Sausage oscillations of coronal loops

Aims. Analytical theory predicts the existence of trapped global (or fundamental) sausage fast magnetoacoustic modes in thick and dense coronal loops only, with the periods estimated as the ratio of double the loop length and the Alfvén speed outside the loop. We extend this study to the leaking regime, considering global sausage modes of long loops with small density contrasts. Methods. Anti-symmetric fast magnetoacoustic perturbations (sausage, or m = 0 modes) of a low β plasma slab with the symmetric Epstein profile of plasma density are modelled numerically. Results. It was found that long loops with sufficiently small density contrast can support global sausage leaky modes of detectable quality. The periods of the leaky modes are found to be approximately determined by the loop length and the external Alfvén speed. If the loop length can be estimated from imaging observations, the observed period of this mode provides us with the information about the Alfvén speed outside the loop. For typical flaring coronal loops, the estimated periods of the global sausage modes are about 5−60 s

Multi-wavelength spatially resolved analysis of quasi-periodic pulsations in a solar flare

Aims. We aim to perform a spatially resolved analysis of a quasi-periodic pulsation event from 8th May 1998 using microwave data from the Nobeyama Radioheliograph and Radiopolarimeter, and X-ray data from the Yohkoh satellite. Methods. Time spectra of the signals integrated over the emission source are constructed with the use of the Lomb-Scargle periodogram method, revealing the presence of a pronounced 16 s periodicity. The Pixon image reconstruction algorithm and Hanaoka algorithm are used to reconstruct images from the hard X-ray data from Yohkoh/HXT and Nobeyama Radioheliograph respectively. The phase relationship of the microwave emission was analysed with the use of cross-correlation techniques. Results. The flaring loop was resolved in the microwave band. The hard X-ray sources are found to be located near the footpoint and at the loop apex determined by the soft X-ray image. The apex source is much fainter than footpoint one. In microwave, all parts of the loop are seen to oscillate with the same period and almost in phase. It was not possible to determine the spatial structure of the oscillation in the hard X-ray band. The period and the coherent spatial structure of the oscillation are indicative of the presence of either an MHD sausage mode or a periodic regime of magnetic reconnectio

A weakly nonlinear Alfvénic pulse in a transversely inhomogeneous medium

The interaction of a weakly nonlinear Alfvénic pulse with an Alfvén speed inhomogeneity in the direction perpendicular to the magnetic field is investigated. Identical to the phase mixing experienced by a harmonic Alfvén wave, sharp transverse gradients are generated in the pulse by the inhomogeneity. In the initial stage of the evolution of an initially plane Alfvénic pulse, the transverse gradients efficiently generate transversely propagating fast magnetoacoustic waves. However, high resolution full MHD numerical simulations of the developed stage of the pulse evolution show that the generation saturates due to destructive wave interference. It is shown that the weakly non-linear description of the generated fast magnetoacoustic wave is well described by the driven wave equation proposed in Nakariakov et al. (1997), and a simple numerical code (2D MacCromack), which solves it with minimal CPU resources, produces identical results to those obtained from the full MHD code (Lare2d, Arber et al. 2001). A parametric study of the phenomenon is undertaken, showing that, contrary to one's expectations, steeper inhomogeneities of the Alfvén speed do not produce higher saturation levels of the fast wave generation. There is a certain optimal gradient of the inhomogeneity that ensures the maximal efficiency of the fast wave generation

Seismology of curved coronal loops with vertically polarised transverse oscillations

Aims. Using a model of vertically polarised fast magnetoacoustic waves in curved coronal loops, the method of coronal seismology is applied to observations of transverse loop oscillations. Methods. A coronal loop is modeled as a curved magnetic slab in the zero plasma-β limit. For an arbitrary piece-wise continuous power law equilibrium density profile, the dispersion relation governing linear vertically polarised fast magnetoacoustic kink waves is derived. The ways in which this model can be used for coronal seismology are explored and applied to two observational examples. Results. The Alfvén speed and equilibrium density profile are determined from observations. It is shown that the mechanism of lateral leakage of fast magnetoacoustic kink oscillations described in this model is efficient. In fact, the damping is so efficient that in order to match predicted values with observational ones, either the loop needs to be highly contrasted or the transverse Alfvén speed profile needs to be close to linear. Possible improvements to make the modeling of lateral wave leakage in loops more realistic, allowing a lower damping efficiency, are discussed

Fast magnetoacoustic wave trains in magnetic funnels of the solar corona

Context: Fast magneto-acoustic waves are highly dispersive in waveguides, so they can generate quasi-periodic wave trains if a localised, impulsive driver is applied. Such wave trains have been observed in the solar corona and may be of use as a seismological tool since they depend upon the plasma structuring perpendicular to the direction of propagation. Aims. We extend existing models of magnetoacoustic waveguides to consider the effects of an expanding magnetic field. The funnel geometry employed includes a field-aligned density structure. Methods: We performed 2D numerical simulations of impulsively generated fast magneto-acoustic perturbations. The effects of the density contrast ratio, density stratification, and spectral profile of the driver upon the excited wave trains were investigated. Results: The density structure acts as a dispersive waveguide for fast magneto-acoustic waves and generates a quasi-periodic wave train similar to previous models. The funnel geometry leads to generating additional wave trains that propagate outside the density structure. These newly discovered wave trains are formed by the leakage of transverse perturbations, but they propagate upwards owing to the refraction caused by the magnetic funnel. Conclusions: The results of our funnel model may be applicable to wave trains observed propagating in the solar corona. They demonstrate similar properties to those found in our simulations

Quasi-periodic modulation of solar and stellar flaring emission by magnetohydrodynamic oscillations in a nearby loop

We propose a new model for quasi-periodic modulation of solar and stellar flaring emission. Fast magnetoacoustic oscillations of a non-flaring loop can interact with a nearby flaring active region. This interaction occurs when part of the oscillation situated outside the loop reaches the regions of steep gradients in magnetic field within an active region and produces periodic variations of electric current density. The modulation depth of these variations is a few orders of magnitude greater than the amplitude of the driving oscillation. The variations of the current can induce current-driven plasma micro-instabilities and thus anomalous resistivity. This can periodically trigger magnetic reconnection, and hence acceleration of charged particles, producing quasi-periodic pulsations of X-ray, optical and radio emission at the arcade footpoints

Wave dynamics in a sunspot umbra

The high spatial and time resolution data obtained with SDO/AIA for the sunspot in active region NOAA 11131 on 08 December 2010 were analysed with the time-distance plot technique and the pixelised wavelet filtering method. Oscillations in the 3 min band dominate in the umbra. The integrated spectrum of umbral oscillations contains distinct narrowband peaks at 1.9 min, 2.3 min, and 2.8 min. The power significantly varies in time, forming distinct oscillation trains. The oscillation power distribution over the sunspot in the horizontal plane reveals that the enhancements of the oscillation amplitude, or wave fronts, have a distinct structure consisting of an evolving two-armed spiral and a stationary circular patch at the spiral origin, situated near the umbra centre. This structure is seen from the temperature minimum to the corona. In time, the spiral rotates anti-clockwise. The wave front spirality is most pronounced during the maximum amplitude phases of the oscillations. In the low-amplitude phases the spiral breaks into arc-shaped patches. The 2D cross-correlation function shows that the oscillations at higher atmospheric levels occur later than at lower layers. The phase speed is estimated to be about 100 km/s. The fine spectral analysis shows that the central patch corresponds to the high-frequency oscillations, while the spiral arms highlight the lower-frequency oscillations in the 3-min band. The vertical and horizontal radial structure of the oscillations is consistent with the model that interprets umbral oscillations as slow magnetoacoustic waves filtered by the atmospheric temperature non-uniformity in the presence of the magnetic field inclination from the vertical. The mechanism for the polar-angle structure of the oscillations, in particular the spirality of the wave fronts, needs to be revealed.Comment: 8 pages, 9 figures, Astronomy and Astrophysics, 201

Fast magnetoacoustic waves in curved coronal loops. I, Trapped and leaky modes

A study of vertically polarised fast magnetoacoustic waves in a curved coronal loop is presented. The loop is modeled as a semi-circular magnetic slab in the zero plasma-β limit. The governing equations for linear waves are derived. We show that the wave mode behaviour depends on the slope of the equilibrium density profile, which is modeled as a piece-wise continuous power law curve of index α. For all profiles, except for α = −4, wave modes are not trapped in the loop and leak out into the external medium through wave tunneling. The particular case of α = −4, which corresponds to a linearly increasing Alfvén speed profile, is examined in more detail as this is the only model that can support trapped wave modes. We compare the results with a straight slab model and find similar behaviour. Coupling between sausage and kink wave modes has not been found in the model

Motion magnification in coronal seismology

We introduce a new method for the investigation of low-amplitude transverse oscillations of solar plasma non-uniformities, such as coronal loops, individual strands in coronal arcades, jets, prominence fibrils, polar plumes, and other contrast features, observed with imaging instruments. The method is based on the two-dimensional dual tree complex wavelet transform (DT$\mathbb{C}$WT). It allows us to magnify transverse, in the plane-of-the-sky, quasi-periodic motions of contrast features in image sequences. The tests performed on the artificial data cubes imitating exponentially decaying, multi-periodic and frequency-modulated kink oscillations of coronal loops showed the effectiveness, reliability and robustness of this technique. The algorithm was found to give linear scaling of the magnified amplitudes with the original amplitudes provided they are sufficiently small. Also, the magnification is independent of the oscillation period in a broad range of the periods. The application of this technique to SDO/AIA EUV data cubes of a non-flaring active region allowed for the improved detection of low-amplitude decay-less oscillations in the majority of loops.Comment: Accepted for publication in Solar Physic

MHD waves at a spherical interface modelling coronal global EIT waves

Energetically eruptive events such as flares and coronal mass ejections (CMEs) are known to generate global waves, propagating over large distances, sometimes comparable to the solar radius. In this contribution EIT waves are modelled as waves propagating at a spherical density interface in the presence of a radially expanding magnetic field. The generation and propagation of EIT waves is studied numerically for coronal parameters. Simple equilibria allow the explanation of the coronal dimming caused by EIT waves as a region of rarified plasma created by a siphon flow