Fast magnetohydrodynamic oscillation of longitudinally inhomogeneous prominence threads: an analogue with quantum harmonic oscillator

Lomineishvili, S. N.; Zaqarashvili, T. V.; Zhelyazkov, I.; Tevzadze, Alexander G.

doi:10.1051/0004-6361/201323225

Cited by 3 publications

(14 citation statements)

References 38 publications

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“…The results computed in the present paper for a thread with a parabolic density profile are in disagreement with those obtained by Lomineishvili et al (2014) using the same model. Lomineishvili et al (2014) claim that the period ratio is 3, but we found that the correct value of the period ratio is 2.22, approximately. Here we explain the source of the discrepancy between the results of Lomineishvili et al (2014) and those of the present paper.…”

Section: Discussioncontrasting

confidence: 88%

“…Lomineishvili et al (2014) claim that the period ratio is 3, but we found that the correct value of the period ratio is 2.22, approximately. Here we explain the source of the discrepancy between the results of Lomineishvili et al (2014) and those of the present paper.…”

Section: Appendix A: Comment On the Paper By Lomineishvili Et Al (2014)mentioning

confidence: 65%

“…We thank Iñigo Arregui for reading a draft of this paper and for giving helpful comments. We also thank Teimuraz Zaqarashvili for discussions on the Lomineishvili et al (2014) paper. We acknowledge support from MINECO and FEDER funds through project AYA2011-22846.…”

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confidence: 98%

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Prominence seismology using the period ratio of transverse thread oscillations

Soler

Goossens

Ballester

2015

A&A

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The ratio of the period of the fundamental mode to that of the first overtone of kink oscillations (hereafter period ratio) is a seismology tool that can be used to infer information about the spatial variation of density along solar magnetic flux tubes. The period ratio is 2 in longitudinally homogeneous thin tubes, but it differs from 2 because of longitudinal inhomogeneity. In this paper we investigate the period ratio in longitudinally inhomogeneous prominence threads and explore its implications for prominence seismology. We numerically solve the two-dimensional eigenvalue problem of kink oscillations in a model of a prominence thread. We take into account three nonuniform density profiles along the thread. In agreement with previous works that used simple piecewise constant density profiles, we find that the period ratio is larger than 2 in prominence threads. When the ratio of the central density to that at the footpoints is fixed, the period ratio depends strongly on the form of the density profile along the thread. The more concentrated the dense prominence plasma near the center of the tube, the larger the period ratio. However, the period ratio is found to be independent of the specific density profile when the spatially averaged density in the thread is the same for all the profiles. An empirical fit of the dependence of the period ratio on the average density is given and its use for prominence seismology is discussed.

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Section: Discussioncontrasting

confidence: 88%

Section: Appendix A: Comment On the Paper By Lomineishvili Et Al (2014)mentioning

confidence: 65%

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Prominence seismology using the period ratio of transverse thread oscillations

Soler

Goossens

Ballester

2015

A&A

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“…Pascoe et al 2009a). Lomineishvili et al (2014) also discuss a kink mode period ratio greater than unity for prominence threads, which are denser at the apex than the footpoints.…”

Section: Discussionmentioning

confidence: 98%

Spatially resolved observation of the fundamental and second harmonic standing kink modes using SDO/AIA

Pascoe

Goddard

Nakariakov

2016

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Aims. We consider a coronal loop kink oscillation observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) which demonstrates two strong spectral components. The period of the lower frequency component being approximately twice that of the shorter frequency component suggests the presence of harmonics. Methods. We examine the presence of two longitudinal harmonics by investigating the spatial dependence of the loop oscillation. The time-dependent displacement of the loop is measured at 15 locations along the loop axis. For each position the detrended displacement is fitted as the sum of two damped sinusoids, having periods P 1 and P 2 , and a damping time τ. The shorter period component exhibits anti-phase oscillations in the loop legs. Results. We interpret the observation in terms of the first (global or fundamental) and second longitudinal harmonics of the standing kink mode. The strong excitation of the second harmonic appears connected to the preceding coronal mass ejection (CME) which displaced one of the loop legs. The oscillation parameters found are P 1 " 5.00˘0.62 minutes, P 2 " 2.20˘0.23 minutes, P 1 {2P 2 " 1.15˘0.22, and τ{P " 3.35˘1.45.

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“…The ratio being greater than unity suggests a negative scale height, also considered by Andries et al (2005) for coronal loops and Lomineishvili et al (2014) for prominence threads.…”

Section: Introductionmentioning

confidence: 96%

Standing sausage modes in curved coronal slabs

Pascoe

Nakariakov

2016

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Context. Magnetohydrodynamic waveguides such as dense coronal loops can support standing modes. The ratios of the periods of oscillations for different longitudinal harmonics depend on the dispersive nature of the waveguide and so may be used as a seismological tool to determine coronal parameters. Aims. We extend models of standing sausage modes in low β coronal loops to include the effects of loop curvature. The behaviour of standing sausage modes in this geometry is used to explain the properties of observed oscillations which cannot be accounted for using straight loop models. Methods. We perform 2D numerical simulations of an oscillating coronal loop, modelled as a dense slab embedded in a potential magnetic field. The loop is field-aligned and so experiences expansion with height in addition to being curved. Standing sausage modes are excited by compressive perturbations of the loop and their properties are studied. Results. The spatial profiles of standing sausage modes are found to be modified by the expanding loop geometry typical for flaring loops and modelled by a potential magnetic field in our simulations. Longitudinal harmonics of order n ą 1 have antinodes which are shifted towards the loop apex and the amplitude of antinodes near the loop apex is smaller than those near the loop footpoints. Conclusions. We find that the observation of standing sausage modes by Nakariakov et al. (2003) is consistent with interpretation in terms of the global mode (n " 1) and third harmonic (n " 3). This interpretation accounts for the period ratio and spatial structure of the observed oscillations.

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Fast magnetohydrodynamic oscillation of longitudinally inhomogeneous prominence threads: an analogue with quantum harmonic oscillator

Cited by 3 publications

References 38 publications

Prominence seismology using the period ratio of transverse thread oscillations

Prominence seismology using the period ratio of transverse thread oscillations

Spatially resolved observation of the fundamental and second harmonic standing kink modes using SDO/AIA

Standing sausage modes in curved coronal slabs

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