3.5 Wave damping and oscillation lifetime

A visual inspection of the data sometimes reveals the existence of outstanding periodic variations and use of the FFT, or even better the periodogram (which yields an increased frequency resolution), is only necessary to derive a precise value of the period. In such cases it usually turns out that the oscillatory amplitude tends to decrease in time in such a way that the periodicity totally disappears after a few periods (e.g., Landman et al., 1977; Tsubaki and Takeuchi, 1986Jump To The Next Citation Point; Wiehr et al., 1989; Molowny-Horas et al., 1999Jump To The Next Citation Point; Terradas et al., 2002Jump To The Next Citation Point; Lin, 2005Jump To The Next Citation Point; Berger et al., 2008Jump To The Next Citation Point; Ning et al., 2009bJump To The Next Citation Point,a), just as found in large amplitude oscillations. This is then interpreted as a sign of wave damping, although the specific mechanism has not been commonly agreed on (see Section 5 for a summary of theoretical results on this topic).

Reliable values of the damping time, τ, have been derived by Molowny-Horas et al. (1999Jump To The Next Citation Point) after fitting the function v0cos(ωt + ϕ) exp(− t∕τ) to Doppler velocity time series recorded simultaneously in different positions of a polar crown prominence (Figure 6View Image). The values of τ thus obtained are usually between 1 and 4 times the corresponding period, in agreement with previous observational reports. In addition, there is one particular case for which the line-of-sight velocity grows in time, but no interpretation of this result is given by these authors.

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Figure 6: Observed Doppler velocity (dots) and fitted function (continuous line) versus time at two different positions in a quiescent prominence. The period is 70 min in both positions and the damping time is 140 and 101 min, respectively. The function fitted to the observational data is of the form v0 cos(ωt + ϕ)exp (− t∕τ) (adapted from Molowny-Horas et al., 1999Jump To The Next Citation Point).

Terradas et al. (2002Jump To The Next Citation Point) performed a deeper investigation of the data of Molowny-Horas et al. (1999Jump To The Next Citation Point). After fitting the same sinusoidal function to all points in the two-dimensional field of view, Terradas et al. (2002Jump To The Next Citation Point) generated two-dimensional maps of various oscillatory parameters, such as the period, damping time and velocity amplitude (Figure 7View Image). Terradas et al. (2002Jump To The Next Citation Point) stressed that there is a region near the prominence edge (54,000 km by 40,000 km in size) in which the correlation coefficient of the fit is rather large and in which the period and damping time are very uniform. The mentioned region is around position x = 80, y = 50 of Figure 7View Image. In Section 3.6.3 we discuss other aspects of this work, which is unique since it is one of a few in which coherent wave behaviour has been found in a large area of a prominence and the only one in which the wave parameters in a two-dimensional prominence area have been computed.

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Figure 7: Results of fitting the function of Figure 6View Image to the Doppler velocity in the whole two-dimensional field of view. The spatial distribution of the fitted period and damping time is shown in the top panels, while that of the correlation coefficient and fitted amplitude is displayed in the bottom panels. The continuous white line (black in the top left panel) represents the approximate position of the prominence edge. The photosphere is slightly outside the image top (from Terradas et al., 2002Jump To The Next Citation Point).

Very often the presence of a periodic signal in the data is not obvious under a visual scrutiny and the FFT or periodogram simply provide the period of such signal, but not its duration. Dividing the time series into shorter intervals and calculating the Fourier spectrum of each of them allows to narrow down the epoch of occurrence of the oscillation. Wiehr et al. (1984) followed this procedure and determined that a 3-min oscillation found in a 2-h Doppler velocity record only existed in the last 40 min of the sample. The wavelet technique, however, is much better suited for the calculation of lifetimes since it can be used to precisely determine the beginning and end of the time interval in which a periodicity, previously detected in the Fourier spectrum, takes place. This approach was used by Molowny-Horas et al. (1997Jump To The Next Citation Point), who obtained a period around 7.5 min in 16 consecutive points, spanning a distance of 7300 km, along the spectrograph slit. The time/frequency diagram of the corresponding 16 time signals indicates that the periodic perturbation is not present for the whole duration of the data and that it only operates for about 12 min (Figure 8View Image). Molowny-Horas et al. (1998) performed a similar study by placing the slit on a filament, rather than on a limb prominence, with comparable results. Two oscillations with periods around 2.7 and 12.5 min were present at consecutive points covering some 2000 and 3300 km, respectively. From the wavelet analysis, the lifetimes of these two perturbations are of the order of 10 and 20 min, respectively. These results provide convincing evidence of the train-like character of some prominence oscillations. Further details of the work by Molowny-Horas et al. (1997Jump To The Next Citation Point) are provided in Section 3.6.2.

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Figure 8: Left: Time-frequency diagrams of the Doppler velocity at several aligned, equispaced points in a quiescent prominence. White/black correspond to large/small wavelet power. Right: Time variation of wavelet power from the diagrams on the left column for a period of 7.5 min (i.e., frequency around 2.2 mHz). The presence of power peaks suggests a finite duration of the perturbation, while the linear displacement of these peaks at the seven positions from t = 28 min to t = 42 min is an indication of a disturbance travelling with a group velocity vg ≥ 4.4 km s–1 (from Molowny-Horas et al., 1997Jump To The Next Citation Point).

Oscillations of prominence threads also display fast attenuation. For example, Lin (2005Jump To The Next Citation Point) detected several periodicities over large areas of a filament, with maximum power at periods of 26, 42, and 78 min. Pronounced Doppler velocity oscillations with 26 min period could only be observed for 2 – 3 periods, after which they became strongly damped.

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