Spectral component imaging of solar X-ray flares

TL;DR

Spectral component imaging reframes solar hard X-ray imaging by solving for component visibilities across all energy channels rather than imaging fixed energy ranges. Formally, $V(u,v,E)=F(E)\,\nu(u,v,E)$ with multiple components leading to $\nu(u,v,E)=\sum_i f_i(E)\,\nu_i(u,v)$, and the problem is solved via a weighted linear least-squares approach using $V=F\nu$. Applied to four flares observed by STIX on Solar Orbiter, the method separates hot and superhot thermal sources and nonthermal footpoints, yielding physically meaningful maps and enabling measurements such as a ~4.8 Mm separation between hot and superhot centroids and a superhot energy content of about 22% of the hot component. The framework accommodates albedo, leverages all energy channels, and can automate image production, paving the way for a comprehensive, component-resolved STIX image database. Overall, spectral component imaging provides a powerful, quantitative tool to probe flare energetics and spatial structure beyond traditional energy-band imaging, with particular strength for characterizing superhot plasmas and complex footpoint configurations.

Abstract

Solar hard X-ray observations provide diagnostics of the hottest plasmas and of nonthermal electron populations present during solar flares and coronal mass ejections. HXR images of specific energy ranges often contain overlapping contributions of these components, complicating their interpretation. This is even more challenging as HXR imagers generally use an indirect imaging system. Our work aims to separately image individual spectral components, such as thermal loops, superhot sources, and nonthermal footpoint sources, rather than obtaining images of specific energy ranges that show a combination of all components. We introduce a new method called spectral component imaging and apply it to observations provided by the Spectrometer/Telescope for Imaging X-rays (STIX) aboard Solar Orbiter. First, the flare integrated HXR spectrum is fitted with individual spectral components to get the relative contributions of each component in each native STIX energy channel. In a second step, a set of linear equations is created based on these weights and the observed, energy-dependent STIX visibilities. The visibilities of the individual spectral components are derived by means of a linear least-squares approach and are subsequently utilized for image reconstructions. We demonstrate the effectiveness of spectral component imaging on four different flares observed by STIX. This method provides powerful diagnostics, particularly for flares with hot and superhot components, allowing us to spatially separate these two thermal components. We apply our methodology to the nonthermal peak of the X7.1 flare SOL2024-10-01, and we find that the superhot component is located 4.8 Mm away from the hot thermal loops. The thermal energy of the superhot component is approximately 20% of the energy content of the hot component, highlighting the significance of superhot components in the total flare energy budget.

Figures (4)

• Figure 1: Panel (a) shows the reconstructed maps of the energy ranges 7-10 keV (magenta) and 22-28 keV (light blue). The percentages give the contribution of the spectral components, thermal in red and nonthermal in blue, respectively. Panel (b) shows the reconstructed maps of the thermal (red) and nonthermal (blue) spectral components as derived from spectral component imaging. Panels (c) and (d) show the comparison of pre-determined energy ranges with the spectral component imaging results for the thermal emission, panel (c), and the nonthermal emission, panel (d). The contour levels shown in all panels are 20, 40, 60, and 80% of the peak values of the maps. Solar Orbiter was at a distance of 0.69 AU to the Sun. Panel (e) shows the spectrum of the time step used for imaging together with the fitted models. Panel (f) shows the $\chi^2$ results for the spectral component imaging approach as a function of energy. The $\chi^2$'s in the legend are the values averaged over all energies.
• Figure 2: Results using specific energy ranges and spectral component imaging for SOL2023-03-07, with Solar Orbiter at a distance of 0.68 AU to the Sun. In panel (a), the maps using the energy ranges 5-8 keV in magenta and 11-18 keV in light blue are shown. These energy ranges are also marked in the spectrum shown in panel (c). In panel (b), the maps of spectral component imaging are shown, solving for a thermal (red) and nonthermal (blue) component, together with the map-$\chi^2$ of the spectral component imaging method. The contour levels shown in the plots are 40, 60, 80%. In panel (c), the spectrum at the time of the image is given. We have fitted a thermal (red), nonthermal (blue), and albedo (grey) component to the spectrum. The temperature of the thermal fit, the power-law index of the nonthermal distribution and the $\chi^2$ of the fit is given in panel (c) as well.
• Figure 3: Results using specific energy ranges and spectral component imaging for SOL2021-09-23, with Solar Orbiter at a distance of 0.60 AU to the Sun. In panel (a), the maps using the energy ranges 5-9 keV in magenta and 22-28 keV in light blue are shown. These energy ranges are also marked in the spectrum shown in panel (c). In panel (b), the maps of spectral component imaging are shown, solving for a thermal (red) and nonthermal (blue) component, together with the map-$\chi^2$ of the spectral component imaging method. The contour levels shown in the plots are 20, 40, 60, 80 %. In panel (c), the spectrum at the time of the image is given. We have fitted a thermal (red), nonthermal (blue), and albedo (grey) component to the spectrum. The temperature of the thermal fit, the power-law index of the nonthermal distribution and the $\chi^2$ of the fit is given in panel (c) as well.
• Figure 4: The top two panels show the spectra of the BKG detector (left) and the imaging detectors (right). We jointly fitted a photon model to the two spectra containing a hot thermal (blue), superhot thermal (red), nonthermal (green), and albedo (grey) component. The total fit is given in black. The ranges between the grey, dashed lines indicate the energy ranges considered for spectral fitting. 3% systematic errors are added in quadrature to the residuals. The colored energy ranges in the spectrum are the ranges used for reconstruction and are shown in the first row of maps. For each energy range, we give the percentage of each spectral component contributing to this energy range. In the second row, we plotted the outcome of spectral component imaging, solving for the three components: hot thermal (blue), superhot thermal (red), and nonthermal (green). The contour levels of all plots shown are 20, 40, 60, 80 % of the maximum. The plots in the right column are EUI 174 Å short exposures with STIX contours. The time range shown here is 22:14:20 - 22:14:50 UTC (Earth time), a time range around the main nonthermal peak measured by STIX. Solar Orbiter is at a distance of 0.29 AU to the Sun.