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Observational Evidence Linking Loop Length and Thermal-Nonthermal Peak Timing in Solar Flares

S. M. Perriyil, S. S. Sadangaya, C. G. Giménez de Castro, P. J. A. Simões

Abstract

We investigate how the magnetic loop length of solar flares relates to the timing between their thermal and nonthermal emission signatures. Our study analyzes a sample of 96 C-, M-, and X-class flares observed between 2013 and 2015 with soft X-rays, hard X-rays, and extreme UV. For each event, we determine the time delay Δt between the hard X-ray and soft X-ray peak, and estimate the flare loop length L from UV footpoints assuming a semicircular geometry. In every case, longer flare loops are consistently associated with larger timing delays. Across the full sample, we find a strong correlation, R = 0.88 between L and Δt. We also quantify how closely each flare follows the Neupert effect using a coefficient RN, defined as the Pearson correlation between the time derivative of the soft X-ray flux and the hard X-ray light curve. Applying correlation thresholds of RN > 0.5 and RN > 0.8 yields subsets of 87 and 46 events, respectively. In both cases, the linear relationship between loop length and peak delay remains clearly expressed. For the RN > 0.5 subset, the correlation is R = 0.87, while the more selective subset with RN > 0.8 displays an even stronger correlation of R = 0.91. These results show that the overall trend persists across increasingly stringent correlation thresholds. The results provide direct observational confirmation that magnetic loop geometry plays a key role in governing the temporal evolution of energy transport in solar flares.

Observational Evidence Linking Loop Length and Thermal-Nonthermal Peak Timing in Solar Flares

Abstract

We investigate how the magnetic loop length of solar flares relates to the timing between their thermal and nonthermal emission signatures. Our study analyzes a sample of 96 C-, M-, and X-class flares observed between 2013 and 2015 with soft X-rays, hard X-rays, and extreme UV. For each event, we determine the time delay Δt between the hard X-ray and soft X-ray peak, and estimate the flare loop length L from UV footpoints assuming a semicircular geometry. In every case, longer flare loops are consistently associated with larger timing delays. Across the full sample, we find a strong correlation, R = 0.88 between L and Δt. We also quantify how closely each flare follows the Neupert effect using a coefficient RN, defined as the Pearson correlation between the time derivative of the soft X-ray flux and the hard X-ray light curve. Applying correlation thresholds of RN > 0.5 and RN > 0.8 yields subsets of 87 and 46 events, respectively. In both cases, the linear relationship between loop length and peak delay remains clearly expressed. For the RN > 0.5 subset, the correlation is R = 0.87, while the more selective subset with RN > 0.8 displays an even stronger correlation of R = 0.91. These results show that the overall trend persists across increasingly stringent correlation thresholds. The results provide direct observational confirmation that magnetic loop geometry plays a key role in governing the temporal evolution of energy transport in solar flares.
Paper Structure (11 sections, 5 equations, 6 figures, 1 table)

This paper contains 11 sections, 5 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Instrumentation and Flare Selection
  3. Methodology
  4. Determination of SXR and HXR Peak Times
  5. Loop Length Determination
  6. Results
  7. Flare Loop Length vs Emission Peak Delay
  8. Subset of Flares Selected by $R_{\mathrm{N}}$ Threshold
  9. Discussion
  10. Conclusions
  11. Software and third party data repository citations

Figures (6)

  • Figure 1: Heliographic positions of the 96 selected flares. All events lie within $\pm60^\circ$ heliographic longitude of the solar-disk center, ensuring minimal projection effects in loop-length estimation. square, circle, and triangle markers denote C, M, and X-class flares, respectively.
  • Figure 2: Temporal profiles of a SOL2013-10-26T05:59 (M2.3) flare showing thermal and nonthermal emission.The top panel displays the SXR flux from GOES 1-8 Å. The middle panel shows the RHESSI 25-50 keV HXR light curve. The uncertainty near the peak time is shown in gray shade. The bottom panel compares the time derivative of the GOES 1-8 Å flux with the RHESSI 25-50 keV emission. The cross correlation ($R_{\mathrm{N}}$) for flare M2.3 is 0.948. Delays and cross correlations of the 96 flares are presented in Table \ref{['tab:sample_flares_15']}.
  • Figure 3: RHESSI 25-50 keV HXR emission contours overlaid on the SDO/AIA 1700 Å image for a SOL2013-04-21T16:00 (C2.9) flare. The two nonthermal footpoints are highlighted in red. The AIA 1700 Å background traces the lower chromospheric emission at the flare site.
  • Figure 4: Magnetic loop length versus the HXR–SXR time delay $\Delta t$ for all 96 flares, color-coded by GOES class.
  • Figure 5: Same as Figure 4, but only for flares with Neupert correlation ($R_{\mathrm{N}}$) $\geq 0.5$ (87 events).
  • ...and 1 more figures