Evolution of Spatial Complexity in Flare Ribbon Substructure and Its Relationship to Magnetic Reconnection Dynamics

Abstract

Recent three-dimensional flare models suggest that flare-ribbon substructure is linked to the fragmentation of the reconnecting current sheet in the corona. Flare-ribbon substructure can therefore potentially serve as a unique diagnostic tool for physical processes in the flare current sheet. In this paper, we describe a new method to quantify the evolution of ribbon substructure, which first extract the ribbon's leading bright front and the quantifies its morphology using the box-counting dimension and Correlation Dimension Mapping (CDM). We first test our method using synthetic observations. We then find that when the flare ribbon boundary has more multi-spatial-scale features (higher box-counting dimension), hard X-ray (HXR) emission and magnetic reconnection rates are the strongest. We also find that the flare-ribbon complexity characterized by CDM has moderate correlation with the IRIS Si IV 1402.77 Å non-thermal velocity (in the negative-polarity ribbon) and reconnection flux rates (in ribbons of both magnetic polarities). We conclude that the build-up of the spatial complexity of the ribbons at multiple spatial scales can serve as an observational proxy for current-sheet fragmentation in the corona.

Figures (7)

• Figure 1: Overview of the M6.5 flare in AR 12371 on 2015 June 22. (a) GOES $1-8$ Å light curve; the IRIS-SJI analysis window is shaded yellow and the IRIS-SG start time is marked by the vertical line. (b) AIA $193$ Å image at 17:51 UT, (c) corresponding HMI B$_z$ magnetogram at 17:51 UT; (d) IRIS-SJI 1330 Å at 17:51 UT. Green and blue boxes show the SJI and SG FOVs, respectively. (e) Normalized time series of variables integrated over respective field of views: IRIS 1330 Å intensity ($I_{\rm UV}$; red), GOES 1--8 Å ($I_{\rm SXR}$; blue dashed) and its time derivative ($dI_{\text{SXR}}/dt$; blue solid), Fermi ($I_{\rm HXR}$) 15--25 keV (green dashed) and 50--100 keV (green solid), and ribbon-derived reconnection flux ($\Phi$; black dashed) and rate ($d\Phi/dt$; black solid).
• Figure 2: Spatial evolution of the FRBLE boundaries and local correlation dimension ($\mathcal{D}$) over IRIS 1330 Å SJI. Images are shown as $\log_{10}$ intensity ($I^*$; 1--$10^{4}$ DN; reversed grayscale). Rows (a1-a9), (b1-b9) and (c1-c9) show nine consecutive IRIS frames, during 17:51--17:53 UT, 17:57--18:00 UT and 18:15--18:18 UT, respectively. Red boxes mark the middle frames: 17:52 UT (a5), 17:58 UT (b5), and 18:16 UT (c5). Colors show $\mathcal{D}$ along the FRBLE: higher values (yellow; $\mathcal{D}>1.5$) indicate more corrugated/complex segments, while lower values (blue/dark; $\mathcal{D}\le 1$) indicate smoother segments.
• Figure 3: Evolution of FRBLE complexity and reconnection proxies. (a--c) Example frames (same as Fig. \ref{['fig:res_Spat_CDM']} a5, b5, c5) showing $\mathcal{D}$ along the FRBLE at 17:52, 17:58, and 18:16 UT. Contours show HMI $B_z$ levels: +500/+1000 G (red), $-500/-1000$ G (blue), and 0 G (white). (d,e) Distributions $w_{\mathcal{D}}$ for the positive and negative polarity ribbons. Solid lines show the mean $\bar{\mathcal{D}}$, dotted lines the 95th percentile, and black dashed lines the box-counting dimension $\mathcal{D}_{\rm BC}$. (f,g) Time series reconnection dynamics proxies in positive and negative magnetic-polarity FRBLEs, respectively. The solid and dashed colored-lines (red and blue) represent the 1330 Å intensity emitted from the FRBLE and full SJI FOV respectively, while the black-dashed line shows the cumulative reconnection rate derived from FRBLE observations. Vertical gray lines mark the times in (a--c).
• Figure 4: Reconnection rate vs. box-counting dimension. Absolute reconnection flux rate $|d\Phi/dt|$ versus box-counting dimension $\mathcal{D}_{\rm BC}$ for the (a) positive and (b) negative polarity FRBLEs. Dots' color encodes time (from $\sim$17:43 UT to $\sim$18:13 UT). Pearson and Spearman coefficients are listed in each panel. Best-fit power-law scales are shown in the lower right of each panel.
• Figure 5: Mean non-thermal velocity vs. mean FRBLE complexity within the IRIS-SG raster region. (a,b) Mean Si IV non-thermal velocity $\bar{\nu}_{\rm non\text{-}thermal}$ in the positive (red) and negative (blue) polarity FRBLE regions inside the raster region (blue rectangle in Fig. \ref{['fig:flare_cont']}). (c,d) Corresponding mean correlation dimension $\bar{\mathcal{D}}$ for the same regions and color scheme.