Observational signature of continuously operating drivers of decayless kink oscillation

Decayless kink oscillations, which are nearly omnipresent in the solar corona, are believed to be driven by continuously operating energy supply. In this letter, we investigate an external continuous excitation of an apparent decayless oscillation during an X1.1 flare on June 20, 2023 (SOL2023-06-20T16:42).The decayless kink oscillation was identified in the coronal loop at extreme ultraviolet (EUV) wavelengths and the associated flare quasi-periodic pulsations (QPPs) were simultaneously observed in passbands of hard X-ray (HXR), microwave, and ultraviolet (UV) emissions. The kink oscillation is detected as a transverse oscillation of the coronal loop, which reveals five apparent cycles with an average period of about 130-10 s. The oscillation amplitude does not show any significantly decay, suggesting a decayless oscillation. At the same time, the solar flare occurs in the vicinity of the oscillating loop and exhibits five main pulses in HXR, microwave, and UV emissions, which could be regarded as flare QPPs. They have similar periods of about 100-130 s, which may indicate successive and repetitive energy releases during the flare impulsive phase. The peak of each loop oscillation cycle appears to follow the pulse of the QPPs, suggesting that the transverse oscillation is closely associated with flare QPPs. Our observations support the scenario where the repetitive energy released following flare QPPs could be invoked as external, continuously operating drivers of the apparent decayless kink oscillation.


Introduction
Kink-mode oscillations are usually identified as transverse os-2 cillations of loop-like structures and they are always charac-3 terized by non-axisymmetric and weakly compressive in the 4 long-wavelength regime (see Nakariakov et al. 2021, for a re-5 cent review).Kink oscillations are well studied magnetohydro-6 dynamic (MHD) waves, since they play a crucial role in diag-7 nosing the solar magnetic field and measuring plasma param-8 eters, namely, "MHD coronal seismology" (e.g., Yuan & Van 9 Doorsselaere 2016; Yang et al. 2020;Chelpanov et al. 2022).
10 They are generally manifested as one of two forms: decaying 11 and decayless oscillations, which are usually dependent on their 12 oscillation amplitudes.The decaying oscillation always reveals 13 a large displacement amplitude, namely, at 1 Mm, it decays 14 fast and only persists for several oscillatory cycles.(Nakariakov 15 et al. 1999;Su et al. 2018;Kumar et al. 2022;Li et al. 2023a,b; 16 Zhang et al. 2023).For the large-amplitude oscillation, the de-17 cay time is about 1.79 times larger than the oscillation period on 18 average (Nechaeva et al. 2019).Conversely, the decayless oscil-19 lation usually shows small but weakly-decay displacement amplitude, which is less than the minor radius of the oscillating loop (Wang et al. 2012;Anfinogentov et al. 2013;Duckenfield et al. 2018;Mandal et al. 2022).The oscillation periods of standing kink waves are measured from sub-minute to dozens of minutes, and they are linearly increasing with the loop lengths (e.g., Anfinogentov et al. 2015;Nechaeva et al. 2019;Zhang et al. 2022;Petrova et al. 2023;Zhong et al. 2023).
It is well accepted that the kink oscillation should be associated with some external eruptions on the Sun (Nakariakov et al. 2021).The decaying kink oscillation is easily found to be driven by an impulsive driver, for instance, an extremeultraviolet (EUV) wave, a solar flare, a flux rope, and a coronal jet (e.g., Zimovets & Nakariakov 2015;Shen et al. 2018Shen et al. , 2019a,b;,b;Reeves et al. 2020).However, the decayless kink oscillation appears to show no apparent association with the solar transient (e.g., Gao et al. 2022;Zhong et al. 2022a;Li & Long 2023).On the other hand, the decayless kink oscillation is nearly omnipresent in the solar atmosphere (Tian et al. 2012;Li (blue) are recorded by GOES-18, which has a time cadence of 1 s.ASO-S/HXI is designed to image solar flares in the HXR energy range of about 15-300 keV.Its time cadence is 4 s in regular observation mode and can be as high as ∼0.125 s in burst mode.In this study, we use the full-disk light curve of three total flux monitors (D92, D93, D94) in the range of 20-80 keV interpolated at a time cadence of 1 s from the full cadence light curve, as shown by the magenta line in Figure 1 (b).KW is used for investigating γ-ray bursts and solar flares, which works in two modes: waiting and triggered modes.The count rate light curve has an accumulation time of 2.944 s in the waiting mode, while it has a varying time resolution (e.g., 2-256 ms) in the triggered mode.Therefore, we interpolate the KW flux at 20-80 keV into an uniform cadence of 2.944 s, as indicated by the green line in Figure 1 (b).We also use the radio dynamic spectra measured by EOVSA and SWAVES, as shown by the background images in Figure 1.SWAVES acquires the radio spectrum with a time cadence of 60 s, and it covers a frequency range of roughly 0.05-16.025MHz.EOVSA is a microwave radioheliograph, which provides the solar spectrum at frequencies of ∼1-18 GHz, and the time cadence could be as high as 1 s.We note that some data gaps appear in the EOVSA spectrum.SDO/AIA takes full-disk solar maps in multiple EUV/UV passbands, and the time cadence of seven EUV passbands is 12 s, while that of two UV passbands is 24 s (Lemen et al. 2012).In this study, we analyze AIA maps in seven passbands of 131 Å (∼10 MK), 94 Å (∼6.3 MK), 193 Å (∼20 MK & ∼1.6 MK), 211 Å (∼2.0 MK), 171 Å (∼0.63 MK), 1600 Å (∼0.1 MK), and 1700 Å (∼0.005MK), as shown in Figure 2. All the AIA maps are pre-processed by aia_prep.pro,and have a same spatial resolution of 1.2 .CHASE provides the spectroscopic observation of the full Sun in wavebands of Hα and Fe I (Li et al. 2022).Here, we use the spectral images at channels of Hα 6562.8Å and Fe I 6569.2Å, which mainly form in the solar chromosphere and photosphere, respectively.Each spatial pixel corresponds to ∼1.04 , and the time cadence is about 71 s.

Results
Figure 1 presents the solar flare observed in passbands of SXR, HXR and radio and microwave emissions.Panel (a) shows fulldisk light curves at GOES 1-8 Å (red) and 0.5-4.0Å (blue) from 16:41 UT to 17:30 UT.The GOES flux indicates an X1.1class flare, which begins at ∼16:42 UT, and reach its maximum at ∼17:09 UT.The orange line represents the local EUV flux in the wavelength of AIA 131 Å, which is integrated over the flare region.Figure 1 (b) shows HXR and microwave fluxes during 16:56-17:15 UT measured by ASO-S/HXI (magenta), KW (green), and EOVSA (cyan), respectively.Those light curves match well with each other, and they all reveal at least five pulses, which could be regarded as flare QPPs.The background images are radio dynamic spectra observed by SWAVES (a) and EOVSA (b), which show type III radio bursts at the lower and higher frequency ranges, suggesting that nonthermal electrons are accelerated via magnetic reconnections during the flare impulsive phase.Hα maps in passbands of AIA 171 Å, 211 Å, 1600 Å, 1700 Å, and CHASE 6562.8Å, they all exhibit double flare ribbons and are spatially correlated with two footpoints seen in the HXR emission, as outlined by the green and magenta contours.The HXR map during 17:04:07-17:04:37 UT is reconstructed by the HXI_CLEAN method (pattern-based CLEAN algorithm for HXI), utilizing the detectors from D19 to D91, namely, the subcollimator group G3 to G10, with a spatial resolution of about 6.5 .We exclude the fine grids of G1 and G2 since they are not calibrated yet and the fine structures are not the focus of this study.It should be pointed out that ASO-S was in calibration mode for other payloads during this flare and was therefore pointing away from the solar disk center.The HXI pointing data was regenerated using a machine-learning method.Panel i presents the CHASE map in the wavelength of Fe I 6569.2Å, and we can see a sunspot, but no signature of the flare radiation.
It is interesting that a bunch of coronal loops can be found in passbands of AIA 171 Å, 211 Å, and 193 Å, as indicated by the cyan arrow.
The online animation (anim.mp4)shows the evolution of the solar flare and the associated coronal loops.It can be seen that the coronal loops appear transverse oscillations follow the flare eruption.In order to capture the appearance of transverse oscillations, one artificial straight slit (S1), which is nearly perpendicular to the loop axis, is selected to generate the time-distance (TD) maps.The cut slit is chosen at the position that is close to the apparent loop apex, where is less overlapping with the neighboring loops, as marked by the cyan arrow in Figure 2. Figure 3 presents the TD maps at slit S1 in passbands of AIA 171 Å, 193 Å, and 211 Å.We can immediately notice that several transverse oscillations appear in these TD maps.Herein, there is only one transverse oscillation that shows five apparent peaks ana- Here, A m represents the displacement amplitude, P is the oscilla-203 tion period, and ψ refers to the initial phase, while f (t) stands for 204 the second-order polynomial approximation.Next, the velocity 205 amplitude (v m ) is obtained by the derivative of the displacement 206 amplitude (cf.Li et al. 2022aLi et al. , 2023a;;Petrova et al. 2023).The 207 overplotted magenta curve in Figure 3 is the best-fitting result 208 with Equation 1 and it appears to agree with the oscillation po-209 sitions ('+').The green line in panel a represents a nonlinear 210 trend of the oscillating loop, which is derived from a second-211 order polynomial approximation.We want to state that the ma-212 genta curve in panels b and c is exactly the same as that in panel a 213 and it seems to be not a good fit in passbands of AIA 193 Å and 214 211 Å.On the other hand, they appear to match with each other 215  In order to identify the quasi-period of flare QPPs, the wavelet transform with the "Morlet" mother function (Torrence & Compo 1998) was applied for the detrended light curves after removing a ∼180 s running average (Tian et al. 2012;Li et al. 2018b), since we want to enhance the short-period oscillation and suppress the long-period trend.Figure 5 shows the Mor- We want to state that the quasi-periods refer to the enhanced 254 power range inside the 99% significance level.The quasi-periods 255 agree with the average period (i.e., ∼130±10 s) of the loop oscil-256 lation, confirming that the transverse oscillation of the coronal 257 loop could be strongly associated the flare QPPs.We did not 258 perform the wavelet transform for the radio data measured by 259 EOVSA because it has some data gaps, resulting into a discon-260 tinuous microwave flux.kink oscillation.The large displacement amplitude could be attributed to the X1.1 flare, which could release a large amount of energies.This is different from previous observations of largeamplitude decayless oscillations that were triggered by small flares (Mandal et al. 2021) or small reconnection events (Li et al. 2020).Mandal et al. (2021) found that the solar flare could only increase oscillation amplitudes but did not change the oscillation nature (see also Shi et al. 2022).However, these studies did not show a distinct one-to-one correspondence over time.In our case, the energy flow appears as "an external driver" induced by a single flare energy release, leading to a large-amplitude kink oscillation of the coronal loop, followed by plasma heating caused by rapid damping (i.e., one oscillation cycle).This process is repeated five times, since the solar flare shows five energy releases via repetitive magnetic reconnections.This model could also explain the small-amplitude decayless oscillation, supposing that the external drivers are continuously existing.However, those external drivers are difficult to observe, mainly because of their fine scales.
Here, we assume the similar damping mechanism in decayless oscillations with the decaying oscillations and it is compensated with continuous energy supply from the ongoing flare energy releases.Then, we can construct an equation like: where E(t) represents the energy (kinetic + magnetic) density averaged over the oscillation cycle, τ, is the decaying time measured for the displacement amplitude, while v m , ρ i , and b are the velocity amplitude, plasma density and magnetic field perturbation, respectively.Then, its derivative dE(t) dt at t=0 will give us an estimation for the oscillation energy losses (ε): In this study, we know that the decayless oscillation has five oscillation cycles, which correspond to five-cycle energy releases from the flare.If the oscillating loop is affected by a periodic force with the oscillation period, the effect of the resonance must take place and the oscillation amplitude would grow over time (Nakariakov et al. 2009).However, the observed amplitude remains constant, suggesting that the wave energy of each oscillation cycle could completely dissipate at a time scale shorter than or approximately equal to one oscillation period, namely, τ ≤ P. According to the resonant absorption theory (Goossens et al. 2002), such a short decay time indicates an abnormal ratio of the loop radius and thickness of the transition layer or an abnormal density ratio inside and outside the loop, either too dense or too rarified.Possible supporting observational evidence to this interpretation is the half-cycle transverse perturbation of the outer loop in Ning et al. (2022).In this work, measuring the loop density may answer this concern but out of the scope of this work.Nevertheless, additional observations and numerical simulations in this direction are necessary for further investigation in the future.

Summary
Using the observations from SDO/AIA, ASO-S/HXI, KW, CHASE, EOVSA, SWAVES, and GOES, we investigated an apparent decayless kink oscillation and the associated flare QPPs.Our main conclusions are summarized as follows: (1) The apparent decayless kink oscillation can be simultaneously seen in passbands of AIA 171 Å,193 Å,and 211 Å,dicating that the oscillating loop is multi-thermal in nature.The oscillation period is measured to be about 130±10 s and the displacement amplitude is as large as ∼1.8±0.15Mm.
(3) The apparent decayless kink oscillation and flare QPPs share the same quasi-period and a significant time difference of about 110 s can be seen between them.Those observational facts provide sufficient evidences that the decayless kink oscillation could be driven by continuously operating energies released from the X1.1 flare.
(4) We propose that the repetitive energy releases behind the flare QPPs could trigger the kink oscillation intermittently for five times, making it apparent decayless.In this interpretation, each cycle of the kink oscillation is assumed to decay rapidly in less than one oscillation period.

Figure 2
Figure 2 shows the multi-wavelength images with a field of view (FOV) of ∼240 ×240 .Panels (a)-(c) plot EUV maps in high-temperature wavelengths of AIA 131 Å, 94 Å, and 193 Å, which display some hot flare loops.The gold rectangle outlines the flare region used to integrate the local flux at AIA 131 Å in Figure 1 (a).While panels d-h illustrate the EUV/UV and

Fig. 2 .
Fig. 2. Multi-wavelength snapshots with a FOV of ∼240 ×240 measured by SDO/AIA at 131 Å (a), 94 Å (b), 193 Å (c), 171 Å (d), 211 Å (e), 1600 Å (f), and 1700 Å (g), and captured by CHASE in passbands of Hα 6562.8Å (h) and Fe I 6569.2Å (i), respectively.The gold box outlines the flare region used to integrate the local flare flux.The cyan arrow indicates the targeted coronal loop, which is used to generate the time-distance map.The magenta contours represents the HXR emission at HXI 30-50 keV, and the contour levels are set 30%, 60%, and 90%.The green contours are derived from the Hα radiation measured by CHASE.An animation that shows the evolution of the solar flare and coronal loop is available online.

Fig. 3 .
Fig. 3. Time-distance maps show the transverse oscillation of the coronal loop at slit S1 in passbands of AIA 171 Å (a), 193 Å (b), and 211 Å (c).The pluses ('+') outline bright centers of the oscillating loop.The magenta curve and the cyan error bars represent the best-fitting result and their fitting uncertainties, whereas the green line indicates the background trend.The Arabic numerals mark five cycles of the loop oscillation.The cyan arrow indicates the slit direction.

Figure 4
Figure 4 (a) presents the oscillating positions ('+') of the coronal loop and the best-fitting result (cyan) after removing the nonlinear trend ( f (t)), the fitting parameters and their uncertainties such as the oscillation period, displacement and velocity amplitudes are also labeled.The normalized HXR flux at HXI 20-80 keV is also drawn, as shown by the magenta curve.One can immediately notice that both the loop oscillation and the HXR flux reveal at least 5 cycles, as marked by the Arabic and English numbers.The cycle of each HXR pulse appears earlier than that of the loop oscillation, and a time difference of about 110 s was estimated via cross correlation.Those observational facts imply that the transverse oscillation of the coronal loop could be strongly associated with the flare QPP in the HXR channel.We also notice that the HXR flux appears much more small sub-peaks, for instance, the HXR pulse "V" contains three sub-peaks, which might be due to the high time resolution of ASO-S/HXI.We then plot local light curves integrated over the flare region (gold rectangle in Figure2), as shown in Figure4 (b).Obviously, the light curves in passbands of AIA 1700 Å (black) and 1600 Å (green) display five apparent peaks, which are almost synchronous with the HXR pulses, as indicated by the dashed vertical lines.On the other hand, the light curves at AIA 171 Å (black) and 211 Å (green) also show five main peaks, while some main peaks also contain sub-peaks, similarly to what has observed in the HXR flux; this suggests the coexistence of multiple periodicities in the flare emission.

Fig. 4 .
Fig. 4. Oscillating positions ('+') after removing the background trend and its best-fitting result, shown in cyan (a).They are taken from the coronal loop at AIA 171 Å, as shown in Figure 3.The magenta curve shows the HXR flux measured by ASO-S/HXI at 20-80 keV during 16:56-17:15 UT.Local light curve integrated over the flare region (indicated by the gold box in Figure 2) in psaabands of AIA 1700 Å (black), 1600 Å(green), 171 Å (red), and 211 Å (orange), respectively (b).The Arabic and English numbers, as well as the dashed vertical lines outline these oscillating peaks.

261 4. Discussion 262
(Anfinogentov et al. 2015;inogentov et al. 2015Mandal et al. 2021;Shi et al. 2022;;;oronal and flare loops, Yuan et al. 2023)a-264 ment threads, and even umbral fibrils (e.g.,Anfinogentov et al. 265  2015;Nechaeva et al. 2019;Li et al. 2020Li et al. , 2022a;; Zhang et al. 266  2022;Yuan et al. 2023).In this letter, we study the transverse 267 oscillation of a coronal loop, which is perpendicular to the loop 268 axis at the apparent loop apex.It shows five significant cycles 269 and reveals no apparent decay in the displacement amplitude, 270 which could be regarded as the decayless kink oscillation(Tian 271  et al. 2012;Anfinogentov et al. 2015;Li & Long 2023).The ob-272 served kink oscillation shows an average period of ∼130±10 s, 273 which is consistent with previous observations that were in the 274 range of tens to hundreds of seconds(Anfinogentov et al. 2015; 275  Li et al. 2020;Mandal et al. 2021;Shi et al. 2022; Zhong et 276  al. 2023).While it has a large displacement amplitude, which 277 is measured to be about 1.8±0.15Mm.Such a large displace-278 ment amplitude is rarely reported in decayless oscillations.Pre-279 periods are also observed in EUV/UV passbands of AIA 1700 Å,