Transverse Kink Oscillations Research Articles

Concurrent Kink and Sausage Waves in A Crescent Shaped Structure Over A Limb Prominence

Abstract A Crescent shaped prominence Structure (CS), over the solar west limb is studied using EIS/HINODE and AIA/SDO. First, the time varying positions of the top and below borders of the CS, along with its central axis are derived. Time evolutions of the Doppler shifts, and Line width of Fe XII 195.119 line are studied over the CS borders. Transverse kink oscillations are observed both in the Solar-Y direction and in the Doppler shifts over the observers’ LOS. One explanation could be the oscillatory direction of the main kink wave build an angle with the observers LOS. This angle is calculated to be equal to 27 degrees for the CS top border. The main kink amplitude velocity and periods are obtained to be 5.3 $\rm km/s$, and 33.4 minutes, respectively. The anti-correlation observed between the brightness and thickness of the CS (with -178.1○) suggests the presence of sausage modes with periods of 20.8 minutes. Based on the AIA imaging, it is suggested that the occurred jets and their afterward dimming are responsible to trigger the sausage mode. The average electron densities of the CS over the time of the study is obtained to be log($\rm n_e$)=9.3$\rm [cm^{-3}]$. The Alfvén velocity, magnetic field, and energy flux of the observed fast kink mode over the CS are estimated to be 16.7 $\rm km/s$, 2.79 $\rm G$, 41.93 $\rm W/m^2$. Considering the magnetic flux conservation inside the CS, expanding the CS cross section, causes the magnetic field to decay with the rate of $\rm 4.95 \times 10^{-4} \, G/sec$.

Transverse kink oscillations of inhomogeneous prominence threads: Numerical analysis and Hα forward modelling

Context. Prominence threads are very long and thin flux tubes that are partially filled with cold plasma. Observations have shown that transverse oscillations are frequent in these solar structures. The observations are usually interpreted as the fundamental kink mode, while the detection of the first harmonic remains elusive. Aims. The properties of oscillations in threads are greatly affected by the density distribution along the flux tube. Here, we aim to study how the density inhomogeneities in the longitudinal and radial directions modify the periods and damping times of kink oscillations and how this effect would be reflected in the observations. Methods. We solved the ideal magnetohydrodynamics equations using two different methods: (a) performing 3D numerical simulations and (b) solving a 2D generalised eigenvalue problem. We studied the dependence of the periods, damping times, and amplitudes of transverse kink oscillations on the ratio between the densities at the centre and at the ends of the tube, and also on the average density. We applied forward modelling to our 3D simulations to compute synthetic Hα profiles. Results. We confirm that the ratio of the period of the fundamental oscillation mode to the period of the first harmonic increases as the ratio of the central density to the footpoint density is increased, or as the averaged density of the tube is decreased. We find that the damping times due to resonant absorption decrease as the central-to-footpoint density ratio increases. Contrary to the case of longitudinally homogeneous tubes, we find that the damping-time-to-period ratio also increases as the density ratio is increased or the average density is reduced. We present snapshots and time-distance diagrams of the emission in the Hα line. Conclusions. The results presented here have implications for the field of prominence seismology. While the Hα emission can be used to detect the fundamental mode, the first harmonic is barely detectable in Hα. This may explain the lack of detections of the first harmonic. A combination of different spectral lines is required to obtain information about the period ratio and to use it to infer physical properties of the threads.

Effect of Magnetic Twist on Nonlinear Transverse Kink Oscillations of Line-tied Magnetic Flux Tubes

Abstract Magnetic twist is thought to play an important role in many structures of the solar atmosphere. One of the effects of twist is to modify the properties of the eigenmodes of magnetic tubes. In the linear regime standing kink solutions are characterized by a change in polarization of the transverse displacement along the twisted tube. In the nonlinear regime, magnetic twist affects the development of shear instabilities that appear at the tube boundary when it is oscillating laterally. These Kelvin–Helmholtz instabilities (KHI) are produced either by the jump in the azimuthal component of the velocity at the edge of the sharp boundary between the internal and external part of the tube or by the continuous small length scales produced by phase mixing when there is a smooth inhomogeneous layer. In this work the effect of twist is consistently investigated by solving the time-dependent problem including the process of energy transfer to the inhomogeneous layer. It is found that twist always delays the appearance of the shear instability, but for tubes with thin inhomogeneous layers the effect is relatively small for moderate values of twist. On the contrary, for tubes with thick layers, the effect of twist is much stronger. This can have some important implications regarding observations of transverse kink modes and the KHI itself.

Damping time of transverse kink oscillations in active region coronal loops observed by AIA/SDO

Damping time of transverse kink oscillations in active region coronal loops observed by AIA/SDO

Transverse, propagating velocity perturbations in solar coronal loops

As waves and oscillations carry both energy and information, they have enormous potential as a plasma heating mechanism and, through seismology, to provide estimates of local plasma properties which are hard to obtain from direct measurements. Being sufficiently near to allow high-resolution observations, the atmosphere of the Sun forms a natural plasma laboratory. Recent observations have revealed that an abundance of waves and oscillations is present in the solar atmosphere, leading to a renewed interest in wave heating mechanisms.This short review paper gives an overview of recently observed transverse, propagating velocity perturbations in coronal loops. These ubiquitous perturbations are observed to undergo strong damping as they propagate. Using 3D numerical simulations of footpoint-driven transverse waves propagating in a coronal plasma with a cylindrical density structure, in combination with analytical modelling, it is demonstrated that the observed velocity perturbations can be understood in terms of coupling of different wave modes in the inhomogeneous boundaries of the loops. Mode coupling in the inhomogeneous boundary layers of the loops leads to the coupling of the transversal (kink) mode to the azimuthal (Alfvén) mode, observed as the decay of the transverse kink oscillations. Both the numerical and analytical results show the spatial profile of the damped wave has a Gaussian shape to begin with, before switching to exponential decay at large heights. In addition, recent analysis of CoMP (Coronal Multi-channel Polarimeter) Doppler shift observations of large, off-limb, trans-equatorial loops shows that Fourier power at the apex appears to be higher in the high-frequency part of the spectrum than expected from theoretical models. This excess high-frequency FFT power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvénic) turbulence.

MODEL COMPARISON FOR THE DENSITY STRUCTURE ACROSS SOLAR CORONAL WAVEGUIDES

The spatial variation of physical quantities, such as the mass density, across solar atmospheric waveguides governs the timescales and spatial scales for wave damping and energy dissipation. The direct measurement of the spatial distribution of density, however, is difficult and indirect seismology inversion methods have been suggested as an alternative. We applied Bayesian inference, model comparison, and model-averaging techniques to the inference of the cross-field density structuring in solar magnetic waveguides using information on periods and damping times for resonantly damped magnetohydrodynamic (MHD) transverse kink oscillations. Three commonly employed alternative profiles were used to model the variation of the mass density across the waveguide boundary. Parameter inference enabled us to obtain information on physical quantities such as the Alfv\'en travel time, the density contrast, and the transverse inhomogeneity length scale. The inference results from alternative density models were compared and their differences quantified. Then, the relative plausibility of the considered models was assessed by performing model comparison. Our results indicate that the evidence in favor of any of the three models is minimal, unless the oscillations are strongly damped. In such a circumstance, the application of model-averaging techniques enables the computation of an evidence-weighted inference that takes into account the plausibility of each model in the calculation of a combined inversion for the unknown physical parameters.

Transverse kink oscillations in the presence of twist

Magnetic twist is thought to play an important role in coronal loops. The effects of magnetic twist on stable magnetohydrodynamic (MHD) waves is poorly understood because they are seldom studied for relevant cases. The goal of this work is to study the fingerprints of magnetic twist on stable transverse kink oscillations. We numerically calculated the eigenmodes of propagating and standing MHD waves for a model of a loop with magnetic twist. The azimuthal component of the magnetic field was assumed to be small in comparison to the longitudinal component. We did not consider resonantly damped modes or kink instabilities in our analysis. For a nonconstant twist the frequencies of the MHD wave modes are split, which has important consequences for standing waves. This is different from the degenerated situation for equilibrium models with constant twist, which are characterised by an azimuthal component of the magnetic field that linearly increases with the radial coordinate. In the presence of twist standing kink solutions are characterised by a change in polarisation of the transverse displacement along the tube. For weak twist, and in the thin tube approximation, the frequency of standing modes is unaltered and the tube oscillates at the kink speed of the corresponding straight tube. The change in polarisation is linearly proportional to the degree of twist. This has implications with regard to observations of kink modes, since the detection of this variation in polarisation can be used as an indirect method to estimate the twist in oscillating loops.

Transverse kink oscillations of expanding coronal loops

We investigate the nature of transverse kink oscillations of loops expanding through the solar corona and how can oscillations be used to diagnose the plasma parameters and the magnetic field. In particular, we aim to analyse how the temporal dependence of the loop length (here modelling the expansion) will affect the P1 /P2 period ratio of transverse loop oscillations. Due to the uncertainty of the loop's shape through its expansion, we discuss separately the case of the loop that maintains its initial semi-circular shape and the case of the loop that from a semi-circular shape evolve into an elliptical shape loop. The equations that describe the oscillations in expanding flux tube are complicated due to the spatial and temporal dependence of coefficients. Using the WKB approximation we find approximative values for periods and their evolution, as well as the period ratio. For small values of time (near the start of the expansion) we can employ a regular perturbation method to find approximative relations for eigenfunctions and eigenfrequencies. Using simple analytical and numerical methods we show that the period of oscillations are affected by the rising of the coronal loop. The change in the period due to the increase in the loop's length is more pronounced for those loops that expand into a more structured (or cooler corona). The deviation of periods will have significant implications in determining the degree of stratification in the solar corona. The effect of expansion on the periods of oscillations is considerable only in the process of expansion of the loop but not when it reached its final stage.

Spatial damping of propagating kink waves due to mode coupling

Aims. We investigate the damping process for propagating transverse velocity oscillations, observed to be ubiquitous in the solar corona, due to mode coupling. Methods. We perform 3D numerical simulations of footpoint-driven transverse waves propagating in a low β coronal plasma with a cylindrical density structure. Mode coupling in an inhomogeneous layer leads to the coupling of the kink mode to the Alfven mode, observed as the decay of the transverse kink oscillations. Results. We consider the spatial damping profile and find a Gaussian damping profile of the form exp(−z/Lg) to be the most congruent with our numerical data, rather than the exponential damping profile of the form exp(−z/Ld) used in normal mode analysis. Our results highlight that the nature of the driver itself will have a substantial influence on observed propagating kink waves. Conclusions. Our study suggests that this modified damping profile should be taken into account when using coronal seismology to infer local plasma properties from observed damped oscillations.

Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads

We analyse the oscillatory properties of resonantly damped transverse kink oscillations in two-dimensional prominence threads. The fine structures are modelled as cylindrically symmetric magnetic flux tubes with a dense central part with prominence plasma properties and an evacuated part, both surrounded by coronal plasma. The equilibrium density is allowed to vary non-uniformly in both the transverse and the longitudinal directions.We examine the influence of longitudinal density structuring on periods, damping times, and damping rates for transverse kink modes computed by numerically solving the linear resistive magnetohydrodynamic (MHD) equations. The relevant parameters are the length of the thread and the density in the evacuated part of the tube, two quantities that are difficult to directly estimate from observations. We find that both of them strongly influence the oscillatory periods and damping times, and to a lesser extent the damping ratios. The analysis of the spatial distribution of perturbations and of the energy flux into the resonances allows us to explain the obtained damping times. Implications for prominence seismology, the physics of resonantly damped kink modes in two-dimensional magnetic flux tubes, and the heating of prominence plasmas are discussed.