Resonant Damping of Solar<i>p</i>‐Modes by the Chromospheric Magnetic Field

Tirry, W. J.; Goossens, Marcel; Pintér, Balázs; Čadež, V. M.; Vanlommel, Petra

doi:10.1086/305958

Cited by 64 publications

(70 citation statements)

References 19 publications

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“…In the TB approximation it is natural to adopt r A = R since l/R 1 and r A ∈ ]R − l/2, R + l/2[. Using the jump condition is not restricted to the thin non-uniform layer as can be seen from, e.g., Tirry & Goossens (1996); Tirry et al (1997Tirry et al ( , 1998; however, this condition requires numerical integration of the ideal MHD equations in a non-uniform plasma up to the dissipative layer. In the present paper we do not intend to use numerical integration of the ideal MHD equations relating to thick boundaries.…”

Section: Inhomogeneous Magnetic Cylindermentioning

confidence: 99%

Selective spatial damping of propagating kink waves due to resonant absorption

Terradas

Goossens

Verth

2010

A&A

Self Cite

126

143

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Context. There is observational evidence of propagating kink waves driven by photospheric motions. These disturbances, interpreted as kink magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the solar corona. Aims. We show that resonant absorption provides a simple explanation to the spatial damping of these waves. Methods. Kink MHD waves are studied using a cylindrical model of solar magnetic flux tubes, which includes a non-uniform layer at the tube boundary. Assuming that the frequency is real and the longitudinal wavenumber complex, the damping length and damping per wavelength produced by resonant absorption are analytically calculated in the thin tube (TT) approximation, valid for coronal waves. This assumption is relaxed in the case of chromospheric tube waves and filament thread waves. Results. The damping length of propagating kink waves due to resonant absorption is a monotonically decreasing function of frequency. For kink waves with low frequencies, the damping length is exactly inversely proportional to frequency, and we denote this as the TGV relation. When moving to high frequencies, the TGV relation continues to be an exceptionally good approximation of the actual dependency of the damping length on frequency. This dependency means that resonant absorption is selective as it favours lowfrequency waves and can efficiently remove high-frequency waves from a broad band spectrum of kink waves. The efficiency of the damping due to resonant absorption depends on the properties of the equilibrium model, in particular on the width of the non-uniform layer and the steepness of the variation in the local Alfvén speed. Conclusions. Resonant absorption is an effective mechanism for the spatial damping of propagating kink waves. It is selective because the damping length is inversely proportional to frequency so that the damping becomes more severe with increasing frequency. This means that radial inhomogeneity can cause solar waveguides to be a natural low-pass filter for broadband disturbances. Kink wave trains travelling along, e.g., coronal loops, will therefore have a greater proportion of the high-frequency components dissipated lower down in the atmosphere. This could have important consequences for the spatial distribution of wave heating in the solar atmosphere.

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Section: Inhomogeneous Magnetic Cylindermentioning

confidence: 99%

Selective spatial damping of propagating kink waves due to resonant absorption

Terradas

Goossens

Verth

2010

A&A

Self Cite

126

143

View full text Add to dashboard Cite

show abstract

“…A method based on the application of the jump conditions at the resonance or resonances, used for example by Tirry et al (1998) or Andries et al (2000); Andries & Goossens (2001), is more appropriate but since this is not the main focus of this paper it will not be further investigated here.…”

Section: Beyond the Tttb Approximation: Full Resistive Eigenvalue Promentioning

confidence: 99%

“…In the past, the influence of a velocity shear on this process due to a longitudinal flow has been studied by Hollweg et al (1990); Peredo & Tataronis (1990), ; Erdélyi et al (1995); Erdélyi & Goossens (1996); Tirry et al (1998). More recently, Andries et al (2000); Andries & Goossens (2001); Erdélyi & Taroyan (2003a,b), have investigated in detail resonant flow instabilities which can occur for velocity shears significantly below the Kelvin-Helmholtz (KH) threshold.…”

Section: Introductionmentioning

confidence: 99%

The effect of longitudinal flow on resonantly damped kink oscillations

Terradas

Goossens

Ballai³

2010

A&A

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Context. The most promising mechanism acting towards damping the kink oscillations of coronal loops is resonant absorption. In this context most of previous studies neglected the effect of the obvious equilibrium flow along magnetic field lines. The flows are in general sub-Alfvénic and hence comparatively slow. Aims. Here we investigate the effect of an equilibrium flow on the resonant absorption of linear kink MHD waves in a cylindrical magnetic flux tube with the aim of determining the changes in the frequency of the forward and backward propagating waves and in the modification of the damping times due to the flow. Methods. A loop model with both the density and the longitudinal flow changing in the radial direction is considered. We use the thin tube thin boundary (TTTB) approximation in order to calculate the damping rates. The full resistive eigenvalue problem is also solved without assuming the TTTB approximation. Results. Using the low ratio of flow and Alfvén speeds we derive simple analytical expressions to the damping rate. The analytical expressions are in good agreement with the resistive eigenmode calculations. Conclusions. Under typical coronal conditions the effect of the flow on the damped kink oscillations is weak when the characteristic scale of the density layer is similar or lower than the characteristic width of the velocity layer. However, in the opposite situation the damping rates can be significantly altered, specially for the backward propagating wave which is undamped while the forward wave is overdamped.

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“…The spectacular behavior of the Ñuctuations in the vicinity of the critical layer(s), coupled with the implications suggested by the nonzero divergence of the wave energy Ñux, have prompted intense interest and investigation of the horizontal magnetic Ðeld limit (see Nye & Thomas 1976 ;Adam 1981Adam , 1986Adam , 1989Adam , 1990and Cally 1984) for a comprehensive mathematical analysis and, e.g., (Zhukov 1990 ;Rosenthal 1990 ;Zhukov 1997 ;& Goossens Pinter, C ‹ adez-, 1998 ;Tirry et al 1998 ;Vanlommel & Goossens 1999 ; for solar applications). A contraPinter dictory point of view has been proposed by Schwartz & Bel (1984), who argue that critical layers are likely to be a "" red herring ÏÏ from an astrophysical point of view.…”

Section: Uniformly Magnetized Atmospherementioning

confidence: 99%

Waves in the Magnetized Solar Atmosphere. I. Basic Processes and Internetwork Oscillations

Rosenthal

Bogdan

Carlsson

et al. 2002

ApJ

160

181

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We have modeled numerically the propagation of waves through magnetic structures in a stratiÐed atmosphere. We Ðrst simulate the propagation of waves through a number of simple, exemplary Ðeld geometries in order to obtain a better insight into the e †ect of di †ering Ðeld structures on the wave speeds, amplitudes, polarizations, direction of propagation, etc., with a view to understanding the wide variety of wavelike and oscillatory processes observed in the solar atmosphere. As a particular example, we then apply the method to oscillations in the chromospheric network and internetwork. We Ðnd that in regions where the Ðeld is signiÐcantly inclined to the vertical, refraction by the rapidly increasing phase speed of the fast modes results in total internal reÑection of the waves at a surface whose altitude is highly variable. We conjecture a relationship between this phenomenon and the observed spatiotemporal intermittancy of the oscillations. By contrast, in regions where the Ðeld is close to vertical, the waves continue to propagate upward, channeled along the Ðeld lines but otherwise largely una †ected by the Ðeld.

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Resonant Damping of Solarp‐Modes by the Chromospheric Magnetic Field

Cited by 64 publications

References 19 publications

Selective spatial damping of propagating kink waves due to resonant absorption

Selective spatial damping of propagating kink waves due to resonant absorption

The effect of longitudinal flow on resonantly damped kink oscillations

Waves in the Magnetized Solar Atmosphere. I. Basic Processes and Internetwork Oscillations

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