Observation of multiple sausage oscillations in cool post-flare loop

Srivastava, A. K.; Zaqarashvili, T. V.; Uddin, Wahab; Dwivedi, B. N.; Kumar, Pankaj

doi:10.1111/j.1365-2966.2008.13532.x

Cited by 89 publications

(89 citation statements)

References 27 publications

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“…This mode, with typical periods in the range 5-30 s, is believed to be detected in the microwave and hard X-ray emission associated with flaring solar loops (e.g. Nakariakov et al 2003;Melnikov et al 2005;Inglis et al 2008), and also in H α emission from cool, post-flare loops (Srivastava et al 2008). The sausage mode is essentially compressible, with the density perturbations in phase with the perturbations of the magnetic field and in anti-phase with the perturbations of the loop minor radius.…”

Section: Introductionmentioning

confidence: 94%

Characteristics of magnetoacoustic sausage modes

Inglis¹,

Doorsselaere²,

Brady³

et al. 2009

A&A

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Aims. We perform an advanced study of the fast magnetoacoustic sausage oscillations of coronal loops in the context of MHD coronal seismology to establish the dependence of the sausage mode period and cut-off wavenumber on the plasma-β of the loopfilling plasma. A parametric study of the ratios for different harmonics of the mode is also carried out. Methods. Full magnetohydrodynamic numerical simulations were performed using Lare2d, simulating hot, dense loops in a magnetic slab environment. The symmetric Epstein profile and a simple step-function profile were both used to model the density structure of the simulated loops. Analytical expressions for the cut-off wavenumber and the harmonic ratio between the second longitudinal harmonic and the fundamental were also examined. Results. It was established that the period of the global sausage mode is only very weakly dependent on the value of the plasma-β inside a coronal loop, which justifies the application of this model to hot flaring loops. The cut-off wavenumber k c for the global mode was found to be dependent on both internal and external values of the plasma-β, again only weakly. By far the most important factor in this case was the value of the density contrast ratio between the loop and the surroundings. Finally, the deviation of the harmonic ratio P 1 /2P 2 from the ideal non-dispersive case was shown to be considerable at low k, again strongly dependent on plasma density. Quantifying the behaviour of the cut-off wavenumber and the harmonic ratio has significant applications to the field of coronal seismology.

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Section: Introductionmentioning

confidence: 94%

Characteristics of magnetoacoustic sausage modes

Inglis¹,

Doorsselaere²,

Brady³

et al. 2009

A&A

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“…For example, the ratio between the periods of first and second harmonics in homogeneous coronal loops is near 2 (Edwin & Roberts 1983), while the stratification may lead to the Article published by EDP Sciences A35, page 1 of 7 significant shift in the ratio (Andries et al 2005b;McEwan et al 2006). There are several observational examples of the simultaneous existence of first and second harmonics of MHD oscillations in coronal loops, which indeed show the deviation of the ratio from 2 (Van Doorsselaere et al 2004Verwichte et al 2004;De Moortel & Brady 2007;Srivastava et al 2008Srivastava et al , 2013Inglis & Nakariakov 2009). …”

Section: Introductionmentioning

confidence: 99%

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

Lomineishvili

Zaqarashvili

Zhelyazkov

et al. 2014

A&A

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Context. Previous works indicate that the frequency ratio of second and first harmonics of kink oscillations tends towards 3 in the case of prominence threads. This is not a straightforward result, so it requires adequate explanation. Aims. We aim to study the magnetohydrodynamic oscillations of longitudinally inhomogeneous prominence threads and to shed light on the problem of the frequency ratio. Methods. The classical Sturm-Liouville problem is used for the threads with longitudinally inhomogeneous plasma density. We show that the spatial variation of total pressure perturbations along the thread is governed by the stationary Schrödinger equation, where the longitudinal inhomogeneity of plasma density stands for the potential energy. The Schrödinger equation appears as the equation of quantum harmonic oscillator for a parabolic profile of plasma density. Consequently, the equation has bounded solutions in terms of Hermite polynomials. Results. Boundary conditions at the thread surface lead to a transcendental dispersion equation with Bessel functions. The thin flux tube approximation of the dispersion equation shows that the frequency of kink waves is proportional to the expression α(2n + 1), where α is the density inhomogeneity parameter, and n the longitudinal mode number. Consequently, the ratio of the frequencies of second and first harmonics tends to 3 in prominence threads. The numerical solution of the dispersion equation shows that the ratio decreases only slightly for thicker tubes in the case of less longitudinal inhomogeneity of the external density, therefore the thin flux tube limit is a good approximation for prominence oscillations. However, stronger longitudinal inhomogeneity of external density may lead to the significant shift in the frequency ratio for wider tubes, and therefore the thin tube approximation may fail. Conclusions. The tendency of frequency ratio of second and first harmonics towards 3 in prominence threads is explained by the analogy of the oscillations with quantum harmonic oscillator, where the density inhomogeneity of the threads plays a role as the potential energy.

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“…Therefore, we basically observe fast MHD pulsation of short periods excited due to flare activity in the flaring loop system. As a result, the observed denser loops can support the non-leaky, trapped global sausage mode in the estimated length and width as well as density contrast Aschwanden et al, 2004;Srivastava et al, 2008). Such flaring/post-flare loops usually have a very high density contrast of the order of 10 2 -10 3 .…”

Section: Resultsmentioning

confidence: 97%

“…Different periods of QPPs may be associated either with different MHD modes simultaneously present in a flaring loop or with different harmonics of the same MHD mode (Melnikov et al, 2005;Van Doorsselaere et al, 2007;Srivastava et al, 2008;Andries et al, 2009;Srivastava & Dwivedi, 2010, e.g. ).…”

Section: Introductionmentioning

confidence: 99%

“…The ratio of the statistically significant QPPs of the simultaneously existing spectral components is important for determining the nature and mechanisms of the pulsations both in observations and theory (Van Doorsselaere et al, 2007;Srivastava et al, 2008;Srivastava & Dwivedi, 2010;Macnamara & Roberts, 2011;Orza & Ballai, 2013;Luna-Cardozo et al, 2012;Erdélyi et al, 2014;Guo et al, 2015, and references cited there). Different periods of QPPs may be associated either with different MHD modes simultaneously present in a flaring loop or with different harmonics of the same MHD mode (Melnikov et al, 2005;Van Doorsselaere et al, 2007;Srivastava et al, 2008;Andries et al, 2009;Srivastava & Dwivedi, 2010, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Study of multi-periodic coronal pulsations during an X-class solar flare

Chowdhury

Srivastava

Dwivedi

et al. 2015

Advances in Space Research

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We investigate quasi-periodic coronal pulsations during the decay phase of an X 3.2 class flare on 14 May 2013, using soft X-ray data from the RHESSI satellite. Periodogram analyses of soft X-ray light curves show that ∼ 53 s and ∼ 72 s periods co-exist in the 3-6, 6-12 and 12-25 KeV energy bands. Considering the typical length of the flaring loop system and observed periodicities, we find that they are associated with multiple (first two harmonics) of fast magnetoacoustic sausage waves. The phase relationship of soft X-ray emissions in different energy bands using cross-correlation technique show that these modes are standing in nature as we do not find the phase lag. Considering the period ratio, we diagnose the local plasma conditions of the flaring region by invoking MHD seismology. The period ratio P 1 /2P 2 is found to be ∼ 0.65, which indicates that such oscillations are most likely excited in longitudinal density stratified loops.

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Observation of multiple sausage oscillations in cool post-flare loop

Cited by 89 publications

References 27 publications

Characteristics of magnetoacoustic sausage modes

Characteristics of magnetoacoustic sausage modes

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

Study of multi-periodic coronal pulsations during an X-class solar flare

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