Observational Evidence Linking Loop Length and Thermal/Nonthermal Peak Timing in Solar Flares
| Nugget | |
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| Number: | 517 |
| 1st Author: | Solomon PERRIYIL |
| 2nd Author: | |
| Published: | February 23, 2026 |
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| Previous Nugget: | A fine-scale bright kernel captured by Hi-C 3 in the post-maximum phase of an M-class solar flare |
Introduction
Solar flares rapidly convert stored magnetic energy into particle acceleration and plasma heating. In the collisional thick-target picture, electrons accelerated in the corona precipitate into the chromosphere and produce hard X-rays (HXR) by bremsstrahlung (e.g., [1]). The deposited energy heats the chromosphere and drives "chromospheric evaporation", filling coronal magnetic loops with hot plasma that emits soft X-rays (SXR). As a result, the SXR peak often occurs after the HXR peak [2]. Previous statistical work suggested that the HXR-SXR peak delay may be related to loop size, but loop lengths were not measured directly (Ref. [3]). Here we test this idea using imaging-based loop-length estimates for a sample of 96 flares.
Methodology
We analyzed 96 solar flares observed between 2013 and 2015 using GOES/XRS soft X-rays, RHESSI hard X-rays, and SDO/AIA ultraviolet images. The SXR peak times were measured from the light curves (Figure 1), and the HXR peak times were measured from RHESSI observations in the 25-50 keV range. The delay was defined as t = t(SXR) - t(HXR). A preflare background was subtracted before determining peaks, and uncertainties were estimated using a Monte Carlo method. Loop lengths were measured using RHESSI and AIA images. RHESSI CLEAN images at the HXR peak were used to identify the two nonthermal footpoints and checked using AIA 1700 Å images. The footpoint separation D was converted into loop length assuming a semicircular loop of length L = πD/2.
Results
We find a clear relationship between magnetic loop length (L) and the delay between the hard X-ray (HXR) and soft X-ray (SXR) peak times (t). Longer loops consistently show larger delays. For the full sample of 96 flares, the correlation is strong (R = 0.88) and the best-fit linear relation is
L = 0.059 t + 13.73 Mm.
We alsoexamine how this trend depends on how closely a flare follows the Neupert effect (Refs. [2,4]. We define a Neupert correlation coefficient RN as the Pearson correlation between the time derivative of the GOES 1-8 Å flux and the RHESSI 25-50 keV light curve. The term "Neupertian" refers to flares that better match the canonical Neupert interpretation, where nonthermal electrons heat the chromosphere and the evaporated plasma fills the loop and produces SXR emission.
When we select flares with RN > 0.5 (87 events), the L-Δt relation remains similar (R = 0.87). For a stricter subset with RN > 0.8 (46 events), the relation becomes tighter (R = 0.91). This indicates that the loop-length versus delay trend is clearest for the most Neupertian flares.
The fitted slopes correspond to characteristic loop-filling speed scales of about 54-61 km/s, while individual events imply average evaporation speeds of about 70-250 km s, consistent with chromospheric evaporation model calculations. Overall, the delay Δt mainly reflects the time required for hot plasma to fill the flare loop.
Table Note
The full flare catalog is available as a machine-readable table in the online article: https://iopscience.iop.org/article/10.3847/1538-4357/ae3061
References
[2] "Comparison of Solar X-Ray Line Emission with Microwave Emission during Flares"
[3] "On the Peak Times of Thermal and Nontheral Emissions in Solar Flares"
[4] "The Neupert effect - What can it tell us about the impulsive and gradual phases of solar flares?"