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 Δ 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 Δ t . We also quantify how closely each flare follows the Neupert effect using a coefficient R N , 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 R N ≥ 0.5 and R N ≥ 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 R N ≥ 0.5 subset, the correlation is R = 0.87, while the more selective subset with R N ≥ 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.