106. A new procedure for detecting periodicities within complex coronal arcades

Author: Farhad Allian, Rekha Jain (The University of Sheffield) and Bradley W. Hindman (University of Colorado Boulder)

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Introduction & Motivation

Amongst the most fascinating features of the dynamic solar atmosphere lie the complex curved loops of illuminatingly hot plasma that are traced by the magnetic field lines. These loops form waveguides that support various magnetohydrodynamic waves and are typically observed to undulate back and forth in the plane-of-the-sky. Distinctively, oscillations generated by impulsive events, such as solar flares, have displacement amplitudes that suddenly grow and diminish within a few wave-periods [1]. Conversely, oscillations in the absence of an obvious driver are observed to oscillate for longer without any significant decay, and with displacement amplitudes on the order of SDO/AIA’s pixel size.

Alongside appropriate mathematical models, coronal loop oscillations remain an indispensable tool to indirectly probe the solar atmosphere. However, such seismological inversions rely on time-series analyses of a clear oscillating loop with well-defined amplitude boundaries. This leads to the unavoidable question: how can we analyse EUV images of coronal loop oscillations with a poor background contrast?


Utilising the high spatial and temporal resolutions of SDO/AIA, we examined EUV imagery of coronal loop oscillations embedded within a complex arcade on 27th January 2014 [2]. This arcade belonged to a multi-polar active region, which exhibited two consecutive M-class flares prior to the initiation of large-amplitude oscillations. Surprisingly, despite the flaring activities being situated next to each other, the second flare did not restart any additional large-amplitude oscillations.

In association with the first flare, we observed a small wavefront propagating away from the solar limb and throughout the arcade. By carefully tracking the wavefront, we estimated an initial projected speed of about 40 km/s. After its initial stage of propagation, the wavefront was obscured by a bundle of loops in the line-of-sight and so further tracking was not possible. This coincidence with the wavefront and the first flare proved difficult to distinctively determine the likely exciter for these large-amplitude oscillations.

Moreover, we investigated the oscillations manifested along two slits placed perpendicular to the apparent arcade, as shown in Figure 1. The bright loop featured in the time-distance image of Slit 1 undergoes a clear decaying large-amplitude oscillation with a periodicity of approximately 13 minutes. However, within this slit and even more so in Slit 2, exists the presence of an overlapping multitude of faint oscillations, perhaps with different periodicities. In such cases, the oscillatory parameters cannot be estimated with fidelity.

Figure 1. EUV images at the beginning of our dataset observed by SDO/AIA 171. Top panel: full-disk image indicating the active region of interest. The zoomed-in area of NOAA11967 is contained in the box. The magenta and green crosses (lines) correspond to the positions (onset times) of the flaring activity, as detected by the GOES instruments. The solid white lines indicate our slits. Bottom panel: Corresponding time-distance images conveying large-amplitude oscillations manifested along our two slits. In addition to the bright loop in Slit 1, there appears to be a faint background oscillating with a different periodicity. Slit 2 shows a further complicated bundle of indistinguishable loop oscillations.

The 2D Autocorrelation Function: Observed & Synthetic Signals

The regularly sampled intensity variations recorded by AIA allows us to use our newly developed analysis procedure which employs spatio-temporal autocorrelations. The main benefit of our procedure is that it reveals the periodicities that remain hidden in the traditional time–distance analysis. In general, the autocorrelation describes the degree of similarity of a given input with itself and as a result, this transformation reveals any periodic structure that is already present in the data. For applications to complex loop systems viewed in time-distance images, as in Figure 1, our procedure simply requires a temporal high-pass filter in order to sharpen the oscillatory features. Thereafter, we generate the autocorrelation as a function of time lag (minutes) and spatial offset (Mm) for our two slits.

Figure 2. Spatio-temporal autocorrelation of the time-distance image of Slit 1. Two main structures are revealed in this transformation: a series of Xs corresponding to the bright loop oscillating at 13 minutes, and a sequence of phase-shifted slopes corresponding to the background periodicity of 10 minutes.

The autocorrelation function for the time-distance image of Slit 1 is shown in Figure 2. The maximum correlation occurs at the zero lag and offset as expected, which is used as the reference point of recurring structures. Noticeably, the focal points of this image are a series of X-like structures in addition to the near-vertical streaks. In order to understand these structures, we generated synthetic signals that consist of a bright oscillating loop embedded in a background of faint, dispersed oscillations, shown in Figure 3. We immediately see that the X-like features are due to the bright oscillating loop correlating with itself. Moreover, the slopes passing through the centers of the Xs arise due to a time shift of the faint background loops along the slit, possibly due to a moving driver or the observed wavefront. The bottom panel of Figure 3 demonstrates the dependency on the relative brightness contrast between the bright loop and the faint phase-shifted background within the autocorrelation. As a result, for time-distance images wherein a bright loop is not distinguished well, the 2D autocorrelation still reveals the dominant periodic structures as a series of strongly correlated slopes.

Figure 3. Synthetic time-distance images (left) and their corresponding autocorrelations (right). A bright loop correlating with itself is revealed as a series of Xs in the 2D autocorrelation. A faint background of oscillations that initiate at different times introduces a phase shift that varies along the slit and is thus revealed as a series of slopes. The superposition of the bright and faint oscillations demonstrates that the prominence of Xs depend on their relative brightness.


  • We have introduced and developed a novel image analysis procedure based on 2D autocorrelations that can be utilised in complex loop systems to reveal the periodicity of the faint background.
  • We have demonstrated that the autocorrelation of a bright loop is revealed as a series of Xs, whereas the faint background oscillations are revealed as a series of phase-shifted slopes. From our observations, we have successfully extracted the dominant periodicity of the bright loop at 13 minutes, as well as the periodicity of the background at 10 minutes. Moreover, the gradient of the background within the 2D autocorrelation corresponds to the group velocity of the wavefield across the slit.
  • Importantly, our method has the salutary feature that it can be successfully applied to coronal arcades for which a typical time-series fitting method would fail due to the poor image contrast, for example, in complex loop systems or when seeking for small-amplitude oscillations. As a result, our procedure can be used to constrain the seismological inversions that are necessary to understand the local plasma conditions of solar coronal arcades.
  • Acknowledgments

    F.A. acknowledges the STFC (UK) studentship. We are grateful for the use of SDO/AIA and GOES data. This research has made use of SunPy, an open-source and free community-developed solar data analysis Python package [3].