Iron Fluorescence in X-class Solar Flares: Aditya-L1/SoLEXS Observations

Abstract: Iron fluorescence is produced by the irradiation of the solar photosphere by coronal X-rays during flares. This study presents the first comprehensive analysis of iron K$α$ fluorescence characteristics in 47 X-class flares observed during the inaugural year of the Solar Low Energy X-ray Spectrometer (SoLEXS) on board India's Aditya-L1 mission. Leveraging the capability of modern silicon drift detectors (SDDs) for simultaneous broadband continuum and line measurements, the Fe K$α$ flux and the exciting flux ($F_{>7.11 \text{ keV}}$) are quantified for each event, establishing a well-determined relationship between them across the sample. The derived fluorescence efficiencies exhibit a center-to-limb dependence consistent with theoretical models, offering a potential diagnostic to probe coronal source heights and viewing geometries. While statistical uncertainties currently limit the ability to track rapid height variations on short timescales, the mean fluorescence efficiency during the flare peak provides a potential constraint on the effective coronal source height. However, this derivation remains subject to a fundamental degeneracy, as the estimated source height cannot be uniquely determined without assuming a specific value for the photospheric iron abundance. These findings demonstrate that SDDs, despite having lower spectral resolution than traditional crystal spectrometers, provide a new diagnostic for the solar iron fluorescence observations.

• The paper demonstrates that SoLEXS can measure photospheric Fe Kα fluorescence and exciting flux simultaneously in 47 X-class flares, enabling model-independent efficiency estimates.
• The analysis finds that fluorescence efficiency declines from about 0.05 near disk center to 0.007 near the limb, matching geometric predictions and indicating emission below coronal flare sources.
• The results show that fluorescence has little effect on fitted flare temperatures but constrains effective source heights to roughly 0.01 solar radii, while revealing unresolved abundance and outlier-event problems.

Overview

This paper presents a systematic analysis of photospheric iron K$\alpha$ fluorescence in 47 X-class solar flares observed during the first year of science operations (2024) of the Solar Low Energy X-ray Spectrometer (SoLEXS) on board Aditya-L1, India's first dedicated solar observatory stationed at Sun–Earth L1 (2605.22573). The study exploits a capability unavailable to earlier crystal-spectrometer missions: simultaneous broadband measurement of both the fluorescent Fe K$\alpha$ line at 6.4 keV and the exciting coronal flux above the 7.11 keV iron K-edge, enabling a direct, model-independent determination of the observed fluorescence efficiency $\Gamma' = F_{K\alpha}/F_{>7.11}$ for each event.

Instrument and observational context

SoLEXS is a Sun-as-a-star soft X-ray spectrometer operating over 2–22 keV with two silicon drift detectors (SDDs) of differing aperture areas; the small-aperture SDD2 ($0.106\ \mathrm{mm^2}$) is used for X-class events to avoid saturation. Its energy resolution is approximately 170 eV FWHM at 5.9 keV — far coarser than the $\Delta E \sim 10$ eV of the SMM Bent Crystal Spectrometer or the Yohkoh Bragg Crystal Spectrometer, but sufficient to separate the neutral Fe K$\alpha$ line from the hot thermal Fe complex near 6.7 keV, since their ~300 eV separation is nearly twice the instrumental FWHM.

A notable strength of the analysis is the careful exclusion of instrumental origins for the 6.4 keV feature. Pre-commissioning spectra taken with the aperture door closed show no detectable Fe K$\alpha$ or Fe K$\beta$ emission from the instrument itself, despite the proximity of the onboard $^{55}$Fe calibration source's Mn K$\beta$ line at 6.49 keV. The L1 vantage point provides a near-100% duty cycle, and 2024 — an exceptionally productive year of Solar Cycle 25 with 54 X-class flares — supplied a sample spanning heliocentric angles from disk center to the limb (13 events at $\alpha$0, 15 at $\alpha$1, 19 at $\alpha$2).

Spectral methodology

Spectra are forward-fitted in Sherpa using a single-temperature isothermal model (f_vth with free abundances, CHIANTI v11) over 2.2–12 keV at 10-second cadence, augmented by empirical Gaussians for Fe K$\alpha$3 (centroid fixed at 6.40 keV), Fe K$\alpha$4 (fixed width, flux ratio fixed at the theoretical branching value of 0.134), and instrumental Ni K$\alpha$5/K$\alpha$6 lines excited within the instrument structure. For a representative near-disk-center X1.0 flare, inclusion of the fluorescence components reduces the reduced $\alpha$7 from 1.49 to 0.98.

The authors address the principal systematic concern — contamination of the 6.4 keV band by Fe xix–xxiv satellite lines from cooler plasma hidden beneath the hot flare component — through both simulation and empirical tests. Under deliberately extreme assumptions (EM of $\alpha$8, coronal/FIP-enhanced abundances), simulated cool-component line flux in the SoLEXS resolution window falls to $\alpha$9 at 7 MK, two orders of magnitude below the hot-component contribution. Two-temperature fits confirm that no physically admissible cool component reproduces the residual: forcing a background EM of $\Gamma' = F_{K\alpha}/F_{>7.11}$0 causes the fit to fail convergence while the 6.4 keV residual persists. This rules out thermal-model incompleteness as the source of the feature, consistent with prior findings from Chandrayaan-2/XSM and STIX analyses.

Temporal behavior and center-to-limb variation

For the representative disk flare (SOL-2024-06-01, $\Gamma' = F_{K\alpha}/F_{>7.11}$1), the Fe K$\Gamma' = F_{K\alpha}/F_{>7.11}$2 flux peaks at $\Gamma' = F_{K\alpha}/F_{>7.11}$3, tracking the exciting flux peak of $\Gamma' = F_{K\alpha}/F_{>7.11}$4 almost synchronously, and matches the magnitude and evolution predicted by the Bai (1979) Monte Carlo framework for a source height near $\Gamma' = F_{K\alpha}/F_{>7.11}$5. The mean peak-phase efficiency is $\Gamma' = F_{K\alpha}/F_{>7.11}$6. By contrast, a limb flare of comparable class and temperature (SOL-2024-05-14, $\Gamma' = F_{K\alpha}/F_{>7.11}$7) shows negligible Fe K$\Gamma' = F_{K\alpha}/F_{>7.11}$8 emission despite a larger exciting flux ($\Gamma' = F_{K\alpha}/F_{>7.11}$9), yielding an efficiency of only $0.106\ \mathrm{mm^2}$0 — a direct geometric confirmation that the emission originates below the coronal source.

Across the full sample, the flare-peak efficiencies exhibit the expected center-to-limb decline, with hotter flares showing systematically lower efficiency as predicted by the temperature dependence of the intrinsic efficiency $0.106\ \mathrm{mm^2}$1. To isolate geometry from thermodynamics, the authors restrict the analysis to time bins with plasma temperatures between 18.5 and 21.5 MK during decay phases (34 flares qualify). The resulting efficiency–angle relation agrees well with theoretical curves for a 20 MK plasma parameterized via Drake (2008), once a photospheric iron abundance of $0.106\ \mathrm{mm^2}$2 is adopted. This abundance exceeds the modern 3D-model value of $0.106\ \mathrm{mm^2}$3 (Asplund et al.) but exactly matches the effective baseline used by Parmar et al. (1984), whose overall efficiency magnitudes this work reproduces.

Four outliers (flares 8, 17, 19, and 43) show anomalously high efficiency, up to $0.106\ \mathrm{mm^2}$4 for the X1.6 event of 2024-05-03; their physical origin is not understood. Limb events also show a systematic excess above theory, attributed plausibly to the breakdown of the thin-shell, homogeneous-photosphere approximation at grazing incidence.

Implications for thermal diagnostics and source heights

Two practical results follow for flare spectroscopy. First, including or omitting the fluorescence Gaussian changes best-fit temperatures by only ~0.2 MK on average, though the thermal-only model underestimates the fitted iron abundance by a mean factor of 0.87 — negligible for most purposes, validating single-isothermal fitting for X-class flare thermometry. Second, the mean peak-phase efficiency constrains the effective coronal source height to a precision of roughly $0.106\ \mathrm{mm^2}$5 for disk events, comparable to what crystal spectrometers achieved decades ago.

Limitations and open questions

The paper is explicit about several constraints. Statistical uncertainties (~0.003 on time-averaged efficiency, ~0.015 per 10-s bin) preclude tracking rapid height variations within individual flares, despite the high cadence theoretically permitting it. A fundamental degeneracy couples the inferred source height to the assumed photospheric iron abundance, so height cannot be uniquely determined without fixing $0.106\ \mathrm{mm^2}$6 — and the required abundance of $0.106\ \mathrm{mm^2}$7 sits above the accepted photospheric value, leaving open whether this reflects model limitations, extended loop geometries, or genuine abundance effects. The four high-efficiency outliers remain unexplained, and limb excesses point to inadequacies in the standard geometric treatment. Whether non-thermal electron impact contributes measurably in rare impulsive episodes remains unresolved, motivating extension of the analysis to M- and C-class flares and searches for anomalous excitation events in the growing SoLEXS archive.

Conclusion

This work establishes broadband SDD spectroscopy as a viable tool for quantitative solar iron-fluorescence studies, demonstrating across 47 X-class flares that photospheric fluorescence dominates the 6.4 keV feature during the gradual phase, that its efficiency follows the predicted center-to-limb and temperature dependences, and that simultaneous measurement of fluorescent and exciting fluxes removes the principal ambiguity of earlier narrow-band studies. The remaining obstacles — statistical precision, the height–abundance degeneracy, and unexplained outlier events — define the specific problems that larger samples and improved instrumentation (higher effective area, ~125 eV resolution) would need to address.