Propagating Kink Waves Research Articles

Propagating kink waves in an open coronal magnetic flux tube with gravitational stratification: Magnetohydrodynamic simulation and forward modelling

Context. In coronal open-field regions, such as coronal holes, there are many transverse waves propagating along magnetic flux tubes, which are generally interpreted as kink waves. Previous studies have highlighted their potential role in coronal heating, solar wind acceleration, and seismological diagnostics of various physical parameters. Aims. This study aims to investigate propagating kink waves, considering both vertical and horizontal density inhomogeneity, using 3D magnetohydrodynamic (MHD) simulations. Methods. We established a 3D MHD model of a gravitationally stratified open flux tube, incorporating a velocity driver at the lower boundary to excite propagating kink waves. Forward modelling was conducted to synthesise observational signatures of the Fe IX 17.1 nm line. Results. Resonant absorption and density stratification both affect the wave amplitude. When diagnosing the relative density profile with velocity amplitude, resonant damping needs to be properly considered to avoid a possible underestimation. In addition, unlike standing modes, propagating waves are believed to be Kelvin-Helmholtz stable. In the presence of vertical stratification, however, the phase mixing of transverse motions around the tube boundary can still induce small-scale structures, partially dissipating wave energy and leading to a temperature increase, especially at higher altitudes. Moreover, we conducted forward modeling to synthesise observational signatures, which revealed the promising potential of future coronal imaging spectrometers such as MUSE in resolving these wave-induced signatures. Also, the synthesised intensity signals exhibit apparent periodic variations, offering a potential method for indirectly observing propagating kink waves with current extreme ultraviolet imagers.

Kink Waves in Twisted and Expanding Magnetic Tubes

We study kink and fluting waves in expanding and twisted magnetic flux tubes. We use the thin-tube and zero-beta plasma approximations. The equilibrium magnetic field is force free with a constant proportionality coefficient between the electrical current and the magnetic field. We derive the equation governing the kink and fluting waves in a tube. Using this equation we study the propagation of kink waves in a particular case of a magnetic tube homogeneous in the axial direction. We show that while there is only one propagating kink wave with the phase speed equal to the kink speed in an untwisted tube, in a twisted tube there are two wave modes, accelerated and decelerated. The phase speed of the accelerated wave exceeds the kink speed, while the phase speed of the decelerated wave is less than the kink speed. We also show that the standing modes are defined by the same eigenvalue problem as that in the case of an untwisted tube. Hence, the frequencies of the standing-wave modes are not affected by the twist. This implies that the seismological results based on the observation of the standing-wave mode frequencies remain valid when the twist is taken into account. The only effect of twist is the variation of the direction of polarisation of the coronal magnetic-loop displacement along the loop. As a result, an apparent node can be detected near the loop apex if only one component of the loop displacement is observed. This can lead to an incorrect conclusion that the observed coronal loop kink oscillation was the first overtone, while in fact it was the fundamental mode.

Coronal Seismology Using Damping of Propagating Kink Waves

We consider the use of propagating kink waves, such as those observed by the Coronal Multi-channel Polarimeter, as a diagnostic technique. The transverse structuring of the plasma may be inferred by the frequency-dependent wave damping, which is attributed to resonant absorption. We include the effect of reflection of waves at the loop footpoints, which leads to the asymmetry parameter, describing the ratio of driven wave power at the footpoints becoming weakly constrained. The classical model of resonant absorption based on an exponential damping profile significantly overestimates the damping rate in coronal loops with low density contrast ratios. The use of the exponential profile in an analysis of observations therefore leads to underestimates for the density contrast ratio and associated parameters such as the heating rate following phase mixing.

Weak Damping of Propagating MHD Kink Waves in the Quiescent Corona

Abstract 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 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 from the Coronal Multi-channel Polarimeter (CoMP). The analysis reveals that the kink waves appear to be weakly damped, which would imply low rates of energy transfer from the large-scale transverse motions to smaller scales via either uniturbulence or resonant absorption. This raises questions about how the observed kink modes would deposit their energy into the coronal plasma. Moreover, these observations, combined with the results of Monte Carlo simulations, lead us to infer that the solar corona displays a spectrum of density ratios, with a smaller density ratio (relative to the ambient corona) in quiescent coronal loops and a higher density ratio in active-region coronal loops.

A Statistical Study of Propagating MHD Kink Waves in the Quiescent Corona

Abstract 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 utilized to generate a catalog of quiescent coronal loops that can be used for studying propagating kink waves. The catalog contains 120 loops observed between 2012 and 2014. This catalog 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 (a measure of wave power entering the corona through each footpoint of a loop) and equilibrium parameter (which provides a measure of the change in wave amplitude) values. The statistical study enables us to establish the presence of a relationship between the rate of damping and the length of the coronal loop, with longer coronal loops displaying weaker wave damping. We suggest the reason for this behavior is related to a decreasing average density contrast between the loop and ambient plasma as loop length increases. The catalog presented here will provide the community with the foundation for the further study of propagating kink waves in the quiet solar corona.

A persistent quiet-Sun small-scale tornado

Context. Vortex flows can foster a variety of wave modes. A recent oscillatory analysis of a persistent 1.7 h vortex flow with a significant substructure has suggested the existence of various types of waves within it. Aims. We investigate the nature and characteristics of waves within this quiet-Sun vortex flow, over the course of an uninterrupted 48-min observing time interval, in order to better understand its physics and dynamics. Methods. We used a cross-wavelet spectral analysis between pairs of Hα and Ca II 8542 Å intensity time series at different wavelengths and, hence, atmospheric heights, acquired with the CRisp Imaging SpectroPolarimeter at the Swedish Solar Telescope, as well as the derived Hα Doppler velocity and full width at half maximum time series. We constructed halftone frequency-phase difference plots and investigated the existence and propagation characteristics of different wave modes. Results. Our analysis suggests the existence of Alfvénic type waves within the vortex flow that propagate upwards with phase speeds of ∼20–30 km s−1. The dominant wave mode seems to be the fast kink wave mode, however, our analysis also suggests the existence of localised Alfvénic torsional waves, which are related to the dynamics of individual chromospheric swirls that characterise the substructure of the vortex flow. The Hα V–I phase difference analysis seems to imply the existence of a standing wave pattern that is possibly arising from the interference of upwards propagating kink waves with downwards propagating ones that are reflected at the transition region or the corona. Moreover, the results provide further evidence that the central chromospheric swirl drives the dynamics of the vortex flow. Conclusions. This is the first exhaustive phase difference analysis within a vortex flow that explores the nature and dynamics of different wave modes within it. The question, however, of whether, and how, the dissipation of the derived wave modes occurs remains open, and given that such structures are ubiquitous on the solar surface, it’s also important to investigate whether they might ultimately play a significant role in the energy budget of the upper layers of the solar atmosphere.

Resonant damping and instability of propagating kink waves in flowing and twisted magnetic flux tubes

ABSTRACT We study the propagation and stability of kink waves in a twisted magnetic tube with the flow. The flow velocity is assumed to be parallel to the magnetic field, and the magnetic field lines are straight outside the tube. The density is constant inside and outside of the tube, and it monotonically decreases from its value inside the tube to that outside in the transitional or boundary layer. The flow speed and magnetic twist monotonically decrease in the transitional layer from their values inside the tube to zero outside. Using the thin tube and thin boundary layer (TTTB) approximation, we derived the dispersion equation determining the dependence of the wave frequency and decrement/increment on the wavenumber. When the kink wave frequency coincides with the local Alfvén frequency at a resonant surface inside the transitional layer, the kink wave is subjected to either resonant damping or resonant instability. We study the properties of kink waves in a particular unperturbed state where there is no flow and magnetic twist in the transitional layer. It is shown that in a tube with flow, the kink waves can propagate without damping for particular values of the flow speed. Kink waves propagating in the flow direction either damp or propagate without damping. Waves propagating in the opposite direction can either propagate without damping, or damp, or become unstable. The theoretical results are applied to the problem of excitation of kink waves in spicules and filaments in the solar atmosphere.

Oscillation of a Small Hα Surge in a Solar Polar Coronal Hole

Abstract Hα surges (i.e., cool/dense collimated plasma ejections) may act as a guide for a propagation of magnetohydrodynamic waves. We report a high-resolution observation of a surge observed with 1.6 m Goode Solar Telescope (GST) on 2009 August 26, from 18:20 UT to 18:45 UT. Characteristics of plasma motions in the surge are determined with the normalizing radial gradient filter and the Fourier motion filter. The shape of the surge is found to change from a “C” shape to an inverse “C” shape after a formation of a cusp, a signature of reconnection. There are apparent upflows seen above the cusp top and downflows below it. The upflows show rising and rotational motions in the right-hand direction, with the rotational speed decreasing with height. Near the cusp top, we find a transverse oscillation of the surge, with the period of ∼2 minutes. There is no change of the oscillation phase below the cusp top, but above the top a phase change is identified, giving a vertical phase speed about 86 km s−1. As the height increases, the initial amplitude of the oscillation increases, and the oscillation damping time decreases from 5.13 to 1.18 minutes. We conclude that the oscillation is a propagating kink wave that is possibly excited by the repetitive spontaneous magnetic reconnection.

Damping of Propagating Kink Waves in the Solar Corona

Abstract Alfvénic waves have gained renewed interest since the existence of ubiquitous propagating kink waves were discovered in the corona. It has long been suggested that Alfvénic waves play an important role in coronal heating and the acceleration of the solar wind. To this effect, it is imperative to understand the mechanisms that enable their energy to be transferred to the plasma. Mode conversion via resonant absorption is believed to be one of the main mechanisms for kink wave damping and it is considered to play a key role in the process of energy transfer. This study examines the damping of propagating kink waves in quiescent coronal loops using the Coronal Multi-channel Polarimeter. A coherence-based method is used to track the Doppler velocity signal of the waves, which enables us to investigate the spatial evolution of velocity perturbations. The power ratio of outward to inward propagating waves is used to estimate the associated damping lengths and quality factors. To enable accurate estimates of these quantities, we provide the first derivation of a likelihood function suitable for fitting models to the ratio of two power spectra obtained from discrete Fourier transforms. Maximum likelihood estimation is used to fit an exponential damping model to the observed variation in power ratio as a function of frequency. We confirm earlier indications that propagating kink waves are undergoing frequency-dependent damping. Additionally, we find that the rate of damping decreases, or equivalently the damping length increases, for longer coronal loops that reach higher in the corona.

Resonant Damping of Propagating Kink Waves in Non-stationary, Longitudinally Stratified, and Expanding Solar Waveguides

Propagating kink waves have been observed in many magnetic waveguides in the solar atmosphere, like coronal magnetic loops, spicules, and fine structures of prominences. There are also observational evidences that these waves are damped. At present resonant absorption is considered as the most likely candidate for explaining this damping. First the attenuation of propagating kink waves due to resonant absorption was studied using the simplest model with a straight magnetic tube and the density only varying in the radial direction. Later a more advanced model with the density also varying along the tube was used. It was shown that the variation of the wave amplitude along the tube is determined by the combined effect of resonant damping and the longitudinal density variation. In our article we extend the analysis of resonant damping of propagating kink waves to take into account the magnetic loop expansion. We also consider non-stationary magnetic tubes to model, for example, cooling coronal loops.

Spatial Damping of Kink MHD Waves in the Presence of Magnetic Twist and Plasma Flow

Abstract Propagating kink magnetohydrodynamic waves in magnetic flux tubes with incompressible plasma have been studied. The plasma has been assumed to flow along the magnetic field lines, and the magnetic field lines have been assumed to be twisted. Both the flow and the magnetic twist reduce the symmetry of the dispersion curves of the kink waves. The magnetic twist modifies the the properties of the forward and backward waves with positive and negative azimuthal wavenumbers, which are under Kelvin–Helmholtz instability due to plasma flow, in different manners. The effect of the magnetic twist on the spatial resonant damping of kink waves depends on the direction of the propagation and azimuthal wavenumber of the wave, and also on the direction of the plasma flow. Our conclusion is that the magnetic twist modifies the properties of the propagating kink waves depending on the wavenumbers of the wave and the direction of the plasma flow.

Propagating wave in active region-loops, located over the solar disk observed by the Interface Region Imaging Spectrograph

Aims. We aim to ascertain the physical parameters of a propagating wave over the solar disk detected by the Interface Region Imaging Spectrograph (IRIS). Methods. Using imaging data from the IRIS and the Solar Dynamic Observatory (SDO), we tracked bright spots to determine the parameters of a propagating transverse wave in active region (AR) loops triggered by activation of a filament. Deriving the Doppler velocity of Si IV line from spectral observations of IRIS, we have determined the rotating directions of active region loops which are relevant to the wave. Results. On 2015 December 19, a filament was located on the polarity inversion line of the NOAA AR 12470. The filament was activated and then caused a C1.1 two-ribbon flare. Between the flare ribbons, two rotation motions of a set of bright loops were observed to appear in turn with opposite directions. Following the end of the second rotation, a propagating wave and an associated transverse oscillation were detected in these bright loops. In 1400 Å channel, there was bright material flowing along the loops in a wave-like manner, with a period of ~128 s and a mean amplitude of ~880 km. For the transverse oscillation, we tracked a given loop and determine the transverse positions of the tracking loop in a limited longitudinal range. In both of 1400 Å and 171 Å channels, approximately four periods are distinguished during the transverse oscillation. The mean period of the oscillation is estimated as ~143 s and the displacement amplitude as between ~1370 km and ~690 km. We interpret these oscillations as a propagating kink wave and obtain its speed of ~1400 km s−1. Conclusions. Our observations reveal that a flare associated with filament activation could trigger a kink propagating wave in active region loops over the solar disk.

The Effect of a Twisted Magnetic Field on the Nature of Kink MHD Waves

We consider a pressureless plasma in a thin magnetic-flux tube with a twisted magnetic field. We study the effect of twisted magnetic field on the nature of propagating kink waves. To do this, the restoring forces of oscillations in the linear ideal magnetohydrodynamics (MHD) were obtained. In the presence of a twisted magnetic field, the ratio of the magnetic-tension force to the gradient of the magnetic pressure increases for the mode with negative azimuthal wave number, but it decreases for the mode with positive azimuthal wave number. For the kink mode with positive azimuthal mode number, the ratio of the forces is more affected by the twisted magnetic field in dense loops. For the kink mode with negative azimuthal mode number, the perturbed magnetic pressure is negligible under some conditions. The magnetic twist increases (diminishes) the damping of the kink waves with positive (negative) azimuthal mode number due to resonant absorption. Our conclusion is that introducing a twisted magnetic field breaks the symmetry between the nature of the kink waves with positive and negative azimuthal wave number, and the wave can be a purely Alfvenic wave in the entire loop.

Propagating kink waves in thin twisted magnetic tubes with continuous equilibrium magnetic field

In this paper, we study kink waves in twisted magnetic tubes. In the equilibrium state there is the electrical current with constant density inside the tube directed along the tube axis. This current creates the azimuthal magnetic field with the magnitude proportional to the distance from the tube axis inside the tube and inversely proportional to this distance outside the tube. We derive the dispersion equations for propagating waves and for unstable perturbations in the long wavelength approximation. We show that there are no solutions to the dispersion equation determining the frequencies of unstable perturbations, which implies that there are no unstable long kink modes. We study the dispersion equation for propagating waves both in the case when the plasma density is larger than that in the surrounding plasma as well as when it is smaller. In the first case we obtain that, depending on the wave number, the dispersion equation for propagating waves has either no solutions, or one solution, or two solutions. In the case when there is one solution, in the approximation of very weak twist, the wave mode propagates with the phase speed slightly larger than the kink speed. This wave mode is called the accelerated kink wave. In the case when there are two solutions to the dispersion equation, one of the two solutions gives the frequency of a quasi-mode that is subjected to the Alfven resonance outside the tube. The other solution gives the frequency of a true eigenmode of linear ideal MHD. In the approximation of very weak twist its phase speed is smaller than the kink speed. This mode is called the decelerated kink wave. In the case of rarefied tube, depending on the wave number, the dispersion equation has either one or three solutions. When there is only one solution, the mode frequency is very close to the Alfven frequency far from the tube, so the wave mode practically coincides with the Alfven wave. When there are three solutions, the largest frequency practically coincides with the Alfven frequency far from the tube. Two other solutions almost coincide. In all cases the wave modes existing in the case of rarefied tube are quasi-modes that are subjected to the Alfven resonance. A possible application of the obtained results to the solar atmospheric seismology is discussed.

Doppler-shift oscillations in the H i Lyαcoronal emission line: spectroscopic signature of propagating kink waves?

Doppler-shift oscillations in the H i Ly<i>α</i>coronal emission line: spectroscopic signature of propagating kink waves?

Quasi-periodic variations in Doppler velocities of Hα spicules

New series of CCD spectral observations of spicules were obtained using 53-cm Lyot coronagraph of Abastumani Astrophysical Observatory (Georgia) at 5500 km height above the solar limb on October 17, 2012 in Hα spectral line. The line-of-sight Doppler velocities of 34 spicules were measured with the cadence of 4.5 s and standard error equal to ±0.3 km/s. Life times of almost all measured spicules were 5–6 min (and longer), therefore they resemble the type I spicules. No short lived structures (similar to type II spicules) were identified during the time series neither inside nor outside the observed spicules. The Doppler velocity time series were processed using Lomb Periodogram Algorithm revealing 4 types of dominating period intervals centered around: 254 s, 136 s, 94 s and 65 s having confidence levels over 95 %. The oscillations with periods around 254 s can be caused by quasi-periodic rebound shocks after the propagation of photospheric pulses. The oscillations with periods around 136 s can be caused by the oscillation of spicules axis at the kink cut-off frequency in gravitationally stratified magnetic tubes. In this case, seismological estimations give the density scale height as 380–540 km for the kink wave speed of 70–100 km/s in spicules. Shorter period oscillations are probably caused by propagating kink waves in spicules.

Resonant Damping of Propagating Kink Waves in Time-Dependent Magnetic Flux Tube

We explore the notion of resonant absorption in a dynamic time-dependent magnetised plasma background. Very many works have investigated resonance in the Alfven and slow MHD continua under both ideal and dissipative MHD regimes. Jump conditions in static and steady systems have been found in previous works, connecting solutions at both sides of the resonant layer. Here, we derive the jump conditions in a temporally dependent, magnetised, inhomogeneous plasma background to leading order in the Wentzel–Kramers–Billouin (WKB) approximation. Next, we exploit the results found in Williamson and Erdelyi (Solar Phys.289, 899, 2014) to describe the evolution of the jump condition in the dynamic model considered. The jump across the resonant point is shown to increase exponentially in time. We determined the damping as a result of the resonance over the same time period and investigated the temporal evolution of the damping itself. We found that the damping coefficient, as a result of the evolution of the resonance, decreases as the density gradient across the transitional layer decreases. This has the consequence that in such time-dependent systems resonant absorption may not be as efficient as time progresses.

Observation of kink waves and their reconnection-like origin in solar spicules

We analyze the time series of Ca II H-line obtained from Hinode/SOT on the solar limb. We follow three cases of upwardly propagating kink waves along a spicule and inverted Y-shaped structures at the cusp of it. The time-distance analysis shows that the axis of spicule undergoes quasi-periodic transverse displacement at different heights from the photosphere. The mean period of transverse displacement is ~ 175 s and the mean amplitude is 1 arc\,sec. The oscillation periods are increasing linearly with height which may be counted as the signature that the spicule is working as a low pass filter and allows only the low frequencies to propagate towards higher heights. The oscillations amplitude is increasing with height due to decrease in density. The phase speeds are increasing until some heights and then decreasing which may be related to the small scale reconnection at the spicule basis. We conclude that transversal displacement of spicules axis can be related to the propagation of kink waves along them. Moreover, we observe signatures of small-scale magnetic reconnection at the cusp of spicules which may excite kink waves.

CONDITIONS FOR TRANSVERSE WAVES PROPAGATION ALONG THIN MAGNETIC FLUX TUBES ON THE SUN

The propagation of kink waves in the thin gravity stratified flux tubes with a generalized magnetic field distribution model is considered in cylindrical geometry. The new kink wave equations for both wave variables are obtained. It is shown that the inclusion of the radial component of an unperturbed tube magnetic field sufficiently transforms the conditions for the propagation of transverse waves. It is demonstrated that, for the models of isothermal and polytropic atmosphere in the tube and its environment, the propagation of kink waves along thin magnetic flux tubes is cutoff-free.

DETERMINATION OF TRANSVERSE DENSITY STRUCTURING FROM PROPAGATING MAGNETOHYDRODYNAMIC WAVES IN THE SOLAR ATMOSPHERE

We present a Bayesian seismology inversion technique for propagating magnetohydrodynamic (MHD) transverse waves observed in coronal waveguides. The technique uses theoretical predictions for the spatial damping of propagating kink waves in transversely inhomogeneous coronal waveguides. It combines wave amplitude damping length scales along the waveguide with theoretical results for resonantly damped propagating kink waves to infer the plasma density variation across the oscillating structures. Provided the spatial dependence of the velocity amplitude along the propagation direction is measured and the existence of two different damping regimes is identified, the technique would enable us to fully constrain the transverse density structuring, providing estimates for the density contrast and its transverse inhomogeneity length scale.