Aplicación y valoración de los resultados (Anexos 9 y 10).

Transverse oscillations of coronal loops were first observed by Aschwanden et al. (1999) and Nakariakov et al. (1999) in the EUV band, inducing a number of observational studies and theoretical modelling. The oscillations are seen as transverse displacements of bright loops, with periods from a few minutes to several tens of minutes. Different loops have different well defined periods, which suggests that the oscillations have natural frequencies of the loop system. The beginning of the oscillation usually coin- cides with a flare or CME with an epicentre nearby (see Sec. 9.3). The oscillations are almost harmonic. After the excitation, kink oscillations experience a rapid decay,

typically fitted with an exponential function with the characteristic decay time equal to 2–4 oscillation periods (although a Gaussian function may be more appropriate, see Sec. 5.5). Hence the quality factor of the oscillations, or the Q-factor, can be defined

asQ=πτ /P and is between 6–25. The decay time scales linearly with the period of

oscillations (see Ofman and Aschwanden 2002, and also Fig. 24). The strong damping is attributed to the effect of resonant absorption, discussed in Sec. 5.5, however, other mechanisms are possible, such as wave leakage, and phase mixing (see Ofman and As- chwanden 2002, for discussion). The amplitude of the oscillations is typically several Mm, that is several minor radii of the loop (radius of the loop’s flux tube cross-section). The typical periods range from a few minutes in short EUV loops to several hours in dense cool filaments of prominences.

The loops of different lengths are observed to have different periods of oscillations. In almost all observed cases only a few periods of oscillations are seen. Occasionally, together with the displacement, periodic variation of the loop brightness is observed. This effect is most likely connected with the periodic variation of the column depth of the oscillating loop segment, caused by its displacement with respect to the LOS (Cooper et al. 2003a; Verwichte et al. 2009).

In the vast majority of cases the oscillations have horizontal polarisation, in other words the loop displacement is parallel to the surface of the Sun. The same polarisation is detected by some occasional quasi-stereoscopic observations (Verwichte et al. 2009). There have not been observational reports of the circular or elliptical polarisation. Usually only the global mode is seen, with the maximum displacement amplitude near the loop top, and only in a few cases higher longitudinal harmonics have been detected (Andries et al. 2009). In all cases, the nodes of the oscillation are observed near the loop footpoints, hence the dense plasma of the chromosphere acts as a rigid wall for the transverse oscillations (c.f. the effect of the ionosphere on the magnetospheric oscillations).

The period of standing kink oscillations is approximately determined as

Pkink≈2L/nLVK, (41)

whereLis the loop length, andnL is the longitudinal harmonic number that indicates

the number of half-wavelengths along the loop (Fig. 26). However, there is a significant deviation, up to 10%, from the equidistant spectrum, i.e., the ratio of the global mode period to the period of the second harmonics is less than 2. This effect is attributed to the interplay between density stratification and flux tube expansion: the Alfv´en speed and hence the kink speed at the loop top and the footpoints are different from each other. The global mode with the maximum at the loop top then samples a lower kink speed than the second harmonics that samples the kink speed in the loop legs (see Andries et al. 2009, for detailed discussion).

Very recently a new regime of standing kink oscillations was discovered (Wang et al. 2012; Nistic`o et al. 2013; Anfinogentov et al. 2013). It was found out that in addition to the intensively studied large-amplitude rapidly-decaying regime, there are also low-amplitude undamped oscillations, near the very threshold of the available spa- tial resolution of the observational instruments. Fig. 25 shows both the decaying and decay-less regimes for the same loop. Oscillation periods in this new regime are not different from the large-amplitude kink oscillations in the same loop. The amplitude is lower than one minor radius of the loop. All segments of the loop are seen to oscillate in phase and hence the oscillations are standing. Usually several cycles of the oscilla- tion are well seen, with the amplitude remaining constant or even growing during the

0 L/2 L 0

Coordinate along loop

Amplitude

0 L/2 L

0

Coordinate along loop

Amplitude

0 L/3 2L/3 L

0

Coordinate along loop

Amplitude

Fig. 26 Displacements of the plasma in the global mode (top left), its second harmonic (top right), and third harmonic (bottom) for a loop of lengthL. The black line shows the position of the undisturbed loop and the red dotted and blue dashed lines indicate the extrema of displacement, corresponding to different phases of the oscillation.

observation. There is no observational indication that the oscillation is excited by any bursty energy release. It is very likely that the apparent end of the oscillation is not caused by any decay, but is simply connected with the deterioration of the observation conditions. The physical mechanism for the decay-less oscillations is still subject to discussion, while the constant amplitude may result from some balance between per- sistent external driving, e.g. by granulation motions, and damping, e.g. by resonant absorption.

Despite intensive study, there are still a number of open questions connected with kink modes. More specifically:

– The excitation mechanism in both decaying and decay-less regimes needs to be revealed.

– In the decaying large-amplitude regime, what is the mechanism for the selectivity of the excitation: why some loops gain the large initial displacement while similar loops situated nearby do not?

– Also, what causes the large initial displacement of the loop in this regime? (See discussion in Sec. 9.3.)

– Why is the horizontal polarisation predominantly excited?

– If the rapid decay of kink oscillations is indeed caused by resonant absorption, the transfer of energy from the kink oscillation to the torsional Alfv´enic motions needs to be observed at least indirectly, e.g. via the increase in the non-thermal broadening of coronal emission lines.

– It is also unclear whether what we see as an oscillating loop is the actual loop, or it is a bundle of smaller scale plasma threads. For sharp transverse profiles of the plasma in the oscillating loop, resonant absorption efficiency is suppressed, and oscillations of good quality should be observed. But, they are not: in all observed cases the decay time is not longer than a few oscillation periods.

Fig. 27 Left: Radio images of an oscillating flaring loop, made at 34 GHz (filled pixels) and 17 GHz (dotted contour curves). The black contour shows the positioning of the 13.9– 22.7 keV hard X-ray sources. The solid line indicates the solar limb. The dotted curves show the heliographic coordinate grid. Centre: The time profiles of the total signal, the modulation depth of the gyrosynchrotron signal at 17 GHz from the Southern leg, the loop top, and the Northern leg of the loop. Left: Fourier power spectra of the modulation depth signals. (From Melnikov et al. 2005).