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

TL;DR

This study demonstrates a strong correlation between magnetic loop length and the timing difference between thermal and nonthermal emissions in solar flares, confirming the influence of loop geometry on energy transport dynamics.

Contribution

It provides the first observational evidence linking flare loop length to the delay between thermal and nonthermal emission peaks, emphasizing the role of magnetic geometry.

Findings

Longer loops are associated with larger timing delays.

Strong correlation (R=0.88) between loop length and delay across 96 flares.

The correlation remains robust under various Neupert effect conformity thresholds.

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 {\Delta}t 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 {\Delta}t. 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.