Observation and Modeling of Shear Evolution of Post-reconnection Flare Loops

TL;DR

This paper develops ORCCA, a data-constrained method to reconstruct the three-dimensional structure of post-reconnection flare loops by fitting each observed PRFL to a family of linear-force-free fields with varying twist $\alpha$, anchored to flare ribbons. Applying ORCCA to the SOL2014-12-18 M6.9 two-ribbon flare, the authors find that the coronal field is best described as a quasi-nonlinear force-free state, with early loops carrying larger $\alpha$ and later loops relaxing toward smaller $\alpha$ as the arcade rises; the observed strong-to-weak shear evolution thus reflects progressive magnetic relaxation rather than a move toward a potential state. The study also quantifies a time delay between footpoint brightening and the appearance of PRFLs in EUV (median ~20–24 minutes) and reveals spatial patterns in $\alpha$ along the ribbons, offering new physical insight into flare energetics. These results provide a concrete framework for improving post-reconnection magnetic models and along-the-loop hydrodynamic simulations, with implications for estimating energy release and plasma evolution in flares.

Abstract

A solar flare releases magnetic energy by reconnecting field lines across a current sheet, thereby allowing their relaxation to a lower energy state. The maximum possible energy is released if all field lines relax to a current-free (potential) state. The progress of a flare's reconnection is often measured as the angle-complement between the observed post-reconnection flare loops and the polarity inversion line of the photospheric magnetic field: shear angle. Many observations have shown strong-to-weak shear evolution over the course of a flare. A field line's shear angle is, however, an imperfect measure of its relaxation. We develop a new technique for observationally inferring the three-dimensional structure of post-reconnection field lines, including their local twist, $α$, which will vanish for potential fields. Our method fits loops in EUV images to extrapolations subject to constraints such as matching the feet of model field lines to observed flare ribbons. We apply the new method to an eruptive two-ribbon flare (SOL2014-12-18T22) which exhibits strong-to-weak shear-angle evolution. We find that, as the flare progresses, $α$ decreases in post reconnection loops anchored to newly brightened ribbons. Our study demonstrates that post-reconnection magnetic field is neither potential nor linear force-free. The method quantifies, for the first time, the time-history of a flare's energetic relaxation. It also quantifies the increasing height of subsequently reconnected field, and the time delay between reconnection forming a flare loop and its appearance in EUV passbands. These results promise to enable improvements in both magnetic modeling and hydrodynamic modeling of flares.

Figures (10)

• Figure 1: Top: post-reconnection flare loops observed in the EUV 304 Å images by AIA at different times. Bottom: (d-e) PRFLs identified from the AIA 304 Å images using the OCCULT code, superimposed on a magnetogram of the photospheric radial magnetic field obtained by HMI at 21:00 UT. The colors indicate the times when the loops were observed in the AIA 304 Å images minus 15 minutes. (f) Evolution of flare ribbons observed in the AIA 1600 Å passband, with the colors of the contour indicating the time the ribbon pixels are brightened, as denoted in the color bar in the right. The orange curve outlines the PIL of the photospheric radial magnetic field (gray scale). All images in this figure have been rotated to 21:00 UT, and the helioprojective coordinates in the figures reflect this reference time.
• Figure 2: (a) A sample of field lines traced at various heights for a given $\alpha$, overlaid on top of an AIA 304 Å image that the (blue) observed loop is identified in. (b): A side view of the same sample of field lines traced with a CEA magnetogram placed at the surface $z=0$, saturated at $\pm$300 G. In both panels, magenta color indicates the observed loop's center pixel, red curves show the sample of model field lines traced at various heights, and the green curve shows the modeled loop that is the best fit to observation.
• Figure 3: (a) An example demonstrating the error metric between an observed loop (blue) and modeled field line (red). The separation $\Delta Y(X)$ is shown by vertical black lines.(b) Histogram of the fitting error $\sigma$ for 2807 loops.
• Figure 4: (a) An example of several tens of observed loops in both AIA 304 Å and 171 Å passbands identified with the OCCULT code (red) within a time window of four minutes, superimposed on an AIA 304 Å image. The loop in cyan is one of the reference loops within this time window. (b) A zoomed-in view of the consolidation, showing 12 observed loops (blue) that match a model loop (green) of the longest observed loop, or reference loop (cyan), with $\sigma \le \sigma_{thr}$.
• Figure 5: (a) Histograms of repeat measurements. Red curve is the histogram of $N$, read from the left axis, with a green curve showing an exponential fit. The blue curve, read from the right axis, is a cumulative histogram. (b) Histograms of the twist $\alpha$ and its standard deviation $\delta_{\alpha}$ of the 439 loops that are observed for more than once ($N > 1$).