Three-dimensional mapping of coronal magnetic field and plasma parameters in a solar flare

Abstract

Diagnosing solar flare conditions is essential for understanding coronal energy release. Using combined microwave and X-ray data, we reconstruct three-dimensional maps of the magnetic field and plasma parameters in the SOL2021-05-07 flare. We use imaging spectroscopy from the Expanded Owens Valley Solar Array (EOVSA) to derive spatial maps of the magnetic field strength, thermal and nonthermal electron densities, and the power-law index of nonthermal electrons through gyrosynchrotron modeling. Simultaneous X-ray observations from Hinode/XRT and Solar Orbiter/STIX, obtained from different vantage points, enable a stereoscopic reconstruction of the flaring loop. By correlating the positions of microwave and thermal X-ray sources, we associate the three-dimensional coordinates with the microwave-derived plasma parameters. We derive observational three-dimensional maps of magnetic field strength, Alfvén speed, and plasma beta in the flaring volume, revealing a magnetically dominated environment. These spatially resolved diagnostics provide valuable constraints for models of magnetic reconnection and flare dynamics and represent a step toward a realistic three-dimensional characterization of energy release in solar eruptive events.

Figures (11)

• Figure 1: Top: Background-subtracted dynamic total power radio spectrum of the 2021-05-07 solar flare observed by EOVSA (top), color scale shows the flux density in solar flux unit (sfu). Bottom: Time profiles at selected frequencies illustrate the burst evolution. The black dashed lines mark the overplotted times of XRT observations.
• Figure 2: Panel a: AIA 94 Å image at 18:56:59 UT showing the flaring region. The EUV flux tube system is partly occulted by the preexisting cool filament (a horizontal absorption feature). Thin colored contours represent 20% of EOVSA microwave brightness at four frequencies indicated in the legend. The thick red contour shows 20% level of the soft X-ray source observed by Hinode/XRT (Be-thick filter) at 18:56:25 UT. Panel b: Total emission measure of the flare region, with the thin green contour marks the region of enhanced thermal density at the levels of 3.6$\times10^{10}$ cm$^{-3}$ and $8\times10^{10}$ cm$^{-3}$, as shown in the bottom panel of Fig. \ref{['Fig:B_n_med']}. Given the peak $EM$ value of $\sim2\times10^{31}$ cm$^{-5}$ and a loop depth of $\sim20^{\prime\prime}$ ($\sim$14 Mm, roughly matching the spatial scale in the plane of the sky), the inferred peak electron density is approximately $1.2\times10^{11}$ cm$^{-3}$, consistent with the $n_{th}$ values inferred from the microwave spectral fitting and shown in panel (c); this is also the same as the one shown in the bottom panel of Fig. \ref{['Fig:B_n_med']}. Note: most of the individual EOVSA images (contours in panel a) do not have loop shapes matching EUV loops; however, the thermal number density inferred from the multifrequency spectral fitting reveals a loop-like structure (shown in panel c), matching the AIA-derived EM map in panel b.
• Figure 3: Heights of the SXR source in the plane made by the solar rotation axis and the geometrical center of the SXR source obtained by ryan2024a from the 3D stereoscopic reconstruction of the joint STIX/XRT data. The green line represents the solar limb. The red contour shows Hinode/XRT 20% brightness at 18:56:25 UT (as in Fig. \ref{['fig:aia_131_EOVSA_XRT']}a). The violet contour shows 10% of the 5.79 GHz EOVSA image taken at 18:55:44 UT.
• Figure 4: Goodness of the spectral fit. Left: $\chi^2$ (=reduced Chi$^2$) map for the time frame of 18:57:24 UT. Red contour shows the XRT brightness contour computed for 18:57:08 UT. Middle: Example of the spatially resolved spectrum from the pixel shown by the red cursor in the left panel and corresponding good spectral model fit shown by the blue curve. The vertical dashed red line marks the spectral peak that demarcates the optically thick (to the left) and thin (to the right) parts of the spectrum. Right: Evolving 2D histogram of the $\chi^2$ metric (colored dots) and the corresponding median values (black symbols with error bars). This demonstrates that the spectral fits are mainly acceptable.
• Figure 5: Parameters inferred from the spectral model fitting and their evolution. Top row: Magnetic field strength. Second row: Thermal electron number density. Third row: Nonthermal electron number density. Bottom row: Nonthermal electron power-law index. Left column: Parameter maps corresponding to the same time frame (18:57:24 UT) as used in Fig. \ref{['Fig_chi-2']}. Each map shows a region of interest (ROI) computed as a 20% contour (in red) of the XRT brightness for 18:57:08 UT. Middle column: Evolution of the fit parameters for the cursor-selected pixel (blue symbols) along with their corresponding median values (horizontal black lines). The selected pixel shown by a cursor in the left panels demonstrates smooth spectra and good spectral fits during the entire duration of the burst. Right column: Evolution of 2D histograms of the parameter distributions within the selected ROI during the entire flare duration. For the nonthermal parameters, evolution of the corresponding median values (symbols with error bars) are shown on top of the 2D histograms to aid the eye. In both the middle and right columns, vertical dotted red lines highlight the selected time frame of the maps displayed in the left column. A horizontal stripe in 2D histogram of the thermal density at $n_{th}\approx 2\times 10^{10}$ cm$^{-3}$ is an artifact, as explained in Fig. \ref{['fig:Bn_hist_1D']}