A New Analysis Procedure for Detecting Periodicities within Complex Solar Coronal Arcades

TL;DR

This paper introduces a novel spatio-temporal auto-correlation analysis method to detect and study periodic oscillations in complex solar coronal arcades, revealing decayless oscillations previously observed only in non-flaring loops.

Contribution

The paper presents a new auto-correlation based analysis procedure that effectively detects multiple periodicities in complex solar coronal structures, outperforming traditional methods in challenging conditions.

Findings

Detected a dominant 12.5-minute periodicity in large-amplitude oscillations.

Discovered 8-minute and 10-minute decayless oscillations in the same arcade.

Validated the new method against traditional time-distance fitting results.

Abstract

We study intensity variations, as measured by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO), in a solar coronal arcade using a newly developed analysis procedure that employs spatio-temporal auto-correlations. We test our new procedure by studying large-amplitude oscillations excited by nearby flaring activity within a complex arcade and detect a dominant periodicity of 12.5 minutes. We compute this period in two ways: from the traditional time-distance fitting method and using our new auto-correlation procedure. The two analyses yield consistent results. The auto-correlation procedure is then implemented on time series for which the traditional method would fail due to the complexity of overlapping loops and a poor contrast between the loops and the background. Using this new procedure, we discover the presence of small-amplitude oscillations within the same arcade with 8-minute and 10-minute periods prior and subsequent to the large-amplitude oscillations, respectively. Consequently, we identify these as "decayless" oscillations that have only been previously observed in non-flaring loop systems.

Tables

Table 1. Table 1: A chronological summary of the impulsive events that occurred in AR11967 as observed by AIA.

Event	Duration (UT)	Comments
Puff	00:55 - 01:05	Visible in all EUV channels.
1st Flare	01:05 - 01:39	M1.0 class.
2nd Flare	02:02 - 02:18	M1.1 class. No puff observed.
Large-amplitude oscillations	01:10 - 04:00	Predominant in $171$, $193$ & $211$ Å.

Table 2. Table 2: Fitted parameters from Time-Distance Methods.

Wavelength (Å)	Amplitude (Mm)	Period (min.)	Damping time (min.)	Phase (∘)
171 (large-amplitude)	(5.20 $\pm$ 0.75)	(13.00 $\pm$ 0.06)	(34.43 $\pm$ 11.12)	(65.99 $\pm$ 3.73)
193 (large-amplitude)	(3.30 $\pm$ 0.76)	(13.02 $\pm$ 0.12)	(48.30 $\pm$ 2.70)	(-98.98 $\pm$ 6.57)
193 (small-amplitude)	(0.68 $\pm$ 0.12)	(14.03 $\pm$ 0.21)	-	(20.38 $\pm$ 10.31)

Equations

$$\left(\begin{array}[]{ccc}1&2&1\\ 0&0&0\\ -1&-2&-1\end{array}\right).$$

$$\tilde{I}(t,x)=I(t,x)-I_b(t,x),$$

$$c(\Delta x,\Delta t)=\int \int \tilde{I}(t,x)\tilde{I}(x\pm \Delta x,t\pm \Delta t)dxdt.$$

Full text

Sun: activity - Sun: atmosphere - Sun: corona - Sun: flares - Sun: oscillations

††journal: ApJ

1 Introduction

Solar coronal arcades consist of brightly illuminated arches of hot plasma referred to as coronal loops. The arcades can act as waveguides for magnetohydrodynamic (MHD) waves, and these waves are of particular interest due to their diagnostic value in estimating the magnetic properties of arcades through seismology. Theoretical studies by Edwin & Roberts (1983) and Roberts et al. (1984) have, so far, formed the basis for most models of wave propagation in solar coronal loops. These studies describe the propagation of magnetohydrodynamic (MHD) waves along straight magnetic tubes. In particular, many previous seismic analyses have attributed the observed oscillations to the motions of fast kink waves. Theoretical studies of the wave propagation in arcades with curved field lines, or loops, have been rarer. Smith et al. (1997) studied fast MHD waves in dense curved potential field loops. Their study focused on the leakage of such waves across field lines. Selwa et al. (2007) considered a similar curved-arcade loop model and concluded that the main source of the wave attenuation was through such leakage. Recently, Hindman & Jain (2015, 2018) have demonstrated that fast MHD waves can be fully trapped by the magnetic field in an arcade under fairly common circumstances. Thus, fast waves can form resonances and wave leakage is not necessarily an essential process.

Since the advent of the Transition Region and Coronal Explorer (TRACE), wave propagation in coronal loops has been observed in the extreme ultraviolet (EUV) as the loops oscillate in response to the passage of transient MHD waves from nearby flares (Aschwanden et al., 1999; Nakariakov et al., 1999; Li et al., 2017). Such loops exhibit transverse standing oscillations with periods ranging from a few minutes to several tens of minutes. Aschwanden et al. (2002) investigated 17 events with TRACE data and concluded that most of the oscillating loops do not fit the simple model of kink eigenmode oscillations, but instead suggest that the oscillations are flare-induced impulsively generated MHD waves, which decay rapidly either due to damping or wave leakage. Such observed large-amplitude attenuation has been generally attributed to resonant absorption, a mode conversion process whereby energy is transferred from the global transverse waves to local Alfvénic waves (e.g Goossens et al., 2002; Ruderman & Roberts, 2002; Hindman & Jain, 2018). An alternate theory has also been proposed that explains the rapid signal attenuation as an interference effect that occurs whenever wave packets propagate along a multi-dimensional waveguide Hindman & Jain (2014).

With high-cadence data from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) (see Lemen et al., 2012), it is now clear that multiple loops within a single magnetic arcade often oscillate jointly (Schrijver et al., 2002; Verwichte et al, 2009). Jain et al. (2015) have reported that small phase shifts exist between such co-oscillating loops and suggest that such shifts could be caused by a moving driver or by the excitation of fast MHD waves that propagate across field lines from one loop to the other.

More recently, a distinct type of oscillation has been reported that is not clearly connected to any impulsive driver (Wang et al., 2012; Anfinogentov et al., 2013; Nisticò et al., 2013). These are low-amplitude oscillations and do not appear to exhibit a temporal decay. As such, some have called these oscillations “decayless”. Anfinogentov et al. (2015) conducted a statistical analysis of 21 non-flaring active regions in the 171 Å bandpass of SDO/AIA in order to estimate the regularity of this phenomenon. The average amplitude in the loop displacement is estimated to be $0.17$ Mm, with periods ranging from $1.5$ minutes to $10$ minutes. The nature of the driver of these oscillations remains unknown and various models have been suggested. Noting that these low-amplitude oscillations have poor phase-coherence over long durations, Hindman & Jain (2014) considered a stochastically driven model of a 2D waveguide representing the entire coronal arcade. The decayless oscillations were excited by a distributed and stochastic source and appeared as a series of interference patterns formed by a multitude of MHD waves traveling through the waveguide. Nakariakov et al. (2016) have suggested that the decayless oscillations suffer the same decay mechanism as the flare-induced waves but supergranulation acts as a stochastic source that replenishes the lost energy.

In this paper, we present a new analysis method that uses auto-correlations of the traditional time-distance images to extract properties of the wave-field within the coronal arcade. This method has the salutary feature that it can be successfully applied to loops and arcades for which the traditional time-distance method would fail because of poor image contrast. We first validate this new method before illustrating these advantages. To do this, we measure the period of coronal loop oscillations using both our new procedure and the traditional time-distance method. We then compare the parameters measured with the two methods. Finally, we demonstrate the utility of the auto-correlation method in the detection of an additional periodicity in the form of low-amplitude oscillations that exist both long before and after the flares.

The paper is organized as follows. In Section 2, we describe the observational data and the chronological events that triggered the coronal loop oscillations. In Section 3, we present the image processing used to generate standard time-distance images of the oscillations. Subsequently, we present the results of a traditional fitting of the oscillations of the loops. In Section 4, we describe our new auto-correlation procedure, compare its results to the traditional method, and present an application of our new procedure to data for which the traditional fitting method would fail. Finally in Section 5, we discuss the implications of our findings.

2 Observational data

We study coronal loop oscillations on the Southeastern limb using EUV images obtained by AIA/SDO with unprecedented spatial ($1$ pixel $\approx$ $0.6$ arcsec) and temporal ($12$ s cadence) resolutions on 2014 January 27. The arcade of interest belonged to a multi-polar active region (AR) NOAA AR11967, which was behind the limb at the time of flare activity, and emerged a day later exhibiting a sunspot. The flaring activity is believed to have originated near the old active region AR11944 (S09, L=101) (see http://www.aurora-service.eu). While the flare is visible in all six EUV wavelengths, the arcade was predominantly visible in the $171$, $193$ and $211$ Å channels and appeared as a bundle of illuminated arched threads, we refer to as loops. The dataset was chosen due to the off-limb nature of the arcade, where the loops have a higher visibility contrast against the darkness of the background. For the entirety of our study, we examined 12 hours ($3600$ time frames) of EUV imagery, starting from 2014 January 26 20:00 UT and ending on 2014 January 27 08:00 UT.

Figure 1 displays a EUV snapshot of the coronal arcade above NOAA AR11967 observed through AIA $171$ Å. The loops in the arcade were seen oscillating around the time of two consecutive M1 class flares, which were behind the Southeastern limb and were recorded in X-rays by the GOES instruments. We investigate, in detail, the oscillations as they manifested along the two slits indicated in the right panel of Figure 1.

Figure 2 shows the recorded X-ray flux by GOES in $4$ Å and $8$ Å. The first flare, located at latitude $16^{\circ}$ South and longitude $88^{\circ}$ East, was an M1.0 class flare, with a start time at 01:05 UT, a peak at 01:22 UT, and an end time at approximately 01:39 UT. After this an M1.1 class flare, at latitude $13^{\circ}$ South and longitude $88^{\circ}$ East, initiated at 02:02 UT, peaked at 02:11 UT, and ended at about 02:18 UT. Just before the first flare, a small wave-front or a puff-like structure (hereafter referred to as the “puff”) was also seen propagating away from the limb and throughout the arcade. Initially, the puff appeared near the limb around 00:40 UT, and became evident at 01:00 when it started moving. The initial motion of the puff from the flare site was visible in the AIA movies at all six EUV wavelengths. The life-time of the puff, as seen in 171 Å passband movie, is also marked in Figure 2 with a double-headed arrow. A summary of the major events are shown in Table 2 See Alzate & Morgan (2016) for details on coronal jets and puffs. Additionally, coinciding with the time of both flares, STEREO-B/SWAVES recorded two Type III radio bursts.