We investigate intensity oscillations observed simultaneously in the quiet chromosphere and in the corona, above an enhanced network area at the boundary of an equatorial coronal hole. A Fourier analysis is applied to a sequence of images observed in the 171 A and 1600 A passbands of TRACE. Four interesting features above the magnetic network are further investigated by using a wavelet analysis. Our results reveal that, in both the 171 A and 1600 A passbands, oscillations above the magnetic network show a lack of power at high frequencies (5.0-8.3 mHz), and a significant power at low (1.3-2.0 mHz) and intermediate frequencies (2.6-4.0 mHz). The global 5-min oscillation is clearly present in the 4 analyzed features when seen in the 1600 A passband, and is also found with enhanced power in feature 1 (leg of a large coronal loop) and feature 2 (legs of a coronal bright point loop) when seen in the 171 A passband. Two features above an enhanced network element (feature 3 and feature 4) show repeated propagating behaviors with a dominant period of 10 min and 5 min, respectively. We suggest these oscillations are likely to be slow magneto-acoustic waves propagating along inclined magnetic field lines, from the lower solar atmosphere into the corona. The energy flux carried by these waves is estimated of the order of 40 erg cm\^{-2} s\^{-1} for the 171 A passband and is far lower than the energy required to heat the quiet corona. For the 1600 A passband, the energy flux is about 1.4*10^6 erg cm\^{-2} s\^{-1}, which is about one third of the required energy budget for the chromosphere.
Collimated ejections of plasma called "coronal hole jets" are commonly observed in polar coronal holes. However, such coronal jets are not only a specific features of polar coronal holes but they can also be found in coronal holes appearing at lower heliographic latitudes. In this paper we present some observations of "equatorial coronal hole jets" made up with data provided by the STEREO/SECCHI instruments during a period comprising March 2007 and December 2007. The jet events are selected by requiring at least some visibility in both COR1 and EUVI instruments. We report 15 jet events, and we…
Spectroscopic diagnostics of solar coronal plasmas critically depends on the uncertainty in the measured line intensities. One of the main sources of uncertainty is instrumental scattered light, which is potentially most important in low-brightness areas. In the solar corona, such areas include polar and equatorial coronal holes, which are the source regions of the solar wind; instrument-scattered light must thus pose a significant obstacle to studies of the source regions of the solar wind. In this paper we investigate the importance of instrument-scattered light on observations of equatorial…
We use full-disk, SOHO/EIT 195 $Å$ calibrated images to measure latitudinal and day to day variations of area and average photon fluxes of the near equatorial coronal holes. In addition, energy emitted by the coronal holes with their temperature and strength of magnetic field structures are estimated. By analyzing data of 2001-2008, we find that variations of average area (A), photon flux (F), radiative energy (E) and temperature (T) of coronal holes are independent of latitude. Whereas inferred strength of magnetic field structure of the coronal holes is dependent on the latitudes and varies …
Because of its distinctive compositional properties and variability, low-speed ($\lesssim 450$ km s$^{-1}$) solar wind is widely believed to originate from coronal streamers, unlike high-speed wind, which comes from coronal holes. An alternative scenario is that the bulk of the slow wind (excluding that in the immediate vicinity of the heliospheric current sheet) originates from rapidly diverging flux tubes rooted inside small coronal holes or just within the boundaries of large holes. This viewpoint is based largely on photospheric field extrapolations, which are subject to considerable uncer…
Small, impulsive jets commonly occur throughout the solar corona, but are especially visible in coronal holes. Evidence is mounting that jets are part of a continuum of eruptions that extends to much larger coronal mass ejections and eruptive flares. Because coronal-hole jets originate in relatively simple magnetic structures, they offer an ideal testbed for theories of energy buildup and release in the full range of solar eruptions. We analyzed an equatorial coronal-hole jet observed by SDO/AIA on 09 January 2014, in which the magnetic-field structure was consistent with the embedded-bipole t…
Axial-Dipole and Equatorial-Dipole Coronal Holes: Congruent Magnetic Geometry, Divergent Evolution
Advanced Heliophysics Inc.（高级日球物理公司）；US Naval Research Laboratory（美国海军研究实验室）；Center for Astrophysics, Harvard & Smithsonian（哈佛-史密森天体物理中心）；European Space Agency, ESTEC（欧洲空间局，欧洲空间研究与技术中心）
Jets (transient/collimated plasma ejections) occur frequently throughout the solar corona and contribute mass/energy to the corona and solar wind. By combining numerical simulations and high-resolution observations, we have made substantial progress recently on determining the energy buildup and release processes in these jets. Here we describe a study of 27 equatorial coronal-hole jets using Solar Dynamics Observatory/AIA and HMI observations on 2013 June 27-28 and 2014 January 8-10. Out of 27 jets, 18 (67%) are associated with mini-filament ejections; the other 9 (33%) do not show mini-filam…
"EIT waves" are freely-propagating global pulses in the low corona which are strongly associated with the initial evolution of coronal mass ejections (CMEs). They are thought to be large-amplitude, fast-mode magnetohydrodynamic waves initially driven by the rapid expansion of a CME in the low corona. An "EIT wave" was observed on 6 July 2012 to impact an adjacent trans-equatorial loop system which then exhibited a decaying oscillation as it returned to rest. Observations of the loop oscillations were used to estimate the magnetic field strength of the loop system by studying the decaying oscil…
Solar coronal loops are commonly subject to oscillations. Observations of coronal oscillations are used to infer physical properties of the coronal plasma using coronal seismology. Excitation and evolution of oscillations in coronal loops is typically studied using highly idealised models of magnetic flux-tubes. In order to improve our understanding of coronal oscillations, it is necessary to consider the effect of realistic magnetic field topology and evolution. We study excitation and evolution of coronal oscillations in three-dimensional self-consistent simulations of solar atmosphere spann…
We detect and analyse transverse oscillations in a coronal loop, lying at the south east limb of the Sun as seen from the \textit{Atmospheric Imaging Assembly} (AIA) onboard \textit{Solar Dynamics Observatory} (SDO). The jet is believed to trigger transverse oscillations in the coronal loop. The jet originates from a region close to the coronal loop on 19$^{\rm th}$ September 2014 at 02:01:35 UT. The length of the loop is estimated to be between 377-539~Mm. Only one complete oscillation is detected with an average period of about $32\pm5$~min. Using MHD seismologic inversion techniques, we est…
We analyse intensity variations, as measured by the Atmospheric Imaging Assembly (AIA) in the 171 Å passband, in two coronal loops embedded within a single coronal magnetic arcade. We detect oscillations in the fundamental mode with periods of roughly 2 minutes and decay times of 5 minutes. The oscillations were initiated by interaction of the arcade with a large wavefront issuing from a flare site. Further, the power spectra of the oscillations evince signatures consistent with oblique propagation to the field lines and for the existence of a 2-D waveguide instead of a 1-D one.
Coronal loop oscillations are common phenomena in the solar corona, which are often classified as decaying and decayless oscillations. Using the high-resolution observation measured by the Extreme Ultraviolet Imager (EUI) onboard the Solar Orbiter, we statistical investigate small-scale transverse oscillations with short periods (<200 s) of coronal loops in an active region, i.e., NOAA 12965. A total of 111 coronal loops are identified in EUI 174 A images, and they all reveal transverse oscillations without any significant decaying, regarding as decayless oscillations. Oscillatory periods are …
The excitation and damping of transversal coronal loop oscillations and quantitative relation between damping time, damping quality (damping time per period), oscillation amplitude, dissipation mechanism and the wake phenomena are investigated. The observed time series data with the \textit{Atmospheric Imaging Assembly} (AIA) telescope on NASA's \textit{Solar Dynamics Observatory} (SDO) satellite on 2015 March 2, consisting of 400 consecutive images with 12 seconds cadence in the 171 $ \rm{Å}$ pass band is analyzed for evidence of transversal oscillations along the coronal loops by Lomb-Scargl…
Coronal seismology is extensively used to estimate properties of the corona, e.g. the coronal magnetic field strength are derived from oscillations observed in coronal loops. We present a three-dimensional coronal simulation including a realistic energy balance in which we observe oscillations of a loop in synthesised coronal emission. We use these results to test the inversions based on coronal seismology. From the simulation of the corona above an active region we synthesise extreme ultraviolet (EUV) emission from the model corona. From this we derive maps of line intensity and Doppler shift…
In this paper, we apply the Rayleigh-Ritz Variational Scheme for studying the transverse oscillations of a magnetic flux tube. The flux tube is considered in low-$β$ solar coronal condition. The perturbations decomposed into irrotational and solenoidal components and MHD equations are reduced as a matrix eigenvalue problem. In the case of longitudinally stratified thin flux tube, the fundamental and higher order kink frequencies are computed. The results are in good agreements with previous studies.
Context: Transverse loop oscillations and loop contractions are commonly associated with solar flares, but the two types of motion have traditionally been regarded as separate phenomena. Aims: We present an observation of coronal loops contracting and oscillating following onset of a flare. We aim to explain why both behaviours are seen together and why only some of the loops oscillate. Methods: A time sequence of SDO/AIA 171 Å images is analysed to identify positions of coronal loops following the onset of M6.4 flare SOL2012-03-09T03:53. We focus on five loops in particular, all of which cont…
In this work we review the efforts that have been done to study the excitation of the standing fast kink body mode in coronal loops. We mainly focus on the time-dependent problem, which is appropriate to describe flare or CME induced kink oscillations. The analytical and numerical studies in slab and cylindrical loop geometries are reviewed. We discuss the results from very simple one-dimensional models to more realistic (but still simple) loop configurations. We emphasise how the results of the initial value problem complement the eigenmode calculations. The possible damping mechanisms of the…
The subject of this study is oscillations in the lower atmosphere in coronal-hole regions, where the conditions are favorable for propagation between the atmospheric layers. Based on spectroscopic observations in photospheric and chromospheric lines, we analysed the features of the oscillations that show signs of propagation between layers of the solar atmosphere. Using the cross-spectrum wavelet algorithm, we found that both chromospheric and photospheric signals under coronal holes share a range of significant oscillations of periods around five minutes, while the signals outside of coronal …
We developed an automated procedure for the identification of transient brightenings in images from the X-ray telescope on-board Hinode taken with an Al Poly filter in the equatorial coronal holes, polar coronal holes, and the quiet Sun with and without transient coronal holes. We found that in comparison to the quiet Sun, the boundaries of coronal holes are abundant with brightening events including areas inside the coronal holes where closed magnetic field structures are present. The visual analysis of these brightenings revealed that around 70% of them in equatorial, polar and transient cor…
Solar jets are fast-moving, elongated brightenings related to ejections seen in both images and spectra on all scales from barely visible chromospheric jets to coronal jets extending up to a few solar radii. The largest, most powerful jets are the source of type III radio bursts, energetic electrons and ions with greatly enhanced $^3$He and heavy element abundances. The frequent coronal jets from polar and equatorial coronal holes may contribute to the solar wind. The primary acceleration mechanism for all jets is believed to be release of magnetic stress via reconnection; however the energy b…
The P1/P2 period ratio of transversal loop oscillations is currently used for the diagnostics of longitudinal structuring of coronal loops as its deviation from 2 is intrinsically connected to the density scale-height along coronal loops and/or the sub-resolution structure of the magnetic field. The same technique can be applied not only to coronal structures, but also to other oscillating magnetic structures. The oscillations in magnetic structures are described by differential equations whose coefficients depend on the longitudinal structure of the plasma. Using a variational principle writt…
Kink oscillations of a coronal loop are observed and studied in detail because they provide a unique probe into the structure of coronal loops through MHD seismology and a potential test of coronal heating through the phase-mixing of Alfvén waves. In particular, recent observations show that standing oscillations of loops often involve also higher harmonics, beside the fundamental mode. The damping of these kink oscillations is explained by mode coupling with Alfvén waves. We investigate the consequences for wave-based coronal heating of higher harmonics and what coronal heating observational …
We investigate the evolutions of two prominences (P1,P2) and two bundles of coronal loops (L1,L2), observed with SDO/AIA near the east solar limb on 2012 September 22. It is found that there were large-amplitude oscillations in P1 and L1, but no detectable motions in P2 and L2. These transverse oscillations were triggered by a large-scale coronal wave, originating from a large flare in a remote active region behind the solar limb. By carefully comparing the locations and heights of these oscillating and non-oscillating structures, we conclude that the propagating height of the wave is between …
The analysis of quickly damped transverse oscillations of solar coronal loops using magneto-hydrodynamic seismology allow us to infer physical parameters that are difficult to measure otherwise. Under the assumption that such damped oscillations are due to the resonant conversion of global modes into Alfven oscillations of the tube surface, we carry out a global seismological analysis of a large set of coronal loops. A Bayesian hierarchical method is used to obtain distributions for coronal loop physical parameters by means of a global analysis of a large number of observations. The resulting …
Damped transverse oscillations of magnetic loops are routinely observed in the solar corona. This phenomenon is interpreted as standing kink magnetohydrodynamic waves, which are damped by resonant absorption owing to plasma inhomogeneity across the magnetic field. The periods and damping times of these oscillations can be used to probe the physical conditions of the coronal medium. Some observations suggest that interaction between neighboring oscillating loops in an active region may be important and can modify the properties of the oscillations compared to those of an isolated loop. Here we …
In this work, we report our multi-wavelength observations of the transverse oscillation of a large scale coronal loop with a length of 350 Mm. The oscillation was induced by a blowout coronal jet, which was related to a circular ribbon flare (CRF) in AR 12434 on 2015 October 16. We aim to determine the physical parameters in the coronal loop, including the Alfven speed and magnetic field strength. The jet induced kink oscillation was observed in extreme-ultraviolet (EUV) wavelengths by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). Line of sight magnetogr…
Aims. We construct a new analytical model of a solar coronal loop that is embedded in a gravitationally stratified and magnetically confined atmosphere. On the basis of this analytical model, we devise a numerical model of solar coronal loops. We adopt it to perform the numerical simulations of its vertical kink oscillations excited by an external driver. Methods. Our model of the solar atmosphere is constructed by adopting a realistic temperature distribution and specifying the curved magnetic field lines that constitute a coronal loop. This loop is described by 2D, ideal magnetohydro- dynami…
Coronal loops exist ubiquitously in the solar atmosphere. These loops puzzle astronomers over half a century. Solar magneto-seismology (SMS) provides a unique way to constrain the physical parameters of coronal loops. Here, we study the evolution of oscillations of a coronal loop observed by the Atmospheric Imaging Assembly (AIA). We measure geometric and physical parameters of the loop oscillations. In particular, we find that the mean period of the oscillations increased from 1048 to 1264 s during three oscillatory cycles. We employ the differential emission measure method and apply the tool…
The effects of both elliptical shape and stage of emergence of the coronal loop on the resonant absorption of standing kink oscillations are studied. To do so, a typical coronal loop is modeled as a zero-beta longitudinally stratified cylindrical magnetic flux tube. We developed the connection formulae for the resonant absorption of standing transversal oscillations of a coronal loop with an elliptical shape, at various stages of its emergence. Using the connection formulae, the dispersion relation is derived and solved numerically to obtain the frequencies and damping rates of the fundamental…
To investigate the excitation of kink oscillations in coronal loops and filaments, a C3.4 circular-ribbon flare (CRF) associated with a blowout jet in active region 12434 on 2015 October 16 is analyzed. The flare excited small-amplitude kink oscillation of a remote coronal loop. The oscillation lasted for $\ge$4 cycles without significant damping. The amplitude and period are 0.3$\pm$0.1 Mm and 207$\pm$12 s. Interestingly, the flare also excited transverse oscillation of a remote filament. The oscillation lasted for $\sim$3.5 cycles with decaying amplitudes. The initial amplitude is 1.7$-$2.2 …
Many phenomena seen in solar atmosphere are connected with underphotospheric processes. MHD oscillation and other dynamical processes observed in quit sun objects are, for example, these phenomena. In our research we use Stereo Behind EUV(171Åand 304Å) observations to study dynamical processes in quiet Sun regions. We found an eruption event in a coronal bright point on the border of a small coronal hole close to the center of the Solar disk. Several oscillating loops became visible inside of the hole after the eruption. We suppose that these loops oscillation were induced by the eruption proc…
We analyse multiwavelength observations of an M2.9/1N flare that occurred in AR NOAA 11112 on 16 October 2010. AIA 211 Å EUV images reveal the presence of a faster coronal wave (decelerating from ~1390 to ~830 km/s) propagating ahead of a slower wave (decelerating from ~416 to ~166 km/s) towards the western limb. The dynamic radio spectrum from Sagamore Hill radio telescope shows the presence of metric type II radio burst, which reveals the presence of a coronal shock wave (speed~800 km/s). The speed of the faster coronal wave derived from AIA 211 Å images is found to be comparable to the coro…
The Effect of Gravitational Stratification on Kink Oscillations in Curved Coronal Loops
Institute of Frontier and Interdisciplinary Science, Shandong University（山东大学前沿交叉科学研究中心）；Shandong Key Laboratory of Space Environment and Exploration Technology, Institute of Space Sciences, Shandong University（山东大学空间科学学院）
We present the first Hinode/EIS observations of 5 min quasi-periodic oscillations detected in a transition-region line (He II) and five coronal lines (Fe X, Fe XII, Fe XIII, Fe XIV, and Fe XV) at the footpoint of a coronal loop. The oscillations exist throughout the whole observation, characterized by a series of wave packets with nearly constant period, typically persisting for 4-6 cycles with a lifetime of 20-30 min. There is an approximate in-phase relation between Doppler shift and intensity oscillations. This provides evidence for slow magnetoacoustic waves propagating upwards from the tr…
We study non-axisymmetric oscillations of a straight magnetic tube with an elliptic cross-section and density varying along the tube. The governing equations for kink and fluting modes in the thin tube approximation are derived. We found that there are two kink modes, polarised along the large and small axes of the elliptic cross-section. We have shown that the ratio of frequencies of the first overtone and fundamental harmonic is the same for both kink modes and independent of the ratio of the ellipse axes. On the basis of this result we concluded that the estimates of the atmospheric scale h…
Recent observational and theoretical studies indicate that the damping of solar coronal loop oscillations depends on the oscillation amplitude. We consider two mechanisms, linear resonant absorption and a nonlinear damping model. We confront theoretical predictions from these models with observed data in the plane of observables defined by the damping ratio and the oscillation amplitude. The structure of the Bayesian evidence in this plane displays a clear separation between the regions where each model is more plausible relative to the other. There is qualitative agreement between the regions…
Decayless kink oscillations of solar coronal loops (or decayless oscillations for short) have attracted great attention since their discovery. Coronal bright points (CBPs) are mini-active regions and consist of loops with a small size. However, decayless oscillations in CBPs have not been widely reported. In this study, we identified this kind of oscillations in some CBPs using 171 Å\, images taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). After using the motion magnification algorithm to increase oscillation amplitudes, we made time-distance maps …
Slow magnetoacoustic oscillations in stellar coronal loops with gravitational stratification are analyzed with a numerical solution of the boundary-value problem for eigenvalues and eigen functions. In this study, we only focus on the resonant periods. The effects of the gravitational stratification, star mass, loop temperature, and loop length on the properties of slow magnetoacoustic oscillations are investigated. It is shown that the discrepancy between stratified and non-stratified loops is higher in density perturbations than velocity perturbations. When the star has larger mass, higher c…
Recent observations have revealed the ubiquitous presence of magnetohydrodynamic (MHD) waves and oscillations in the solar corona. The aim of this review is to present recent progress in the observational study of four types of wave (or oscillation) phenomena mainly occurring in active region coronal loops, including (i) flare-induced slow mode oscillations, (ii) fast kink mode oscillations, (iii) propagating slow magnetoacoustic waves, and (iv) ubiquitous propagating kink (Alfvenic) waves. This review not only comprehensively outlines various aspects of these waves and coronal seismology, but…
Decayless kink oscillations of solar coronal loops are studied in terms of a low-dimensional model based on a randomly driven Rayleigh oscillator with coefficients experiencing random fluctuations. The model considers kink oscillations as natural modes of coronal loops, decaying by linear resonant absorption. The damping is counteracted by random motions of the loop footpoints and the interaction of the loop with external quasi-steady flows with random fluctuations. In other words, the model combines the self-oscillatory and randomly driven mechanisms for the decayless behaviour. The random si…
Coronal holes are the dark patches in the solar corona associated with relatively cool, less dense plasma and unipolar fields. The fast component of the solar wind emanates from these regions. Several observations reveal the presence of magnetohydrodynamic (MHD) waves in coronal holes which are believed to play a key role in the acceleration of fast solar wind. The recent advent of high-resolution instruments had brought us many new insights on the properties of MHD waves in coronal holes which are reviewed in this article. The advances made in the identification of compressive slow MHD waves …
Determining the Polarisation of a Coronal Standing Kink Oscillation Using Spectral Imaging Techniques with the Coronal Multi-channel Polarimeter (CoMP)
The collective transverse coronal loop oscillations seem to be detected in the observational studies. In this regard, Luna et al. (2009, ApJ, 692, 1582) modeled the collective kinklike normal modes of several cylindrical loops system using the T-matrix theory. This paper investigates the effects of longitudinal density stratification along the loop axis, on the collective kinklike modes of system of coronal loops. The coronal loops system is modeled as cylinders of parallel flux tubes, with two ends of each loop at the dense photosphere. The flux tubes are considered as uniform magnetic fields…
The relatively large-amplitude decaying regime of transverse oscillations of coronal loops has been known for two decades and interpreted in terms of MHD kink modes of cylindrical plasma waveguides. Recent observational analysis has revealed the so-called decay-less small-amplitude oscillations, with a multi-harmonic structure being detected. Several models have been proposed to explain them. In particular, decay-less oscillations have been described in terms of standing kink waves driven with continuous monoperiodic motions of loop footpoints, in terms of a simple oscillator model of forced o…
Solar coronal loops represent the variety of fast, intermediate, and slow normal mode oscillations. In this study, the transverse oscillations of the loops with a few-minutes period and also with damping caused by the resonant absorption were analyzed using extreme ultraviolet (EUV) images of the Sun. We employed the 171 $Å$ data recorded by Solar Dynamic Observatory (SDO)/Atmospheric Imaging Assembly (AIA) to analyze the parameters of coronal loop oscillations such as period, damping time, loop length, and loop width. For the loop observed on 11 October 2013, the period and the damping of thi…
We aim to study the influence of radiative cooling on the standing kink oscillations of a coronal loop. Using the FLASH code, we solved the 3D ideal magnetohydrodynamic equations. Our model consists of a straight, density enhanced and gravitationally stratified magnetic flux tube. We perturbed the system initially, leading to a transverse oscillation of the structure, and followed its evolution for a number of periods. A realistic radiative cooling is implemented. Results are compared to available analytical theory. We find that in the linear regime (i.e. low amplitude perturbation and slow co…
Context. Transverse oscillations of coronal structures are currently intensively studied to explore the associated magnetohydrodynamic wave physics and perform seismology of the local medium. Aims. We make a first attempt to measure the thermodynamic evolution of a sample of coronal loops that undergo decaying kink oscillations in response to an eruption in the corresponding active region. Methods. Using data from the six coronal wavelengths of SDO/AIA, we performed a differential emission measure (DEM) analysis of 15 coronal loops before, during, and after the eruption and oscillation. Result…
We present measurements of periodicity for transverse loop oscillations during the periods of activity of two remote and separated (both temporally and spatially) flares. The oscillations are observed in the same location more than 100 Mm away from the visible footpoints of the loops. Evidence for several possible excitation sources is presented. After close examination, we find that the eruptions during the flaring activities play an important role in triggering the oscillations. We investigate periodicities using time-distance, Fast Fourier Transform, and Wavelet techniques. Despite differen…
Evidence of flare induced, large-amplitude, decay-less transverse oscillations is presented. A system of multi-thermal coronal loops as observed with the Atmospheric Imaging Assembly (AIA), exhibit decay-less transverse oscillations after a flare erupts nearby one of the loop footpoints. Measured oscillation periods lie between 4.2 min and 6.9 min wherein the displacement amplitudes range from 0.17 Mm to 1.16 Mm. A motion-magnification technique is employed to detect the pre-flare decay-less oscillations. These oscillations have similar periods (between 3.7 min and 5.0 min) like the previous o…
In this Letter, we perform a detailed analysis of the M5.5-class eruptive flare occurring in active region 12929 on 2022 January 20. The eruption of a hot channel generates a fast coronal mass ejection (CME) and a dome-shaped extreme-ultraviolet (EUV) wave at speeds of 740$-$860 km s$^{-1}$. The CME is associated with a type II radio burst, implying that the EUV wave is a fast-mode shock wave. During the impulsive phase, the flare shows quasi-periodic pulsations (QPPs) in EUV, hard X-ray, and radio wavelengths. The periods of QPPs range from 18 s to 113 s, indicating that flare energy is relea…
