# Measurement of magnetic field and relativistic electrons along a solar flare current sheet

## Abstract

In the standard model of solar flares, a large-scale reconnection current sheet is postulated to be the central engine for powering the flare energy release1,2,3 and accelerating particles4,5,6. However, where and how the energy release and particle acceleration occur remain unclear owing to the lack of measurements of the magnetic properties of the current sheet. Here we report the measurement of the spatially resolved magnetic field and flare-accelerated relativistic electrons along a current-sheet feature in a solar flare. The measured magnetic field profile shows a local maximum where the reconnecting field lines of opposite polarities closely approach each other, known as the reconnection X point. The measurements also reveal a local minimum near the bottom of the current sheet above the flare loop-top, referred to as a ‘magnetic bottle’. This spatial structure agrees with theoretical predictions1,7 and numerical modelling results. A strong reconnection electric field of about 4,000 V m−1 is inferred near the X point. This location, however, shows a local depletion of microwave-emitting relativistic electrons. These electrons instead concentrate at or near the magnetic bottle structure, where more than 99% of them reside at each instant. Our observations suggest that the loop-top magnetic bottle is probably the primary site for accelerating and confining the relativistic electrons.

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## Data availability

The data that support the plots within this paper and other findings are available at http://ovsa.njit.edu (EOVSA), https://hesperia.gsfc.nasa.gov (RHESSI) and http://jsoc.stanford.edu (SDO), or from the corresponding author upon reasonable request.

## Code availability

The microwave spectral fitting software, GSFIT, is available in the community-contributed SolarSoftWare (SSW) repository, under the packages category, at https://www.lmsal.com/solarsoft/ssw/packages/gsfit. Fast gyrosynchrotron codes are available within the GX_simulator package in the SSW distribution at https://www.lmsal.com/solarsoft/ssw/packages/gx_simulator. Codes for calculating the theoretical magnetic model are available from the corresponding author upon reasonable request. Public software packages utilized in this study include SunCASA (https://github.com/suncasa/suncasa), CASA39 (https://casa.nrao.edu), SunPy40 (https://sunpy.org), Astropy41 (https://www.astropy.org), Athena++34 (https://princetonuniversity.github.io/athena), emcee48 (https://emcee.readthedocs.io), and LMFIT (https://lmfit.github.io/lmfit-py).

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## Acknowledgements

EOVSA operation is supported by NSF grant AST-1910354. The work is supported partly by NASA DRIVE Science Center grant 80NSSC20K0627. B.C., D.E.G., G.D.F., G.M.N. and S.Y. are supported by NASA grants NNX17AB82G, 80NSSC18K1128, 80NSSC19K0068, 80NSSC18K0667 and NSF grants AGS-1654382, AGS-1723436, AST-1735405, AGS-1743321 and AGS-1817277 to the New Jersey Institute of Technology. K.K.R. and C.S. are supported by NASA grants NNX17AB82G and 80NSSC19K0853 and NSF grants AGS-1723425, AGS-1723313 and AST-1735525 to the Smithsonian Astrophysical Observatory. F.G. is supported by NSF grant AST-1735414 and DOE grant DE-SC0018240. S.K. is supported by NASA contract NAS 5-98033 for RHESSI. J.L. is supported by the Strategic Priority Research Program of the Chinese Academy of Sciences with grants XDA17040507, QYZDJ-SSWSLH012 and XDA15010900, NSFC grant 11933009, the project of the Group for Innovation of Yunnan Province grant 2018HC023, and the Yunnan Yunling Scholar Project. X.K. is supported by NSFC grants 11873036 and 11790303, the Young Elite Scientists Sponsorship Program by CAST, and the Young Scholars Program of Shandong University. The MHD simulations performed for this work were conducted on the Smithsonian High Performance Cluster of the Smithsonian Institution, and used resources of the National Energy Research Scientific Computing Center.

## Author information

Authors

### Contributions

B.C. conceived the study, carried out the data reduction, analysis, interpretation and manuscript preparation. C.S. performed the MHD simulation and contributed to the observation–modelling comparison. D.E.G. led the construction and operation of EOVSA, and contributed to the microwave data calibration and interpretation. K.K.R. provided codes for the theoretical magnetic model and contributed to the observation–modelling comparison. G.D.F. provided codes for calculating gyrosynchrotron radiation and contributed to microwave spectral fitting. S.Y. contributed to microwave data calibration and EUV data analysis. S.K. performed hard X-ray imaging and contributed to the interpretation of data. J.L. contributed to MHD simulation. F.G. and X.K. contributed to the interpretation of data. G.M.N. contributed to microwave spectral fitting. All authors discussed the results and contributed to manuscript preparation.

### Corresponding author

Correspondence to Bin Chen.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data

### Extended Data Fig. 1 Magnetic modelling of the X8.2 eruptive solar flare event on 2017 September 10.

a, Representative magnetic field lines from the theoretical standard flare model of Lin & Forbes1. b, and c, Results from the numerical resistive two-and-half-dimensional MHD model in the weak and strong guide field Bz case, respectively. Background is SDO/AIA time-series images of the EUV 211-Å filter band. The thin vertical structure with red-orange colour near x = 0 Mm is the RCS with an enhanced electric current density jz. The first panel in each row shows the initial conditions of the magnetic modeling, which consist of a line current that represents the magnetic flux rope (red circle symbol) and a pair of bipolar magnetic sources at the solar surface (point sources in theoretical model and line sources in MHD).

### Extended Data Fig. 2 Magnetic field variation across and along the RCS in the MHD simulation.

a, Enlarged view of the central RCS region in the MHD model (white box in the right panels of Extended Data Fig. 1b,c). The RCS exhibits itself as the vertical feature with a strong current density jz. b, Height variation of the total magnetic field strength B(y) along the RCS (at x = 0 Mm; vertical dashed line in a). Dashed and dotted curves represent results from the full-resolution MHD model at x = 0 Mm and x = 1 Mm. Solid curve is the B(y) profile obtained after convolution with EOVSA’s instrument resolution. The latter contains key information about the average magnetic field in the immediate vicinity of the RCS (same as the red curve in Fig. 3b), which compares favorably with results derived from EOVSA microwave observations. c, Spatial variation of the x, y, z components of the magnetic field vector across the RCS (Bx(x), By(x), Bz(x)) obtained at y = 31 Mm (horizontal line in a). d, Total magnetic field variation across the RCS B(x). Dashed and solid curves show, respectively, the result from the full-resolution MHD model and that after convolution with EOVSA instrument resolution. Note the sharp dip at the very center of the current sheet is smoothed out. (e)–(h) Same as above, but for the stronger guide field Bz case.

### Extended Data Fig. 3 MCMC analysis for an example spatially resolved microwave spectrum.

The spectrum is taken from the location labelled ‘2’ in Fig. 2c. Red lines/circles in each panel indicate the final fit results from the MCMC analysis. Corresponding spectra and residuals calculated from each MCMC sampling in the multi-parameter space are shown in the upper right panel as grey curves. Red curves are the final fit spectrum and residual. Note the total number density of energetic electrons shown in the corner plot is the result integrated above 100 keV ($${n}_{e}^{ \,{>}\,100}$$), which is different from the value of $${n}_{e}^{ \,{>}\,300}$$ shown in Fig. 2d.

### Extended Data Fig. 4 MCMC analysis for an example spatially resolved microwave spectrum with two spectral components.

The spectrum is taken from the location labelled ‘3’ in Fig. 2c. The corner plots are similar to Extended Data Fig. 3, but they show MCMC results with two source components. Parameters with subscripts ‘1’ and ‘2’ indicate the physical parameter for the two components, respectively. Red curve and dashed black curve in the upper right panel shows, respectively, the fit spectrum with both components and the spectrum calculated from the component with a stronger magnetic field only (that is, component with subscript ‘1’).

## Supplementary information

### Supplementary Video 1

Animation accompanying Fig. 4. The animation shows the flare evolution from 15:51:45 UT to 16:06:09 UT on 2017 September 10. Panels a and c are identical to those in Fig. 4. Panel b shows SDO/AIA 171-Å running-ratio time-series images. Examples of the plasma inflows converging towards the RCS from the − x and + x sides are marked in the xt plot in a as blue and red curves and in b as triangles with the same colour. Plasma downflows below the RCS are marked as green curves in the ty plot in c and in b as green triangles. The moving horizontal/vertical bar in panels a/c indicates the corresponding time.

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Chen, B., Shen, C., Gary, D.E. et al. Measurement of magnetic field and relativistic electrons along a solar flare current sheet. Nat Astron (2020). https://doi.org/10.1038/s41550-020-1147-7

• Accepted:

• Published:

• ### Mapping the magnetic field in the solar corona through magnetoseismology

• ZiHao Yang
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• , Steven Tomczyk
• , Richard Morton
• , XianYong Bai
• , Tanmoy Samanta
•  & YaJie Chen

Science China Technological Sciences (2020)