6.3 Seismology of propagating transverse thread oscillations

Transverse thread oscillations observed by Lin et al. (2009Jump To The Next Citation Point) and discussed in Section 3.6.4 show evidence of waves propagating along individual threads. Ten of the swaying threads were chosen by Lin et al. (2009Jump To The Next Citation Point) for further investigation, and for each selected thread two or three perpendicular cuts were made in order to measure the properties of the propagating waves. Periods and amplitudes of the waves, as well as their phase velocity, were derived for each thread. Lin et al. (2009Jump To The Next Citation Point) interpreted the observed events as propagating MHD kink waves supported by the thread body. This mode is the only one producing a significant transverse displacement of the cylinder axis. In addition, it also produces short-period oscillations of the order of minutes, compatible with the observed periods (see Section 4.4.1).

If an infinitely long, straight, cylindrical thread model, with the tube fully filled with cool and dense material (Figure 31View Image), is assumed, a comparison between the observed wave properties and the theoretical prediction can be made. This enabled Lin et al. (2009Jump To The Next Citation Point) to obtain estimates for some physical parameters of interest, namely the Alfvén speed and the magnetic field strength in the studied threads. To this end, the observed phase velocity was directly associated to the kink speed

[ ]1∕2 ck = ωk-= vAp -2ζ--- , (37 ) kz 1 + ζ
where Equation (22View Equation) for the kink frequency has been used. In this expression vAp is the Alfvén speed in the prominence thread and ζ = ρp∕ρc is the density contrast. Both quantities are unknown, hence no unique solution to Equation (37View Equation) can be obtained from the observed period alone. In the limit of high density contrast, typical of prominence plasmas, the ratio ρp∕ρc is very large and the ratio c2k∕v2Ap is almost independent from it (see Figure 63View Imagea). The kink speed can then be approximated by
√ -- ck ≈ 2vAp. (38 )
Lin et al. (2009Jump To The Next Citation Point) assumed that thread oscillations observed from the Hα sequences were the result of a propagating kink mode, which implies that the measured phase velocity, c p, is equal to the kink speed. Then, the thread Alfvén speed can be computed from
-cp- vAp ≈ √2--. (39 )

The inferred values of vAp for the ten selected threads are displayed in Table 2 in Lin et al. (2009Jump To The Next Citation Point). The results show a strong dispersion, suggesting that the physical conditions in different threads were very different in spite of belonging to the same filament. This result clearly reflects the highly inhomogeneous nature of solar prominences. Once the Alfvén speed in each thread was determined, the magnetic field strength could be computed after a value for the thread density was assumed. For the analyzed events, and considering a typical value ρp = 5 × 10–11 kg m–3, magnetic field strengths in the range 0.9 – 3.5 G were obtained (see Figure 63View Imageb).

View Image

Figure 63: (a) Ratio 2 2 ck∕v Ap (solid line) as a function of the density contrast, ζ. The dotted line corresponds to the value of the ratio 2 2 ck∕vAp for ζ → ∞. (b) Magnetic field strength as a function of the internal density, ρp, corresponding to four selected threads (from Lin et al., 2009Jump To The Next Citation Point).

  Go to previous page Go up Go to next page