure 13 depends on a model-chosen volume and the model-based nonthermal energy lower bound is dominated by an ad hoc flux tube.

major comments (3)

[Section 8.2, Eq. (3)] The thermal energy W_GBM_th scales as sqrt(V) with V taken from Loop 2 of the trial-and-error 3D model of Section 6 rather than from an independent imaging measurement. Because the 3D model was tuned to reproduce the same microwave and X-ray data used elsewhere in the energy budget, V is not an independent constraint; the spectral fits determine EM = n^2 V, so density and volume are degenerate. The manuscript acknowledges this in Section 8.2, but it does not quantify the impact on the budget. Since a factor-of-four increase in V would double W_GBM_th and could erase the margin of nonthermal sufficiency seen in Figure 13, the paper should present a sensitivity analysis over plausible volumes (e.g., from the ROI volume used in Section 9.2) or obtain an independent volume constraint before drawing the no-direct-heating conclusion.
[Section 9.1] The statement 'there was no direct plasma heating in this flare and that the entire thermal emission was due to the plasma's response to the nonthermal energy deposition' is stronger than what the preceding analysis establishes. The evidence shows that the nonthermal deposition is sufficient and that the thermal and nonthermal energies are correlated, but sufficiency plus correlation does not rule out an additional direct-heating contribution. The conclusion should be softened to a statement of consistency with a nonthermal-dominated scenario, or supplemented with a quantitative upper limit on any direct-heating component.
[Section 8.3 and Table 1] The model-based lower bound Wnth > 2.4e28 erg is dominated by the nonthermal energy of Loop 3 (2.49e27 erg in Table 1), a third flux tube introduced in Section 6 to account for the low-frequency spectral flattening. The parameters of this loop are the least constrained part of the model, and the escape-time upper bound tau_esc < 1 s is inferred indirectly from the lack of a measurable HXR-microwave delay rather than measured directly. The claim that the model-based estimate is 'consistent with' W_GBM_nth therefore rests on the weakest model component; a sensitivity study varying Loop 3 properties and tau_esc is needed to support this comparison.

minor comments (5)

[Section 9.2] The source volume is given as V ≈ 6e26 cm^-3; the units should be cm^3.
[Section 1] The abbreviation 'SHR' in the introduction appears to be a typo and should be 'SXR' for soft X-ray.
[Figure 13] The red histogram shows dW_GBM_nth/dt in arbitrary units, which makes it difficult to compare the deposition rate with the thermal energy curves; a physical scale would improve the figure.
[Section 5.1] The statement that Emax 'clustered around 2 MeV' would be more informative if the distribution of fitted values and uncertainties were shown rather than described qualitatively.
[Section 4] The parameter ddepth = dwidth = 5 [px] is introduced without explaining how dwidth was measured from the EM maps; a brief description of the loop-width determination would clarify the thermal energy estimate in Eq. (2).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the sufficiency conclusion is an empirical energy comparison; the model-dependent X-ray volume in Eq. (3) is an explicitly acknowledged robustness limitation, not a constructional identity.

full rationale

The paper's central comparison (Fig. 13) contrasts the cumulative nonthermal energy W_GBM_nth (Eq. 4) with thermal energies W_AIA_th (Eq. 2) and W_GBM_th (Eq. 3). W_GBM_nth is derived from Fermi/GBM thick-target fits; W_AIA_th is derived from AIA DEM maps; neither is defined in terms of the other or in terms of the sufficiency conclusion. The only potentially circular-looking input is the use of the 3D-model volume V=1.49e26 cm^3 in Eq. (3), taken from Loop 2 of a model that was fine-tuned to match the same microwave, X-ray, and EUV data (Sec. 6). This is a real degeneracy: only EM=n^2 V is spectrally constrained, and the paper explicitly concedes in Sec. 8.2 that 'given the lack of X-ray imaging data, we might have incorrectly ascribed the hottest plasma to loop 2; it is possible that another, smaller or bigger loop with proportionally smaller/larger volume, is in fact the main contributor to the thermal X-ray emission.' However, this is an acknowledged measurement/modeling uncertainty, not a circular reduction: Eq. (3) does not equal any fitted parameter or the target conclusion by construction, and the sufficiency claim also rests on the independent AIA thermal energy. Self-citations to EOVSA inversion methods (Fleishman et al. 2020, 2022) and to the cold-flare classification (Lysenko et al. 2018, 2023) supply external published tools and definitions; they are not load-bearing proofs of the energy budget. The model-based lower bound Wnth>2.4e28 erg (Sec. 8.3) is an auxiliary consistency check, not the primary evidence. No fitted parameter is renamed as a prediction, and no uniqueness theorem or ansatz is imported by citation to force the result. Therefore no circular step is exhibited.

Assumptions & free parameters 5 free parameters · 6 assumptions · 1 invented entities

The paper is a data-analysis case study, not a first-principles derivation. Many parameters are fitted or tuned to match the observations. The most consequential ad hoc element is the third flux tube, which dominates the model nonthermal energy yet is only needed for low-frequency flattening. The Fermi/GBM thermal energy depends on a model-selected volume. The central claim is not built from free energy balance equations; it rests on order-of-magnitude matching of independently derived thermal and nonthermal energies.

free parameters (5)

Low-energy cutoff Ec (Fermi/GBM thick-target fit) = 18-49 keV range in Fig. 4d
Used directly in Eq. (4); the nonthermal energy deposition is highly sensitive to Ec.
High-energy cutoff Emax (EOVSA spectral fit) = 2 MeV (fixed)
Initially free; clustered near 2 MeV, then fixed in the adopted five-parameter fit.
E_min = 15 keV (EOVSA nonthermal density threshold) = 15 keV (adopted)
Sets the nonthermal number density; the anti-correlation between nnth and radio flux is attributed to this choice.
LOS depth ddepth = 5 pixels = 5 px (mean loop width)
Converts DEM maps to thermal energy density; a single scaling factor for the source depth along the line of sight.
3D model loop parameters (B, nth, nnth, delta, energy ranges) = Values in Table 1
Chosen by trial and error with the AMPP/GSFIT pipeline to match microwave, X-ray, and EUV data; no formal uncertainty.

assumptions (6)

standard math Tikhonov-regularized DEM inversion from six AIA bands recovers the coronal differential emission measure
Section 4; standard method from Hannah & Kontar (2012, 2013), relies on smoothness regularization.
domain assumption The thick-target model f_thick2 describes the HXR emission of accelerated electrons
Section 3.1; used to fit Fermi/GBM and Konus-Wind spectra and to derive F0, Ec, delta.
domain assumption Gyrosynchrotron emission from each pixel is homogeneous with a single power-law electron distribution
Section 5.2; GSFIT forward model; the paper notes systematic uncertainties from neighbor spectra mismatch.
domain assumption NLFFF extrapolation from the HMI magnetogram represents the coronal connectivity at the flare site
Section 6; used to build the 3D model; pre- and post-flare extrapolations show similar connectivity.
domain assumption AIA is insensitive to the hottest (>10 MK) plasma, which must be supplied by Fermi/GBM data
Section 4; acknowledged limitation; the two instruments see different temperature components.
ad hoc to paper Three flux tubes are sufficient to model the flare
Section 6; loops 1 and 2 are inferred from two microwave sources, loop 3 is added ad hoc for low-frequency flattening.

invented entities (1)

Third flux tube (Loop 3)
purpose: Explains low-frequency spectral flattening near 2.5 GHz and dominates the model's instantaneous nonthermal energy
Its geometry, loop-top field (~20 G), and electron population are not directly constrained by imaging; it is inferred solely from the low-frequency excess. The model-based nonthermal energy lower bound in Section 8.3 depends heavily on this component.

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Cite this review

Pith. "Pith review of Energy budget in the 2017-09-07 "cold" solar flare." pith.science (2026). https://pith.science/paper/LIGZI7FR

@misc{pith2026250615501,
  author       = {Pith},
  title        = {Pith review of: Energy budget in the 2017-09-07 "cold" solar flare},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LIGZI7FR}},
  note         = {Machine review of arXiv:2506.15501}
}

read the original abstract

A subclass of early impulsive solar flares, cold flares, was proposed to represent a clean case, where the release of the free magnetic energy (almost) entirely goes to acceleration of the nonthermal electrons, while the observed thermal response is entirely driven by the nonthermal energy deposition to the ambient plasma. This paper studies one more example of a cold flare, which was observed by a unique combination of instruments. In particular, this is the first cold flare observed with the Expanded Owens Valley Solar Array and, thus, for which the dynamical measurement of the coronal magnetic field and other parameters at the flare site is possible. With these new data, we quantified the coronal magnetic field at the flare site, but did not find statistically significant variations of the magnetic field within the measurement uncertainties. We estimated that the uncertainty in the corresponding magnetic energy exceeds the thermal and nonthermal energies by an order of magnitude; thus, there should be sufficient free energy to drive the flare. We discovered a very prominent soft-hard-soft spectral evolution of the microwave-producing nonthermal electrons. We computed energy partitions and concluded that the nonthermal energy deposition is likely sufficient to drive the flare thermal response similarly to other cold flares.

Figures

Figures reproduced from arXiv: 2506.15501 by the authors.

**Figure 1.** Overview of the 2017-Sep-07 flare. From top to bottom: (a) Fermi/GBM light curves at several energy ranges indicated by the legend. The gray—dark gray— gray—light gray areas indicate the breakdown onto the time ranges, where the model spectral fitting of the Fermi/GBM data was performed using averaging over, respectively, 20— 4—20—60 s time intervals. Vertical arrows point on time frames, where the Fermi/GBM spectra… view at source ↗

**Figure 2.** AIA maps taken during the impulsive phase of the September 07, 2017 flare with overlaid EOVSA map 30, 50, and 70% contours at 10.41 GHz (red lines) taken at 18:41:39.5 UT, which corresponds to the maximum of the microwave emission. main, Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA; Lemen et al. 2012) data are available to quantify the thermal properties of the flaring plasma. The EUV light cur… view at source ↗

**Figure 3.** Examples of the Konus-Wind and Fermi/GBM fits (blue histogram) with isothermal (green histogram) plus thick target model (red histogram) during the nonthermal peak at 18:41:39 UT (left panel) and later 18:41:40-18:41:44 UT, 18:41:56- 18:42:00 UT (middle and right panels). The X-ray averaged data and the background level are shown with black and gray histograms respectively. Bottom panels indicate residuals. malized … view at source ↗

Figures from the paper (9 more)

**Figure 4.** Figure 4: Time evolution of T (a), EM (b), and nonthermal parameters F0, Ec, δ (c, d, e) for the 2017-Sep-07 flare. (a) Fermi/GBM temperature (black) from the isothermal model for spatially unresolved full solar disk, temperature calculated from GOES (red), and AIA temperature (…

**Figure 5.** Figure 5: Maps of plasma parameters obtained with the regularized DEM maps based on SDO/AIA data: the mean temperature map (top left), the emission measure map (top right), χ 2 map (bottom left), and the thermal energy density map (bottom right) for the 10th time interval (18:4…

**Figure 6.** Figure 6: Quality of the spectral fit. Left: χ 2 map for the time frame of 18:41:39.500 UT capped at χ 2 = 3. Other panels: examples of the spatially resolved spectra and their corresponding fits from the locations indicated by the red cursor and white and black squares, respect…

**Figure 7.** Figure 7: Inferred Parameters and Their Evolution. Top Row: Magnetic field strength. Second Row: Thermal electron number density. Third Row: Non-thermal electron number density. Bottom Row: Non-thermal electron power-law index. Left Column: Parameter maps corresponding to a spec…

**Figure 8.** Figure 8: Evolution of the nonthermal number density above 100 keV and fit uncertainties (blue lines and symbols) in the pixel marked by the cursor in [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 9.** Figure 9: Visualization of 3D model connectivity. Left: three red lines show the axes of three flux tubes used for emission simulation shown in [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

**Figure 10.** Figure 10: Visualization of the 3D model. Three flux tubes are shown on top of Bz magnetogram with sets of green lines, while their axes are shown with red lines. The bluish volume shows spatial distribution of the nonthermal electrons in these flux tubes. The nonthermal electro…

**Figure 11.** Figure 11: Maps of the weighted magnetic field Bweighted(x, y), and nonthermal and thermal number densities for the model introduced in [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

**Figure 12.** Figure 12: Evolution of the thermal energy WAIA th computed from the DEM maps inside the ROI shown in [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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