No unique solution to the seismological problem of standing kink MHD waves

The aim of this paper is to point out that the classic seismological problem using observations and theoretical expressions for the periods and damping times of transverse standing magnetohydrodynamic (MHD) waves in coronal loops is better referred to as a reduced seismological problem. Reduced emphasises the fact that only a small number of characteristic quantities of the equilibrium profiles can be determined. Reduced also implies that there is no unique solution to the full seismological problem. Even the reduced seismological problem does not allow a unique solution. Bayesian inference results support our mathematical arguments and offer insight into the relationship between the algebraic and the probabilistic inversions.Comment: 10 pages, accepted in A&

Spatial Damping of Propagating Kink Waves Due to Resonant Absorption: Effect of Background Flow

Observations show the ubiquitous presence of propagating magnetohydrodynamic (MHD) kink waves in the solar atmosphere. Waves and flows are often observed simultaneously. Due to plasma inhomogeneity in the perpendicular direction to the magnetic field, kink waves are spatially damped by resonant absorption. The presence of flow may affect the wave spatial damping. Here, we investigate the effect of longitudinal background flow on the propagation and spatial damping of resonant kink waves in transversely nonuniform magnetic flux tubes. We combine approximate analytical theory with numerical investigation. The analytical theory uses the thin tube (TT) and thin boundary (TB) approximations to obtain expressions for the wavelength and the damping length. Numerically, we verify the previously obtained analytical expressions by means of the full solution of the resistive MHD eigenvalue problem beyond the TT and TB approximations. We find that the backward and forward propagating waves have different wavelengths and are damped on length scales that are inversely proportional to the frequency as in the static case. However, the factor of proportionality depends on the characteristics of the flow, so that the damping length differs from its static analogue. For slow, sub-Alfvenic flows the backward propagating wave gets damped on a shorter length scale than in the absence of flow, while for the forward propagating wave the damping length is longer. The different properties of the waves depending on their direction of propagation with respect to the background flow may be detected by the observations and may be relevant for seismological applications.Comment: Accepted for publication in Ap

Resonantly Damped Propagating Kink Waves in Longitudinally Stratified Solar Waveguides

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 observed by the Coronal Multi-Channel Polarimeter (CoMP). In the present study, for the first time we investigate the properties of propagating kink waves in solar waveguides including the effects of both longitudinal and transverse plasma inhomogeneity. Importantly, it is found that the wavelength is only dependent on the longitudinal stratification and the amplitude is simply a product of the two effects. In light of these results the advancement of solar atmospheric magnetoseismology by exploiting high spatial/temporal resolution observations of propagating kink waves in magnetic waveguides to determine the length scales of the plasma inhomogeneity along and transverse to the direction of the magnetic field is discussed.Comment: Accepted for publication in Ap

Spatial magneto-seismology : effect of density stratification on the first harmonic amplitude profile of transversal coronal loop oscillations

Context. The new generation of extreme-ultraviolet (EUV) imagers onboard missions such as the Solar Dynamics Observatory (SDO)and Solar Orbiter (SO) will provide the most accurate spatial measurements of post-flare coronal loop oscillations yet. The amplitude profiles of these loop oscillations contain important information about plasma fine structure in the corona. Aims. We show that the position of the anti-nodes of the amplitude profile of the first harmonic of the standing fast kink wave of a coronal loop relate to the plasma density stratification of that loop. Methods. The MHD kink transversal waves of coronal loops are modelled both numerically and analytically. The numerical model implements the implicit finite element code pollux. Dispersion relations are derived and solved analytically. The results of the two methods are compared and verified. Results. Density stratification causes the anti-nodes of the first harmonic to shift towards the loop footpoints. The greater the density stratification, the larger the shift. The anti-node shift of the first harmonic of a semi-circular coronal loop with a density scale height H = 50 Mm and loop half length L = 100 Mm is approximately 5.6Mm. Shifts in the Mm range are measureable quantities providing valuable information about the subresolution structure of coronal loops. Conclusions. The measurement of the anti-node shift of the first harmonic of the standing fast kink wave of coronal loops is potentially a new tool in the field of solar magneto-seismology, providing a novel complementary method of probing plasma fine structure in the corona

On the scaling of the damping time for resonantly damped oscillations in coronal loops

There is not as yet full agreement on the mechanism that causes the rapid damping of the oscillations observed by TRACE in coronal loops. It has been suggested that the variation of the observed values of the damping time as function of the corresponding observed values of the period contains information on the possible damping mechanism. The aim of this Letter is to show that, for resonant absorption, this is definitely not the case unless detailed a priori information on the individual loops is available

Generalized phase mixing: Turbulence-like behaviour from unidirectionally propagating MHD waves

We present the results of three-dimensional (3D) ideal magnetohydrodynamics (MHD) simulations on the dynamics of a perpendicularly inhomogeneous plasma disturbed by propagating Alfv\'enic waves. Simpler versions of this scenario have been extensively studied as the phenomenon of phase mixing. We show that, by generalizing the textbook version of phase mixing, interesting phenomena are obtained, such as turbulence-like behavior and complex current-sheet structure, a novelty in longitudinally homogeneous plasma excited by unidirectionally propagating waves. This constitutes an important finding for turbulence-related phenomena in astrophysics in general, relaxing the conditions that have to be fulfilled in order to generate turbulent behavior

Wave pressure and energy cascade rate of kink waves computed with Elsasser variables

Numerical simulations have revealed a new type of turbulence of unidirectional waves in a plasma that is perpendicularly structured (Magyar et al. 2017), named uniturbulence. For this new type of turbulence, the transverse structuring modifies the upward propagating wave to have both Elsasser variables, leading to the well-known perpendicular cascade. In this paper, we study an analytical description of the non-linear evolution of kink waves in a cylindrical flux tube, which are prone to uniturbulence. We show that they lead to a non-linear cascade for both propagating and standing waves. We calculate explicit expressions for the wave pressure and energy cascade rate. The computed damping rate {\tau}/P depends on the density contrast of the flux tube and the background plasma and is inversely proportional to the amplitude of the kink wave. The dependence on the density contrast shows that it plays a role especially in the lower solar corona. These expressions may be added in Alfven wave driven models of the solar atmosphere (such as AWSOM, van der Holst et al. 2014), modifying it to UAWSOM (Uniturbulence and Alfven Wave Solar Model)

Mixed properties of magnetohydrodynamic waves undergoing resonant absorption in the cusp continuum

Observations of magnetohydrodynamic (MHD) waves in the structured solar atmosphere have shown that these waves are damped and can thus contribute to atmospheric heating. In this paper, we focus on the damping mechanism of resonant absorption in the cusp continuum. This process takes places when waves travel through an inhomogeneous plasma. Our aim is to determine the properties of MHD waves undergoing resonant absorption in the cusp continuum in the transition layer of a cylindrical solar atmospheric structure, such as a photospheric pore or a coronal loop. Depending on which quantities dominate, one can assess what type of classical MHD wave the modes in question resemble most. In order to study the properties of these waves, we analytically determine the spatial profiles of compression, displacement, and vorticity for waves with frequencies in the cusp continuum, which undergo resonant absorption. We confirm these analytical derivations via numerical calculations of the profiles in the resistive MHD framework. We show that the dominant quantities for the modes in the cusp continuum are the displacement parallel to the background magnetic field and the vorticity component in the azimuthal direction (i.e. perpendicular to the background magnetic field and along the loop boundary)