114. Hidden Coronal Loop Strands within Hi-C 2.1 Data

Author: Thomas Williams and Robert W. Walsh at the University of Central Lancashire.

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Observational investigations of coronal loop structure have been undertaken since the 1940s [1]; however, due to insufficient spatial resolution of current and previous instrumentation, the definitive widths of these fundamental structures have not been fully resolved. Recent high-resolution data from NASA’s Interface Region Imaging Spectrometer (IRIS; [2]) and the High-resolution Coronal imager (Hi-C; [3]) have led to coronal loop width studies in unprecedented detail.

Hi-C Observations

Recent work with 17.2 nm observations investigates loops from five regions within the field of view of the latest Hi-C (2.1) flight [4,5]. As with [6], coronal strand widths of ~513 km were determined for four of the five regions analysed. In the final region, which exhibits low emission, low density loops, much narrower coronal strands are found of ~388 km width, placing those structures below the width of a single AIA pixel. The fact that these strands are above the resolution limit of Hi-C (220-340 km [5]) suggests that Hi-C may be beginning to resolve a key spatial scale of coronal loops.

Notably, [4] also find example structures that may not be fully resolved within the Hi-C data. These relate to smaller ‘bumps’ or turning points in the cross-section intensity profiles that are larger than the observational error bars but do not constitute a completely isolated strand. Could these be the result of projection effects of overlapping structures along the integrated line of sight for this optically thin plasma, or are they the result of further structures beneath even the resolving abilities of Hi-C?

Figure 1.Reverse colour image of the Hi-C 2.1 field of view, which has been sharpened using Multi-Scale Gaussian Normalisation (MGN, [7]). The cross-section slice locations are indicated and those shown and numbered in green are shown more explicitly in Figures 2 and 3.


To answer this, a selection of slices is taken from the Hi-C 2.1 field-of-view (Figure 1) where these non-Gaussian shaped structures are seen. Following the method of [4], each slice is time-averaged for ~60 s and summed across a width of three-pixels to increase the signal-to-noise ratio. Cubic spline interpolation is then employed to generate and subtract the background intensity of each slice. To estimate the number of strands hidden within the cross-sectional profiles, a non-linear least-squares curve fitting method is employed to fit a number of Gaussians to the observed intensity profile. The correct number of Gaussian profiles fitted to each cross-sectional slice is determined by using the Akaike Information Criteria (AIC; [8]) model selection method. AIC evaluates how well a fit is supported by the data by rewarding a fit for the accuracy relative to the original Hi-C data, but punishes each fit as the complexity increases i.e. as the number of Gaussians fitted increases. The use of AIC helps mitigate the potential for over(under)-fitting the Hi-C data as the number of Gaussians fitted is taken as the model best supported by the data.

Figure. 2 A close-up view of slices 1-4 whose cross-sections are shown in Figure 3. Note: image is in reverse colour and MGN sharpened.
Figure. 3 The intensity profiles of the Hi-C 2.1 cross-sectional slices (1 – 4 in Figure 2) are shown in blue. The Gaussian profiles (grey) generated by the nonlinear least-squares fitting algorithm and the subsequent fit (red) are also plotted for the four example slices.


A total of 183 Gaussian profiles are fitted to twenty-four Hi-C cross sectional slices, the positions of which are shown in Figure 1. A closer view of four sample slices shown in Figure 2 and their cross-sections are displayed in Figure 3. In the cross-section plots, the original intensity (blue) is compared to the best AIC-determined fit (red) and the Gaussian profiles (grey) that generate said fit. Overall, the observed intensity is well reproduced though there are minor discrepancies that can be observed (e.g. Slice 2: positions 5’’ and 13’’). These could be eradicated by fitting more Gaussian profiles, however AIC determines that additional Gaussians are not supported by the Hi-C data.

The full-width at half-maximum (FWHM) of the 183 Gaussian profiles are collated into occurrence frequency plots (Figure 4) with the same spatial binning as [4] along with their 1-σ errors returned from the curve fitting method. As with [4], the most frequent spatial width of the measured strands is ~500 km, whilst the majority lie between 200 – 800 km, yielding a similar median (645 km) to previous 19.3 nm Hi-C width measurements [9].

Furthermore, ~21% of widths exceed 1000 km whilst ~32% of the strands studied are at the SDO/AIA resolving scale of 600-1000 km. From this, ~47% of the strands are beneath the resolving scale of SDO/AIA. The  Hi-C strand widths obtained reveal the presence of numerous strands (~32% of the 183 Gaussian widths) whose FWHMs are beneath the most frequent strand widths seen previously [~513 km; 4] Similarly, ~17% are below an AIA pixel width of 435 km. Comparatively then, only ~6% of the strands are actually at the smallest scale at which Hi-C can resolve structures [220-340 km, 5].

Figure. 4 a) Occurrence frequency plot of the 183 FWHM measurements for the fitted Gaussian curves with a bin width of 125 km ; b) a subset of the Gaussian profiles plotted at bin widths of 62.5 km that correspond to the most populous widths in a). The dashed vertical navy (red) lines indicate the low (high) emission strand widths obtained in [4]. Panel c) shows the one-sigma errors for the 183 widths obtained for the Gaussian profiles.


This work outlines a follow-up analysis to [4], in which non-Gaussian shaped loop profiles not fully resolved within the Hi-C data were found. Employing a nonlinear least-squares curve-fitting method, a total of 183 Gaussian profiles are fitted to these partially resolved Hi-C structures. The fact that (i) the FWHM of these Gaussians are  at the same spatial scales as previous high-resolution findings [4,6,9] and (ii) ~94% of strand widths measured are above the Hi-C resolving scale (220-340 km) provides strong evidence that structures with non-Gaussian distributions are likely the result of overlapping structures along the integrated line of sight rather than the result of an amalgamation of strands beneath even the resolving capabilities of instruments like Hi-C.

This work has been published in The Astrophysical Journal and a full-text version can be found here.


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