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

Wide-spectrum slow magnetoacoustic waves in coronal loops

A model interpreting variations of EUV brightness upward propagating in solar coronal loops as slow magnetoacoustic waves is developed. A loop is considered to have a non-zero plane inclination angle and offset of the circular loop centre from the baseline. The model also incorporates effects of dissipation and gravitational stratification. A linear evolutionary equation is derived and applied to investigations of slow wave dynamics. Both the non-zero plane inclination and the offset decrease the growth of the wave amplitude due to stratification. It is shown that wide-spectrum slow magnetoacoustic waves, consistent with currently available observations in the low frequency part of the spectrum, can provide a rate of heat deposition sufficient to heat the loop. In this scenario, the heat would be deposited near the loop footpoints, which agrees with the current observational data

Standing kink waves in sigmoid coronal loops : implications for coronal seismology

Using full three-dimensional magnetohydrodynamic numerical simulations, we study the effects of magnetic field sigmoidity or helicity on the properties of the fundamental kink oscillation of solar coronal loops. Our model consists of a single denser coronal loop, embedded in a plasma with dipolar force-free magnetic field with a constant α-parameter. For the loop with no sigmoidity, we find that the numerically determined oscillation period of the fundamental kink mode matches the theoretical period calculated using WKB theory. In contrast, with increasing sigmoidity of the loop, the actual period is increasingly smaller than the one estimated by WKB theory. Translated through coronal seismology, increasing sigmoidity results in magnetic field estimates that are increasingly shifting toward higher values, and even surpassing the average value for the highest α value considered. Nevertheless, the estimated range of the coronal magnetic field value lies within the minimal/maximal limits, proving the robustness coronal seismology. We propose that the discrepancy in the estimations of the absolute value of the force-free magnetic field could be exploited seismologically to determine the free energy of coronal loops, if averages of the internal magnetic field and density can be reliably estimated by other methods

A three dimensional magnetohydrodynamic pulse in a transversely inhomogeneous medium

Interaction of impulsively generated MHD waves with a one-dimensional plasma inhomogeneity, transverse to the magnetic field, is considered in the three-dimensional regime. Because of the transverse inhomogeneity, MHD fluctuations, even if they do not include initially any density perturbation, evolve toward states where the compressible components tend to become predominant. The propagating MHD pulse asymptotically reaches a quasi-steady state with the final levels of density perturbation weakly depending on the degree of non-planeness of the pulse in the homogeneous transverse direction and somewhat stronger depending on plasma . Our study demonstrates the necessity of incorporation of compressible and 3D effects in theory of Alfvén wave phase mixing. However, as far as the dynamics of weakly non-plane Alfvén waves is concerned it can still be qualitatively understood in terms of the previous 2.5D models

A developed stage of Alfven wave phase mixing

Alfven wave phase mixing is an extensively studied mechanism for dissipating wave energy in an inhomogeneous medium. It is common in the vast majority of phase mixing papers to assume that even though short scale lengths and steep gradients develop as a result of phase mixing, nonlinear wave coupling does not occur. However, weakly nonlinear studies have shown that phase mixing generates magnetoacoustic modes. Numerical results are presented which show the nonlinear generation of magnetosonic waves by Alfven wave phase mixing. The efficiency of the effect is determined by the wave amplitude, the frequency of the Alfven waves and the gradient in the background Alfven speed. Weakly nonlinear theory has shown that the amplitude of the fast magnetosonic wave grows linearly in time. The simulations presented in this paper extend this result to later times and show saturation of the fast magnetosonic component at amplitudes much lower than that of the Alfven wave. For the case where Alfven waves are driven at the boundary, simulating photospheric footpoint motion, a clear modulation of the saturated amplitude is observed. All the results in this paper are for a low amplitude (<=0.1), single frequency Alfven wave and a uniform background magnetic field in a two dimensional domain. For this simplified geometry, and with a monochromatic driver, we concluded that the nonlinear generation of fast modes has little effect on classical phase mixing

X-ray and EUV Observations of Simultaneous Short and Long Period Oscillations in Hot Coronal Arcade Loops

We report decaying quasi-periodic intensity oscillations in the X-ray (6-12 keV) and extreme ultraviolet (EUV) channels (131, 94, 1600, 304 \AA) observed by the Fermi GBM (Gamma-ray Burst Monitor) and SDO/AIA, respectively, during a C-class flare. The estimated period of oscillation and decay time in the X-ray channel (6-12 keV) was about 202 s and 154 s, respectively. A similar oscillation period was detected at the footpoint of the arcade loops in the AIA 1600 and 304 \AA channels. Simultaneously, AIA hot channels (94 and 131 \AA) reveal propagating EUV disturbances bouncing back and forth between the footpoints of the arcade loops. The period of the oscillation and decay time were about 409 s and 1121 s, respectively. The characteristic phase speed of the wave is about 560 km/s for about 115 Mm loop length, which is roughly consistent with the sound speed at the temperature about 10-16 MK (480-608 km/s). These EUV oscillations are consistent with the SOHO/SUMER Doppler-shift oscillations interpreted as the global standing slow magnetoacoustic wave excited by a flare. The flare occurred at one of the footpoints of the arcade loops, where the magnetic topology was a 3D fan-spine with a null-point. Repetitive reconnection at this footpoint could cause the periodic acceleration of non-thermal electrons that propagated to the opposite footpoint along the arcade and precipitating there, causing the observed 202-s periodicity. Other possible interpretations, e.g. the second harmonics of the slow mode are also discussed.Comment: ApJ (in press), 13 pages, 6 figure

Determination of the coronal magnetic field by coronal loop oscillations

We develop a new method for the determination of the absolute value of the magnetic field strength in coronal closed magnetic structures, based on the analysis of flare-generated oscillations of coronal loops. Interpretation of the oscillations observed in terms of global standing kink waves allows to connect the period of the oscillations and the loops length with the magnetic field strength in the loops. For loop oscillations observed with TRACE on 14th July 1998 and 4th July 1999, we estimate the magnetic field strength as 4-30 G. Using TRACE 171 Å and 195 Å images of the loop, taken on 4th July 1999 to determine the plasma density, we estimate the magnetic field in the loop as 13 +- 9 G. Improved diagnostic of the loop length, the oscillation period, and the plasma density in the loop will significantly improve the method's precision

Decay-less kink oscillations in coronal loops

Context: Kink oscillations of coronal loops in an off-limb active region are detected with the Imaging Assembly Array (AIA) instruments of the Solar Dynamics Observatory (SDO) at 171 Å. Aims: We aim to measure periods and amplitudes of kink oscillations of different loops and to determinate the evolution of the oscillation phase along the oscillating loop. Methods: Oscillating coronal loops were visually identified in the field of view of SDO/AIA and STEREO/EUVI-A: the loop length was derived by three-dimensional analysis. Several slits were taken along the loops to assemble time-distance maps. We identified oscillatory patterns and retrieved periods and amplitudes of the oscillations. We applied the cross-correlation technique to estimate the phase shift between oscillations at different segments of oscillating loops. Results: We found that all analysed loops show low-amplitude undamped transverse oscillations. Oscillation periods of loops in the same active region range from 2.5 to 11 min, and are different for different loops. The displacement amplitude is lower than 1 Mm. The oscillation phase is constant along each analysed loop. The spatial structure of the phase of the oscillations corresponds to the fundamental standing kink mode. We conclude that the observed behaviour is consistent with the empirical model in terms of a damped harmonic resonator affected by a non-resonant continuously operating external force