Coronal Seismology by Means of Kink Oscillation Overtones

Andries, Jesse; Doorsselaere, Tom Van; Roberts, B.; Verth, G.; Verwichte, E.; Erdélyi, R.

doi:10.1007/s11214-009-9561-2

Cited by 210 publications

(224 citation statements)

References 75 publications

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“…We found that the twist enhances this ratio when ζ < 7 and reduces it when ζ > 7. In general, when q 6, the difference between this ratio and 2 is similar to the values obtained in the simultaneous observations of the fundamental harmonic and first overtone of the coronal loop kink oscillations (Verwichte et al 2004;van Doorsselaere et al 2007van Doorsselaere et al , 2009Andries et al 2009). This result implies that the observed deviation of the frequency ratio from 2 can be related not only with the density variation along the loop and loop expansion, but also with the presence of magnetic twist.…”

Section: Discussionsupporting

confidence: 84%

“…This property causes the decrease in the frequency ratio. It was suggested by Andries et al (2005) as a tool for estimating the density scale height in the corona using simultaneous observations of the fundamental harmonic and first overtone of coronal loop kink oscillations (see also the review by Andries et al 2009). The second property is the coronal loop expansion.…”

Section: After Integration This Equation Reduces Tomentioning

confidence: 99%

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Standing kink oscillations of thin twisted magnetic tubes with continuous equilibrium magnetic field

Terradas

2015

A&A

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In this article we study standing kink waves in twisted magnetic tubes. We use the cold plasma and thin tube approximation. We assume that the plasma density is constant inside and outside the tube. We also assume that the magnetic twist is weak and take the ratio of the azimuthal and axial component of the magnetic field to be of the order of ratio of the tube radius and tube length. The azimuthal component of the magnetic field is proportional to the distance from the tube axis inside the tube, and inversely proportional to this distance outside the tube. Using the method of asymptotic expansions we derived the governing integral equation that determines the eigenfrequencies and eigenmodes of the tube kink oscillations. In the approximation of a very weak twist, we calculated analytically the corrections to the frequencies of the fundamental mode and first overtone of a straight magnetic tube related to the presence of twist. The analytical results are compared with the numerical results obtained using the full set of linear ideal magnetohydrodynamic equations. We also calculated the ratio of frequencies of the fist overtone and fundamental mode. We found that the magnetic twist enhances this ratio for moderate values of the density ratio, and reduces this ratio for large values of the density ratio. In general, the deviation of the frequency ratio from 2 caused by the magnetic twist is comparable to that found in simultaneous observations of the fundamental mode and first overtone of the coronal loop kink oscillations. Finally, we studied the eigenmode polarization. We found that, in a particular case of linear polarization, the polarization direction rotates along the tube.

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Section: Discussionsupporting

confidence: 84%

Section: After Integration This Equation Reduces Tomentioning

confidence: 99%

Standing kink oscillations of thin twisted magnetic tubes with continuous equilibrium magnetic field

Terradas

2015

A&A

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“…Andries et al (2005b) showed that this effect leads to the reduction of the ratio of the fundamental mode to the first overtone frequency below the canonical value of 2 of a homogeneous loop. On the basis of this result, Andries et al (2005a) suggested the method of estimation of the atmospheric scale height in the solar corona, using the frequency ratio (see also McEwan et al 2008, or for a review Andries et al 2009). Dymova & Ruderman (2005) showed that kink oscillations of thin magnetic tubes with the density varying along the tube can be described by the wave equation with the phase speed equal to the local kink speed.…”

Section: Introductionmentioning

confidence: 99%

Kink oscillations of cooling coronal loops with variable cross-section

Shukhobodskiy

Erdélyi

2017

A&A

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We study kink waves and oscillations in a thin expanding magnetic tube in the presence of flow. The tube consists of a core region and a thin transitional region at the tube boundary. In this region the plasma density monotonically decreases from its value in the core region to the value outside the tube. Both the plasma density and velocity of background flow vary along the tube and in time. Using the multiscale expansions we derive the system of two equations describing the kink oscillations. When there is no transitional layer the oscillations are described by the first of these two equations. We use this equation to study the effect of plasma density variation with time on kink oscillations of an expanding tube with a sharp boundary. We assume that the characteristic time of the density variation is much greater than the characteristic time of kink oscillations. Then we use the Wentzel-Kramer-Brillouin (WKB) method to derive the expression for the adiabatic invariant, which is the quantity that is conserved when the plasma density varies. The general theoretical results are applied to the kink oscillations of coronal magnetic loops. We consider an expanding loop with the half-circle shape and assume that the plasma temperature inside a loop decays exponentially with time. We numerically calculated the dependences of the fundamental mode frequency, the ratio of frequencies of the first overtone and fundamental mode, and the oscillation amplitude on time. We obtained that the oscillation frequency and amplitude increase and the frequency ratio decreases due to cooling. The amplitude increase is stronger for loops with a greater expansion factor. This effect is also more pronounced for higher loops. However, it is fairly moderate even for loops that are quite high.

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“…These tubes form an "elastic medium" and may therefore act as waveguides. The propagation of linear waves along magnetic cylinders has been studied extensively (see, for example, Defouw, 1976or Roberts, 1981, or the reviews by Andries et al, 2009, De Moortel, 2009, Mathioudakis, Jess, and Erdélyi, 2013or Wang, 2011. Aspects of the propagation of nonlinear waves have also been studied, with the relevant theory and a number of important results summarised in Ruderman (2003), Ruderman (2006) and Ballai and Ruderman (2011).…”

Section: Introductionmentioning

confidence: 99%

Propagation of Long-Wavelength Nonlinear Slow Sausage Waves in Stratified Magnetic Flux Tubes

Barbulescu

Erdélyi

2016

Sol Phys

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The propagation of nonlinear, long-wavelength, slow sausage waves in an expanding magnetic flux tube, embedded in a non-magnetic stratified environment, is discussed. The governing equation for surface waves, which is akin to the Leibovich-Roberts equation, is derived using the method of multiple scales. The solitary wave solution of the equation is obtained numerically. The results obtained are illustrative of a solitary wave whose properties are highly dependent on the degree of stratification.

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Coronal Seismology by Means of Kink Oscillation Overtones

Cited by 210 publications

References 75 publications

Standing kink oscillations of thin twisted magnetic tubes with continuous equilibrium magnetic field

Standing kink oscillations of thin twisted magnetic tubes with continuous equilibrium magnetic field

Kink oscillations of cooling coronal loops with variable cross-section

Propagation of Long-Wavelength Nonlinear Slow Sausage Waves in Stratified Magnetic Flux Tubes

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