Microwave imaging spectroscopy of the 2017 September 10 X8.2 solar limb flare showed for the first time that the coronal magnetic field in a flaring volume decays at about 5 G per second for roughly two minutes, releasing enough magnetic energy to power the flare, its eruption, its accelerated particles, and its plasma heating, and implying an effective turbulent magnetic diffusivity orders of magnitude above the classical collisional value. Because that measurement involved a single, partially occulted event, it remains unestablished whether such field decay is a general energy-release mechanism of solar flares, what typical decay rates and energy partitions occur across flare classes, and what turbulent process supplies the inferred diffusivity. The problem is to determine, from spatially resolved microwave measurements of the evolving coronal magnetic field in a representative sample of flares, together with coordinated photospheric vector magnetograms and multiwavelength extreme-ultraviolet (EUV) and X-ray observations, under what conditions coronal magnetic-field decay takes place, whether it is quantitatively sufficient to power flares, and what turbulence drives it.

Background

A solar flare is a sudden release of up to roughly 103210^{32} erg of energy in the Sun's corona, the tenuous magnetized plasma atmosphere above the visible surface. Flares are graded by GOES class (C, M, X), a logarithmic scale based on the soft X-ray flux measured near Earth. The accepted picture is that flares are powered by free magnetic energy — energy stored in the coronal magnetic field in excess of the lowest-energy potential configuration — released through magnetic reconnection, the rapid reconfiguration of field lines that converts stored magnetic energy into heat, bulk and turbulent plasma motion, and beams of accelerated particles. Directly testing this picture has been difficult: the coronal field is too weak and diffuse for the Zeeman polarimetry (polarized-light signatures of the Zeeman effect, the magnetic splitting of spectral lines) used to measure solar surface fields, so coronal field strengths have usually been estimated indirectly, by extrapolating photospheric magnetograms into three-dimensional models such as the nonlinear force-free field (NLFFF), a reconstruction that assumes the coronal field exerts no net Lorentz force and matches the photospheric vector field at its lower boundary.

Microwave emission offers a direct alternative. Mildly relativistic electrons spiraling along magnetic field lines produce gyrosynchrotron radiation, a broadband microwave continuum whose spectrum and polarization depend on the magnetic field strength BB and on the energy distribution of the emitting electrons. The Expanded Owens Valley Solar Array (EOVSA), a radio interferometer performing imaging spectroscopy across roughly 1-18 GHz with about one-second cadence, can invert this radiation to map the coronal magnetic field and the thermal and nonthermal electron distributions in flaring regions as they evolve.

Using EOVSA observations of the 2017 September 10 X8.2 limb flare, Fleishman and colleagues mapped the evolving coronal magnetic field over the flaring volume. The field decayed at about 5 G per second for roughly two minutes within a subvolume of about 102810^{28} cubic centimeters; the associated decrease in stored magnetic energy sufficed to power the flare, including the accompanying eruption, particle acceleration, and plasma heating. The decay rate implies electric fields strong enough to account for the observed electron acceleration, but it is orders of magnitude faster than ordinary resistive diffusion under the classical Spitzer conductivity — the electrical conductivity that Coulomb collisions impart to an ionized plasma — can achieve, so an effective turbulent magnetic diffusivity — a field-transport coefficient produced by turbulent plasma motions, analogous to an enhanced diffusion constant — must be at work.

The result, however, rests on one event, and a partially occulted limb flare at that (an event at the Sun's apparent edge, its lower portions hidden behind the solar disk): contemporaneous photospheric vector data needed for direct comparison with extrapolated equilibrium field models were unavailable; the thermal and turbulent-kinetic energy densities could only be estimated with auxiliary extreme-ultraviolet (EUV) inputs; the electric-field amplitude depends on the adopted macroscopic length scale, taken as 5 arcsec in that study; and the turbulence itself — its onset, spatial structure, spectrum, and intermittency — was not characterized. Later work has both confirmed the phenomenon in a second event (an on-disk X1.1 flare in 2022 with decay rates up to about 10 G per second) and found no statistically significant field variation in a cold flare, an early-impulsive flare type in which almost all released energy goes into electron acceleration with little thermal response. Whether coronal magnetic-field decay is the general energy source of solar flares, and what makes it fast, is therefore an open empirical question.

Problem Statement

Determine whether the decay of the coronal magnetic field observed in the 2017 September 10 X8.2 flare is a general property of solar flares and the quantitatively sufficient source of flare energy, and identify the turbulent mechanism that supplies the required effective magnetic diffusivity. Concretely, using spatially resolved microwave imaging spectroscopy (gyrosynchrotron inversion) with coordinated photospheric vector magnetograms and multiwavelength EUV and X-ray observations: (1) measure the time evolution of the coronal magnetic field B(t)B(t) over the flaring volume for a sample of flares representative of the observed population in GOES soft X-ray class and configuration; (2) for each event, quantify the rate and spatial pattern of any field decay, compare the microwave-inferred B(t)B(t) with contemporaneous photosphere-based nonlinear force-free field (NLFFF) extrapolations, and close the flare energy budget — magnetic energy decrease versus thermal, kinetic, and nonthermal particle energies — with quantified uncertainties; (3) characterize the effective turbulent diffusivity implied by the observed decay, including its onset, spatial structure, spectrum, and intermittency, and its relation to reconnection and particle acceleration; and (4) delimit the conditions under which prominent field decay occurs or fails to occur across flare types (for example cold flares — early-impulsive events with little thermal response — confined versus eruptive events, and limb versus disk geometry), so that it is established for which flares coronal magnetic-field decay powers the energy release.

These four parts are jointly necessary. Establishing B(t)B(t) and the energy budget for individual events (parts (1)-(2)) shows whether a decay occurs and whether it is quantitatively sufficient in those flares, but it does not by itself establish generality or identify the mechanism; parts (3)-(4) are required to determine what turbulence supplies the effective diffusivity and for which flares the decay is the operative energy source. Representativeness is fixed by the selection rule rather than by a prescribed count: a sample is representative when it is drawn by an explicit, unbiased criterion spanning the stated GOES soft X-ray class and configuration axes and is large enough that the decay rates, the energy partitions, and the diffusivity properties can each be reported with quantified uncertainties. The headline question is settled when, for such a sample, the fraction of flares showing decay above measurement uncertainty, the sufficiency of the corresponding magnetic-energy decrease within the stated uncertainties, and the dependence of both on flare conditions (part (4)) have been determined together with the mechanism (part (3)).

References

  1. Fleishman, G. D., Gary, D. E., Chen, B., Kuroda, N., Yu, S., & Nita, G. M. (2020). Decay of the coronal magnetic field can release sufficient energy to power a solar flare. Science, 367, 278-280. DOI: 10.1126/science.aax6874. https://doi.org/10.1126/science.aax6874
  2. Chen, B., Shen, C., Gary, D. E., Reeves, K. K., Fleishman, G. D., Yu, S., Guo, F., Krucker, S., Lin, J., Nita, G. M., & Kong, X. (2020). Measurement of magnetic field and relativistic electrons along a solar flare current sheet. Nature Astronomy, 4, 1140-1147. DOI: 10.1038/s41550-020-1147-7. https://doi.org/10.1038/s41550-020-1147-7
  3. Wei, Y., Chen, B., Yu, S., Wang, H., Jing, J., & Gary, D. E. (2021). Coronal Magnetic Field Measurements along a Partially Erupting Filament in a Solar Flare. The Astrophysical Journal, 923, 213. DOI: 10.3847/1538-4357/ac2f99. https://doi.org/10.3847/1538-4357/ac2f99
  4. Fleishman, G. D., Nita, G. M., Chen, B., Yu, S., & Gary, D. E. (2022). Solar flare accelerates nearly all electrons in a large coronal volume. Nature, 606, 674-677. DOI: 10.1038/s41586-022-04728-8. https://doi.org/10.1038/s41586-022-04728-8
  5. Chen, B., Gary, D. E., Yu, S., Mondal, S., Fleishman, G. D., Li, X., Shen, C., Guo, F., White, S. M., Bastian, T. S., Saint-Hilaire, P., Drake, J. F., Dahlin, J., Glesener, L., Ji, H., Veronig, A., Oka, M., Reeves, K. K., & Karpen, J. (2023). Quantifying Energy Release in Solar Flares and Solar Eruptive Events: New Frontiers with a Next-Generation Solar Radio Facility. arXiv:2301.12192. https://arxiv.org/abs/2301.12192
  6. Fleishman, G. D., Motorina, G. G., Yu, S., & Nita, G. M. (2025). Energy Budget in the 2017 September 7 “Cold” Solar Flare. The Astrophysical Journal, 988, 260. DOI: 10.3847/1538-4357/ade983. arXiv:2506.15501. https://doi.org/10.3847/1538-4357/ade983
  7. Fleishman, G. D., Kaltman, T., & Yu, S. (2026). Dynamics of the Coronal Magnetic Field in the 2022 October 2 X-class Flare. The Astrophysical Journal, 999, 179. DOI: 10.3847/1538-4357/ae42c8. arXiv:2602.05024. https://doi.org/10.3847/1538-4357/ae42c8
  8. Kaltman, T., Yu, S., Fleishman, G. D., & Ryan, D. F. (2026). Three-dimensional mapping of coronal magnetic field and plasma parameters in a solar flare. arXiv:2602.11853. https://arxiv.org/abs/2602.11853
  9. Fleishman, G. D., Kaltman, T., Yu, S., & Nita, G. M. (2026). Spectral Evolution of Mildly Relativistic Electrons in Solar Flares. The Astrophysical Journal, 1007, 180. DOI: 10.3847/1538-4357/ae8f43. https://doi.org/10.3847/1538-4357/ae8f43
  10. Fleishman, G. D., Oparin, I., Nita, G. M., Chen, B., Yu, S., & Gary, D. E. (2026). Megaelectronvolt-peaked electrons in a coronal source of a solar flare. Nature Astronomy, 10, 363-370. DOI: 10.1038/s41550-025-02754-w. https://doi.org/10.1038/s41550-025-02754-w