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

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

Problem Statement
Solar flares release vast amounts of energy, heating coronal plasma to tens of millions of Kelvin and generating intense soft X-ray emission. A fraction of these X-rays irradiates the cooler, denser solar photosphere, inducing inner-shell ionization of iron atoms. This process results in the emission of characteristic fluorescent radiation, most notably the Fe Kα line at 6.4 keV. While the physical mechanism of this fluorescence was established theoretically by Bai (1979) and observed by early crystal spectrometers (e.g., SMM, Yohkoh), a critical limitation persisted: these instruments possessed narrow energy passbands. They could resolve the fluorescence lines but could not simultaneously measure the broadband "exciting flux" (X-rays > 7.11 keV) required to calculate the fluorescence efficiency directly. Consequently, previous studies relied on model-dependent estimates for the exciting flux, introducing significant uncertainty in constraining the excitation mechanism and deriving coronal source heights.

Methodology
This study presents the first comprehensive analysis of iron fluorescence using data from the Solar Low Energy X-ray Spectrometer (SoLEXS) aboard India's Aditya-L1 mission. The analysis focuses on 47 X-class flares observed during the mission's inaugural year (2024).

• Instrumentation: SoLEXS utilizes Silicon Drift Detectors (SDDs) operating in the 2–22 keV range with a spectral resolution of ~170 eV (FWHM) at 5.9 keV. Unlike crystal spectrometers, SDDs provide continuous broadband coverage, enabling the simultaneous measurement of the Fe Kα line and the continuum flux above the iron K-edge (7.11 keV).
• Data Selection: The sample was restricted to X-class flares to ensure sufficient signal-to-noise for the weak fluorescence lines. Data were exclusively drawn from the SDD2 detector (smaller aperture) to avoid saturation during intense events.
• Spectral Modeling: The authors employed a forward-fitting technique using the fvth model (modified to allow variable abundances) from the sunkit-spex package. To isolate the fluorescence signal, the model was augmented with empirical Gaussian profiles for Fe Kα (6.40 keV), Fe Kβ (7.06 keV), and instrumental Ni fluorescence lines.
• Flux Quantification: The Fe Kα photon flux ($F_{K\alpha}$) was derived from the integrated area of the best-fit Gaussian. The exciting flux ($F_{>7.11}$) was calculated by directly integrating the observed counts above 7.11 keV, corrected for the instrument's effective area, without assuming a specific thermal or non-thermal spectral shape.
• Validation: The study rigorously tested for potential contaminants, including satellite lines from lower-ionization iron states (Fe XIX–XXIV) and contributions from cooler plasma components. Sensitivity analyses using the CHIANTI database and two-temperature modeling confirmed that these factors are negligible compared to the observed fluorescence signal.

Key Contributions and Results

1. Direct Efficiency Measurement: By simultaneously measuring $F_{K\alpha}$ and $F_{>7.11}$, the study establishes a direct, model-independent relationship between the fluorescent line flux and the exciting coronal flux. This allows for the calculation of the observed fluorescence efficiency ($\Gamma' = F_{K\alpha} / F_{>7.11}$) for each event.
2. Center-to-Limb Variation: The analysis confirms a strong geometric dependence of the fluorescence signal. Flares near the solar disk center ($\theta \approx 0^\circ$) exhibit high fluorescence efficiency, while those near the limb ($\theta \approx 90^\circ$) show significant suppression. This trend aligns with theoretical predictions regarding optical depth and viewing geometry.
3. Temperature Dependence: The results demonstrate an inverse relationship between plasma temperature and fluorescence efficiency. Higher temperature flares (harder X-ray spectra) produce lower fluorescence efficiencies, consistent with the reduced photoionization cross-section at higher photon energies.
4. Source Height Constraints: By comparing observed efficiencies with theoretical models (Bai 1979; Drake, Ercolano, and Swartz 2008), the study attempts to constrain the effective coronal source height ($h$). The data generally align with models assuming a photospheric iron abundance of $5.5 \times 10^{-5}$.
5. Thermal Parameter Robustness: The study demonstrates that including fluorescence components in the spectral fit does not significantly alter the derived plasma temperature (differences < 0.2 MK) but does slightly improve the accuracy of derived iron abundances compared to thermal-only models.

Significance and Claims
The paper claims that this work validates the photospheric iron fluorescence model using modern broadband SDD technology. The primary significance lies in the ability to directly measure the exciting flux, thereby removing the ambiguity inherent in previous narrow-band studies.

The authors assert that while the statistical uncertainties in the current dataset (derived from 10-second bins) are too large to track rapid, short-timescale variations in coronal source height, the mean fluorescence efficiency during the flare peak provides a viable constraint on the effective coronal source height.

However, the paper maintains a modest stance regarding the precision of these height determinations. It explicitly highlights a fundamental degeneracy: the observed Kα flux depends on both the coronal source height and the photospheric iron abundance. Without an independently fixed value for the iron abundance, the source height cannot be uniquely determined. The study notes that the derived abundance ($5.5 \times 10^{-5}$) required to match the data is higher than modern standard values ($3.16 \times 10^{-5}$) but agrees with values used in historical analyses (Parmar et al. 1984) to achieve consistency.

Finally, the authors conclude that despite the moderate spectral resolution of SDDs compared to crystal spectrometers, they provide a powerful new diagnostic tool for solar iron fluorescence, capable of characterizing the dominant thermal phase of flares and offering a pathway to future, more precise geometric diagnostics as instrumentation improves.