3.4 Spatial distribution of oscillations

It now appears well established that small amplitude, periodic changes in solar prominences do not normally affect the whole object at a time, but are of local nature instead, and that this conclusion is independent of the oscillatory period. Thus, variations with a given period are seldom reported to occur over the whole prominence (see Tsubaki and Takeuchi, 1986Jump To The Next Citation Point). One case in which a periodic signal is present in all slit positions was presented by Balthasar et al. (1988), who detected long-period oscillations over the whole height of three limb prominences by placing a vertical spectrograph slit on them. In contrast, it is usually found that only a few consecutive points along the slit present time variations with a definite period, while all other points lack any kind of periodicity (e.g., Tsubaki and Takeuchi, 1986Jump To The Next Citation Point; Suematsu et al., 1990Jump To The Next Citation Point; Balthasar et al., 1993; Balthasar and Wiehr, 1994; Suetterlin et al., 1997; Molowny-Horas et al., 1997Jump To The Next Citation Point).

The works mentioned in the previous paragraph use a spectrograph slit to detect oscillations; obviously, a two-dimensional data set is much more advantageous when it comes to ascertaining which part of a prominence is affected by oscillations. Terradas et al. (2002Jump To The Next Citation Point) reported on the propagation of waves over a large region (some 54,000 km by 40,000 km in size) in a limb prominence and high spatial resolution observations with Hinode/SOT (Berger et al., 2008Jump To The Next Citation Point) also show oscillations that affect a small area of a prominence. See also the discussion in Section 3.6.4 of the work by Lin et al. (2007Jump To The Next Citation Point) that gives evidence of coherent Doppler shift oscillations over a rectangular area 3.4 arcsec × 10 arcsec in size.

Other observations with high spatial resolution have shown that individual threads or small groups of threads may oscillate independently from the rest of the prominence with their own periods (Thompson and Schmieder, 1991Jump To The Next Citation Point; Yi et al., 1991Jump To The Next Citation Point). Figure 4View Image displays some of the results in Yi et al. (1991Jump To The Next Citation Point). It is clear that threads 1, 4, 13, and 14 oscillate in phase with their own period, which ranges from 9 to 14 min. In addition, Tsubaki et al. (1988Jump To The Next Citation Point) obtained successively two time series of spectra by placing the spectrograph slit first at a height of 30,000 km above the solar limb and next 40,000 km above the limb. A group of vertical threads detached from the prominence main body displayed 10.7-min periodic variations at both heights, which was a first indication that threads can oscillate collectively. After these preliminary studies, much attention has been given to the detection of thread oscillations (Lin et al., 2003Jump To The Next Citation Point; Lin, 2005Jump To The Next Citation Point; Lin et al., 2005, 2007Jump To The Next Citation Point, 2009Jump To The Next Citation Point; Okamoto et al., 2007Jump To The Next Citation Point; Ning et al., 2009bJump To The Next Citation Point,aJump To The Next Citation Point). Apart from reporting on thread oscillations, these works have also provided detailed information about wave features such as the period, wavelength, and phase speed. Because of the importance of these quantities in the seismology of prominences, these works are discussed in more detail in Section 3.6.4.

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Figure 4: Temporal variation of the Doppler velocity along threads of a solar filament. Numbers on the right label the various threads. For each thread, the curves correspond to the Doppler velocity measured at different points along the thread (from Yi et al., 1991Jump To The Next Citation Point).

There is also some evidence that velocity oscillations are more easily detected at the edges of prominences or where the material seems fainter, while they sometimes look harder to detect at the prominence main body (Tsubaki and Takeuchi, 1986Jump To The Next Citation Point; Tsubaki et al., 1988Jump To The Next Citation Point; Suematsu et al., 1990Jump To The Next Citation Point; Thompson and Schmieder, 1991Jump To The Next Citation Point; Terradas et al., 2002Jump To The Next Citation Point). This result has occasionally been interpreted as the consequence of integrating the velocity signals coming from various moving elements along the line-of-sight. This explanation, however, would imply the presence of broader spectral lines at the positions showing periodic variations, which is not observed, so other explanations are also possible (Suematsu et al., 1990Jump To The Next Citation Point). Mashnich et al. (2009a,b) gave evidence that different parts of filaments may support different periodicities: short-period variations (with periods shorter than 10 min) had coherence scales shorter than 10 arcsec and were detected near the edges of filaments placed close to the Sun’s central meridian. These oscillations, hence, were characterized preferentially by vertical plasma displacements. On the other hand, variations with period around 1 h occured in different positions of the filament and the size of the oscillating area was not larger than 15 – 20 arcsec. In addition, these oscillations had an amplitude that increased by an order of magnitude or more in filaments far from the solar center compared to those near the center of the Sun’s disk. Then, these oscillations showed a mainly horizontal velocity.

More information about the spatial distribution of prominence oscillations comes from Ning et al. (2009bJump To The Next Citation Point), who detected transverse oscillations of 13 threads in a quiescent prominence observed with Hinode/SOT. These authors found that prominence threads in the upper part of the prominence oscillate independently, whereas oscillations in the lower part of the prominence do not follow this pattern. Furthermore, the oscillatory periods were short (between 210 to 525 s), with the dominant one appearing at 5 min (more information is given in Section 3.6.4). In a subsequent work, Ning et al. (2009aJump To The Next Citation Point) used the same data set to analyze the motions of two spines in the same quiescent prominence. The spine is synonymous with the horizontal fine structure along the filament axis and is the highest part of the prominence. In the observations of Ning et al. (2009aJump To The Next Citation Point), the spines showed drifting motions that were removed by the subtraction of a linear trend, which allowed the authors to uncover the existence of oscillations with a very similar period (around 98 min) in both structures. Further insight into the behaviour of the spines comes from a fit of a function A [0]sin(2πt∕A [1 ] + A [2])exp (A[3]t) to the detrended data. Here A[0] is the oscillatory amplitude, A [1 ] the period, A[2] the oscillatory phase, and − 1∕A [3] the damping time. The detrended signals and the function fits are displayed in Figure 5View Image, which includes the fitted parameters, that give the following information: from the oscillatory amplitude, the peak velocities of the spines are 1 and 5 km s–1. The periods are almost identical (96.5 and 98.5 min) and the phase difference is 149°, which means that the spines oscillated almost in anti-phase. These results about the period and phase were taken by Ning et al. (2009aJump To The Next Citation Point) as an indication of a collective behaviour of the two structures. These authors considered an analogy with the transverse MHD oscillations of two cylinders (a problem studied by Luna et al., 2008Jump To The Next Citation Point, and discussed in Section 4.4) and concluded that a coupling of kink-like modes can give the observed behaviour. In particular, the Ax mode of the system has motions resembling the anti-phase oscillatory behaviour found by Ning et al. (2009aJump To The Next Citation Point).

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Figure 5: Displacement of two spines of a quiescent prominence (thin lines) and best fits using the function A [0]sin(2πt∕A [1 ] + A [2])exp (A[3]t) (thick lines). The fitted values of the parameters A [0] to A [3] are written at the bottom of the figure. Note that the values of A[3] displayed in the figure cannot be correct since they give a very strong amplification/damping that totally disagrees with the almost undamped behaviour of the thick lines (from Ning et al., 2009aJump To The Next Citation Point).

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