In addition, Equation (34) may give unrealistically short decay times comparable with the oscillation period. It is not clear how the phenomenon of resonant absorption can happen in those cases when the decay time is comparable with the oscillation period and, consequently, the oscillation is not harmonic, making the resonance impossible. In any case, resonant absorption remains a plausible interpretation of the decay.
Another alternative interpretation is connected with the effect of phasemixing (Roberts, 2000; Ofman and Aschwanden, 2002) (see Section 2.2.2). The decay of a standing Alfvén waves by phasemixing, given by Equation (17), becomes after assuming that :
In principle is the shear Reynolds number, , with the kinematic shear viscosity coefficient. If we take the theoretical values for , then the decay time due to phasemixing is orders of magnitude longer than the observed decay. Ofman and Aschwanden (2002) claimed that, due to microturbulence or kinetic processes modifying the velocity distribution of ions, could be of the same order as the bulk viscosity coefficient, practically returning back to the idea suggested by Nakariakov et al. (1999). Hence, decay due to phasemixing can be of the same order as the observed decay. We would like to emphasise that in the case discussed here, the phase mixing mechanism does not involve the torsional modes, but is connected with kink perturbations of neighbouring loops.A different approach to the problem is based on the leakage of wave energy from the loop. Cally (1986, 2003) showed that the fast kink mode is almost identical to a fast leaky kink mode. In the long wavelength limit both modes propagate at the kink speed. In the limit of the plasma tending to zero, the amplitude of the leaky kink mode decreases as it radiates into the coronal environment with a decay time (Cally, 2003, note a factor error in his expression)
which, unless the loop width is considerably larger than the observed loop emission width, is too long to explain the observed decay, especially for large loops (see Figure 13). For example for a loop of length , needs to be in the range of .The wave energy may also leak through its footpoints. Roberts (2000) concluded from the theoretical study by Berghmans and de Bruyne (1995) that this type of leakage is insufficient to explain the observed decay. De Pontieu et al. (2001), though, argued that this study did not take the chromosphere into account. The amplitude decay of an Alfvén wave leaking into a chromosphere with density scaleheight , typically , is (Hollweg, 1984)
which is about five times longer than the observed decay (see Figure 13). This was confirmed by the numerical study by Ofman (2002), who also pointed out some inconsistencies in the work by De Pontieu et al. (2001). A similar study of footpoint leakage of fast kink modes themselves has not yet been undertaken but it should take into account the stratification of the external medium and the magnetic field divergence with height. Both effects are expected to increase the efficiency of the reflection of kink modes at the footpoints and, consequently, reduce the leakage.Ofman and Aschwanden (2002) suggested that observationally determined scaling laws, connecting the decay times with oscillation periods and lengths of oscillating loops, may provide some information allowing us to distinguish between the interpretations discussed above. Indeed different decay mechanisms give different scaling laws: coronal leakage (), footpoint leakage (), resonant absorption (), and phasemixing (). By using the fact that the period is proportional to the loop length, one can be eliminated in favour of the other.
Ofman and Aschwanden (2002) determined scaling laws from observational decay times measured by Nakariakov et al. (1999) and Aschwanden et al. (2002). In particular they found that . They concluded that the mechanism of phasemixing agrees best with the scaling laws. They, though, assumed that the length in Equation (35) is proportional to the length of the loop to obtain a modified scaling law for phasemixing:
There is indeed a good correspondence between the theoretical and observational power law index. However, it is not clear why should be proportional to . If the original scaling law for phasemixing is considered, then the difference is larger than one standard deviation. Also, the mechanism of resonant absorption, which has a power law index of 1 falls within one standard deviation of the observationally determined power law index and can, therefore, not be excluded. The mechanisms of coronal and footpoint leakage have power law indices of and , respectively, which is clearly not consistent with observations.Figure 13 shows the observationally determined decay times as a function of wavelength and period and uses measurements from Nakariakov et al. (1999), Aschwanden et al. (2002), Wang and Solanki (2004), and Verwichte et al. (2004), which adds two more measurements compared with the study of Ofman and Aschwanden (2002). We have to bear in mind, though, that the measurement from Wang and Solanki (2004) refers to a vertically polarised oscillation and that the measurement from Verwichte et al. (2004) is an averaged value from seven damped kink oscillations in a prominence driven loop arcade. The data points are fitted by power laws which have the dependencies and . The dependence on the wavelength seems to favour phasemixing, without excluding resonant absorption, and the dependence on period seems to favour resonant absorption but is also consistent with the modified scaling law for phasemixing. In any case, more examples are needed as the data are too scattered.

Further development of this discussion on the decay of kink oscillations is connected with the improvement of the observational statistics and highresolution 3D numerical modelling of oscillating loops. In particular, an important issue is whether the loop crosssection remains unperturbed during kink oscillations. Also, the question of the excitation of these modes, connected with the observational fact that the kink oscillations are a rather rare phenomenon, is still open.
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