Resonant absorption is considered as a crucial mechanism for the damping of the coronal loop oscillations and plasma heating. We study resonant absorption of the coronal loop kink oscillations excited by such external drivers as flares on the assumption that there is an intermediate shear flow region surrounding the loop. We find that for long coronal loops resonant absorption can be highly enhanced or reduced depending sensitively on the magnitude and direction of the flow and the spatial extent of the flow region when the transitional layer is thin. For short coronal loops, high flow speed and thick transitional layer are needed to have a substantial resonant absorption. We provide a potential picture to explain the results where the external Alfvén speed and phase speed of the wave are important parameters. These results imply that the transport of the external wave energy into the loop is significantly changed by the shear flow region, which may cause the selective excitation of the coronal loop oscillations.
There is ample evidence of twisted magnetic structures in the solar corona. This motivates us to consider the magnetic twist as the cause of Alfven frequency continuum in the coronal loops, which can support the resonant absorption as a rapid damping mechanism for the observed coronal kink magnetohydrodynamic (MHD) oscillations. We model a coronal loop with a straight cylindrical magnetic flux tube which has constant but different densities in the interior and exterior regions. The magnetic field is assumed to be constant and aligned with the cylinder axis everywhere except a thin layer near t…
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…
Kink magnetohydrodynamic (MHD) waves are frequently observed in various magnetic structures of the solar atmosphere. They may contribute significantly to coronal heating and could be used as a tool to diagnose the solar plasma. In this study, we synthesise the \ion{Fe}{9} $\lambda171.073$ emission of a coronal loop supporting a standing kink MHD mode. The kink MHD wave solution of a plasma cylinder is mapped into a semi-torus structure to simulate a curved coronal loop. We decompose the solution into a quasi-rigid kink motion and a quadrupole term, which dominate the plasma inside and outside …
Highly twisted magnetic flux ropes, with finite length, are subject to kink instabilities, and could lead to a number of eruptive phenomena in the solar atmosphere, including flares, coronal mass ejections (CMEs) and coronal jets. The kink instability threshold, which is the maximum twist a kink-stable magnetic flux rope could contain, has been widely studied in analytical models and numerical simulations, but still needs to be examined by observations. In this article, we will study twists released by 30 off-limb rotational solar coronal jets, and compare the observational findings with theor…
Using full three-dimensional magnetohydrodynamic numerical simulations, we study the effects of magnetic field sigmoidity or helicity on the properties of the fundamental kink oscillation of solar coronal loops. Our model consists of a single denser coronal loop, embedded in a plasma with dipolar force-free magnetic field with a constant alpha-parameter. For the loop with no sigmoidity, we find that the numerically determined oscillation period of the fundamental kink mode matches the theoretical period calculated using WKB theory. In contrast, with increasing sigmoidity of the loop, the actua…
Srivastava et al. (2010) have observed a highly twisted coronal loop, which was anchored in AR10960 during the period 04:43 UT-04:52 UT on 4 June 2007. The loop length and radius are approximately 80 Mm and 4 Mm, with a twist of 11.5 $π$. These observations are used as initial conditions in a three dimensional nonlinear magnetohydrodynamic simulation with parallel thermal conduction included. The initial unstable equilibrium evolves into the kink instability, from which synthetic observables are generated for various high-temperature filters of SDO/AIA. These observables include temporal and s…
We numerically follow the response of density-enhanced slabs to impulsive, localized, transverse velocity perturbations by working in the framework of ideal magnetohydrodynamics (MHD). Both linear and nonlinear regimes are addressed. Kink wave trains are seen to develop along the examined slabs, sharing the characteristics that more oscillatory patterns emerge with time and that the apparent wavelength increases with distance at a given instant. Two features nonetheless arise due to nonlinearity, one being a density cavity close to the exciter and the other being the appearance of shocks both …
Using MHD seismology by observed kink waves, the magnetic field profile of a coronal streamer has been investigated. STEREO-B/EUVI temporal image data on 7 March 2012 shows an evolution of two consecutive EUV waves that interact with the footpoint of a coronal streamer evident in the co-spatial and co-temporal STEREO-B/COR-I observations. The evolution of EUV waves is clearly evident in STEREO-B/EUVI, and its energy exchange with coronal streamer generates kink oscillations. We estimate the phase velocities of the kink wave perturbations by tracking it at different heights of the coronal strea…
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…
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…
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）
Determining the Polarisation of a Coronal Standing Kink Oscillation Using Spectral Imaging Techniques with the Coronal Multi-channel Polarimeter (CoMP)
We present the observations of an extreme ultraviolet (EUV) wave, a quasi-periodic fast-propagating (QFP) magnetosonic wave, and a kink wave that were simultaneously associated with the impingement of a coronal jet upon a group of coronal loops. After the interaction, the coronal loop showed obvious kink oscillation that had a period of about 428 seconds. In the meantime, a large-scale EUV wave and a QFP wave are observed on the west of the interaction position. It is interesting that the QFP wave showed refraction effect during its passing through two strong magnetic regions. The angular exte…
We review and discuss insights on ideal magnetohydrodynamic (MHD) instabilities that can play a role in destabilizing solar coronal flux rope structures. For single flux ropes, failed or actual eruptions may result from internal or external kink evolutions, or from torus unstable configurations. We highlight recent findings from 3D magnetic field reconstructions and simulations where kink and torus instabilities play a prominent role. For interacting current systems, we critically discuss different routes to coronal dynamics and global eruptions, due to current channel coalescence or to tilt-k…
Propagating transverse waves are thought to be a key transporter of Poynting flux throughout the Sun's atmosphere. Recent studies have shown that these transverse motions, interpreted as the magnetohydrodynamic kink mode, are prevalent throughout the corona. The associated energy estimates suggest the waves carry enough energy to meet the demands of the coronal radiative losses in the quiescent Sun. However, it is still unclear how the waves deposit their energy into the coronal plasma. We present the results from a large-scale study of propagating kink waves in the quiescent corona using data…
Key Laboratory of Solar Activity and Space Weather, School of Aerospace, Harbin Institute of Technology, Shenzhen（哈尔滨工业大学深圳航天学院太阳活动与空间天气重点实验室）；Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick（华威大学物理部聚变、太空与天体物理中心）；G-LAMP NEXUS Institute/School of Space Research, Kyung Hee University（庆熙大学太空研究学院 G-LAMP NEXUS 研究所）；Centro de Investigacion en Astronomía, Universidad Bernardo O’Higgins（贝尔纳多·奥希金斯大学天文学研究中心）；Institute of Solar-Terrestrial Physics SB RAS（俄罗斯科学院西伯利亚分院太阳-地球物理研究所）
There are observational evidences for the existence of twisted magnetic field in the solar corona. This inspires us to investigate the effect of a twisted magnetic field on the evolution of magnetohydrodynamic (MHD) kink waves in coronal loops. To this aim, we solve the incompressible linearized MHD equations in a magnetically twisted nonuniform coronal flux tube in the limit of long wavelengths. Our results show that a twisted magnetic field can enhance or diminish the rate of phase-mixing of the Alfvén continuum modes and the decay rate of the global kink oscillation depending on the twist m…
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…
Magnetohydrodynamic waves are believed to play a significant role in coronal heating, and could be used for remote diagnostics of solar plasma. Both the heating and diagnostic applications rely on a correct inversion (or backward modelling) of the observables into the thermal and magnetic structures of the plasma. However, owing to the limited availability of observables, this is an ill-posed issue. Forward Modelling is to establish a plausible mapping of plasma structuring into observables. In this study, we set up forward models of standing kink modes in coronal loops and simulate optically …
This paper separately evaluates the effects of inclination and asymmetry of solar coronal loops on the resonant absorption of kink magnetohydrodynamic (MHD) oscillations. We modelled a typical coronal loop by a straight and axisymmetric cylindrical magnetic flux tube filled with cold plasma. We solved the dispersion relation numerically for different values of the longitudinal mass density stratification. We show that, in inclined and asymmetric loops, the frequencies and their corresponding damping rates of the fundamental and first-overtone modes of kink oscillations are smaller in compariso…
The signatures of energy release and energy transport for a kink-unstable coronal flux rope are investigated via forward modelling. Synthetic intensity and Doppler maps are generated from a 3D numerical simulation. The CHIANTI database is used to compute intensities for three Hinode/EIS emission lines that cover the thermal range of the loop. The intensities and Doppler velocities at simulation resolution are spatially degraded to the Hinode/EIS pixel size (1\arcsec), convolved using a Gaussian point-spread function (3\arcsec), and exposed for a characteristic time of 50 seconds. The synthetic…
Kink oscillations of coronal loops, i.e., standing kink waves, is one of the most studied dynamic phenomena in the solar corona. The oscillations are excited by impulsive energy releases, such as low coronal eruptions. Typical periods of the oscillations are from a few to several minutes, and are found to increase linearly with the increase in the major radius of the oscillating loops. It clearly demonstrates that kink oscillations are natural modes of the loops, and can be described as standing fast magnetoacoustic waves with the wavelength determined by the length of the loop. Kink oscillati…
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…
It has been shown that resonant absorption is a robust physical mechanism to explain the observed damping of magnetohydrodynamic (MHD) kink waves in the solar atmosphere due to naturally occurring plasma inhomogeneity in the direction transverse to the direction of the magnetic field. Theoretical studies of this damping mechanism were greatly inspired by the first observations of post-flare standing kink modes in coronal loops using the Transition Region And Coronal Explorer (TRACE). More recently, these studies have been extended to explain the attenuation of propagating coronal kink waves ob…
There are observational evidences for the existence of twisted magnetic field in the solar corona. Here, we have investigated resonant damping of the magnetohydrodynamic (MHD) kink waves in magnetic flux tubes. A realistic model of the tube with continuous magnetic twist and radially inhomogeneous density profile has been considered. We have obtained the dispersion relation of the kink wave using the solution to the linear MHD equations outside the density inhomogeneity and the appropriate connection formula to the solutions across the thin transitional boundary layer. The dependence of the os…
The Coronal Multi-channel Polarimeter (CoMP) has opened up exciting opportunities to probe transverse MHD waves in the Sun's corona. The archive of CoMP data is utilised to generate a catalogue of quiescent coronal loops that can be used for studying propagating kink waves. The catalogue contains 120 loops observed between 2012-2014. This catalogue is further used to undertake a statistical study of propagating kink waves in the quiet regions of the solar corona, investigating phase speeds, loop lengths, footpoint power ratio and equilibrium parameter values. The statistical study enables us t…
It is known from numerical simulations that thermal conduction along magnetic field lines plays an important role in the evolution of the kink instability in coronal loops. This study presents the observational signatures of the kink instability in long coronal loops when parallel thermal conduction is included. The 3D nonlinear magnetohydrodynamic equations are solved numerically to simulate the evolution of a coronal loop that is initially in an unstable equilibrium. The loop has length 80 Mm, width 8 Mm and an initial maximum twist of Phi = 11.5 pi, where Phi is a function of the radius. Th…
Ever since their detection two decades ago, standing kink oscillations in coronal loops have been extensively studied both observationally and theoretically. Almost all driven coronal loop oscillations (e.g., by flares) are observed to damp through time often with Gaussian or exponential profiles. Intriguingly, however, it has been shown theoretically that the amplitudes of some oscillations could be modified from Gaussian or exponential profiles if cooling is present in the coronal loop systems. Indeed, in some cases the oscillation amplitude can even increase through time. In this article, w…
A detailed analysis of a coronal loop oscillation event is presented, using data from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) for the first time. The loop oscillation event occurred on 2010 Oct 16, 19:05-19:35 UT, was triggered by an M2.9 GOES-class flare, located inside a highly inclined cone of a narrow-angle CME. This oscillation event had a number of unusual features: (i) Excitation of kink-mode oscillations in vertical polarization (in the loop plane); (ii) Coupled cross-sectional and density oscillations with identical periods; (iii) no detecta…
Impulsively excited wave trains are of considerable interest in solar coronal seismology. To our knowledge, however, it remains to examine the three-dimensional (3D) dispersive propagation of impulsive kink waves in straight, field-aligned, symmetric, low-beta, slab equilibria that are structured only in one transverse direction. We offer a study here, starting with an analysis of linear oblique kink modes from an eigenvalue problem perspective. Two features are numerically found for continuous and step structuring alike, one being that the group and phase velocities may lie on opposite sides …
We examine resonantly damped kink modes in straight coronal slabs, paying special attention to the effects of the formulation for the transverse density distribution ("profile"). We work in the framework of pressure-less, gravity-free, resistive magnetohydrodynamics, and we adopt the dissipative-eigenmode perspective. The density profile is restricted to be one-dimensional, but nonetheless allowed to take a generic form characterized by a continuous transition layer connecting a uniform interior to a uniform exterior. A dispersion relation (DR) is derived in the thin-boundary limit, yielding a…
Coronal waves are an important aspect of the dynamics of the plasma in the corona. Wavefront dislocations are topological features of most waves in nature and also of magnetohydrodynamic waves. Are there dislocations in coronal waves? The finding and explanation of dislocations may shed light on the nature and characteristics of the propagating waves, their interaction in the corona and in general on the plasma dynamics. We positively identify dislocations in coronal waves observed by the Coronal Multi-channel Polarimeter (CoMP) as singularities in the Doppler shifts of emission coronal lines.…
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…
In this Letter we establish clear evidence for the resonant absorption damping mechanism by analyzing observational data from the novel Coronal Multi-Channel Polarimeter (CoMP). This instrument has established that in the solar corona there are ubiquitous propagating low amplitude ($\approx$1 km s$^{-1}$) Alfvénic waves with a wide range of frequencies. Realistically interpreting these waves as the kink mode from magnetohydrodynamic (MHD) wave theory, they should exhibit a frequency dependent damping length due to resonant absorption, governed by the TGV relation showing that transversal plasm…
Coronal loop oscillations are common phenomena in the solar corona, which are often classified as decaying and decayless oscillations. Using the high-resolution observation measured by the Extreme Ultraviolet Imager (EUI) onboard the Solar Orbiter, we statistical investigate small-scale transverse oscillations with short periods (<200 s) of coronal loops in an active region, i.e., NOAA 12965. A total of 111 coronal loops are identified in EUI 174 A images, and they all reveal transverse oscillations without any significant decaying, regarding as decayless oscillations. Oscillatory periods are …
We report the observation of the first two harmonics of the horizontally polarized kink waves excited in a coronal loop system lying at south-east of AR 11719 on 2013 April 11. The detected periods of the fundamental mode ($P_1$), its first overtone ($P_2$) in the northern half, and that in the southern one are $530.2 \pm 13.3$, $300.4 \pm 27.7$, and $334.7 \pm 22.1$ s, respectively. The periods of the first overtone in the two halves are the same considering uncertainties in the measurement. We estimate the average electron density, temperature, and length of the loop system as $(5.1 \pm 0.8)…
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 …
Solar flares are associated with intense soft X-ray emission generated by the hot flaring plasma. Kink unstable twisted flux-ropes provide a source of magnetic energy which can be released impulsively and account for the flare plasma heating. We compute the temporal evolution of the thermal X-ray emission in kink-unstable coronal loops using MHD simulations and discuss the results of with respect to solar flare observations. The model consists of a highly twisted loop embedded in a region of uniform and untwisted coronal magnetic field. We let the kink instability develop, compute the evolutio…
There are ubiquitous flows observed in the solar atmosphere of sub-Alfvénic speeds, however after flaring and coronal mass ejection events flows can become Alfvénic. In this Letter, we derive an expression for the standing kink mode frequency due to siphon flow in coronal loops, valid for both low and high speed regimes. It is found that siphon flow introduces a linear spatially dependent phase shift along coronal loops and asymmetric eigenfunctions. We demonstrate how this theory can be used to determine the kink and flow speed of oscillating coronal loops with reference to an observational c…
The cross sections of solar coronal loops are suggested to be rarely circular. We examine linear kink oscillations in straight, density-enhanced, magnetic cylinders with elliptical cross-sections by solving the three-dimensional magnetohydrodynamic equations from an initial-value-problem perspective. Motivated by relevant eigen-mode analyses, we distinguish between two independent polarizations, one along the major axis (the M-modes) and the other along the minor one (the m-modes). We find that, as happens for coronal loops with circular cross-sections, the apparent damping of the transverse d…
Decayless kink oscillations of an ensemble of loops are captured simultaneously by the High Resolution Imager (HRI) of the Extreme Ultraviolet Imager (EUI) and the Atmospheric Imaging Assembly (AIA) from 22:58 UT on 5 November to 00:27 UT on 6 November 2021. Oscillations are analysed by processing image sequences taken by the two instruments with a motion magnification technique. The analysed loops are around 51 Mm in length, and oscillate with short periods of 1-3 min (1.6 min in average) and displacement amplitudes of 27-83 km. The signals recorded by AIA are delayed by 66 s as compared to H…
It has been proposed that the million degree temperature of the corona is due to the combined effect of barely-detectable energy releases, so called nanoflares, that occur throughout the solar atmosphere. Alas, the nanoflare density and brightness implied by this hypothesis means that conclusive verification is beyond present observational abilities. Nevertheless, we investigate the plausibility of the nanoflare hypothesis by constructing a magnetohydrodynamic (MHD) model that can derive the energy of a nanoflare from the nature of an ideal kink instability. The set of energy-releasing instabi…
