Régnier et al. (2001) consider the possible theoretical modes that can explain their observations of oscillations in an active region filament. The slab model with a uniform and inclined magnetic field by Joarder and Roberts (1993b) is used (see Figure 29). The dispersion relations for Alfvén modes and magnetoacoustic modes are considered. They provide the frequency of six fundamental modes: the symmetric Alfvén, slow and fast kink modes and the antisymmetric Alfvén, slow and fast sausage modes, as a function of the prominence parameters. Observations provide with estimates for the width (8000 km) and length (63,000 km) of the filament. Assumptions on other parameters, such as the temperature of the filament (8000 K) and of its environment (106 K), the density of the slab (1012 cm–3), the magnetic field strength (20 G) and for the angle between the magnetic field and the long axis of the slab (25°) are made. The dispersion relations are then solved by using these parameters and the corresponding periods are obtained and classified.
Observations and Fourier analysis of Doppler velocity time series enable Régnier et al. (2001) to detect intermediate (between 5 and 20 min in this case) and long (> 40 min) period oscillations. From the comparison between the observed and calculated frequencies, an identification method of the oscillation modes in the observed filament is presented. The method makes use of the fact that the frequency ratio of the fundamental even Alfvén mode to the fundamental odd Alfvén mode only depends on the ratio of the half-with of the slab to the half-length of the filament. This quantity is measurable. The same applies to the frequency ratios involving the slow kink/sausage and fast kink/sausage modes. Parametric calculations for the frequencies as a function of the magnetic field strength and the inclination angle, while keeping the slab density constant, are next performed. A diagnostic of the observed filament is obtained by looking for the parameters values that enable the matching of theoretical and observed frequencies. By following this method, the angle between the magnetic field and the long axis of the slab is estimated to be 18°. Using this value, an algebraic relation for the magnetic field strength as a function of the slab density is derived.
A more involved and ambitious diagnostic, using the Joarder and Roberts (1993b) slab model, was performed by Pouget et al. (2006). The long duration and high temporal resolution observations with CDS/SoHO enable these authors to detect and measure the entire range of periodicities theoretically expected in a filament. In particular both the short (less that 10 min) and the long ones (more than 40 min) are detected.
The detailed analysis of three filaments is presented. The seismic inversion technique closely follows that by Régnier et al. (2001), in the sense that the first step towards the diagnostic is the use of frequency ratios between fundamental even/odd (kink/sausage) modes. These ratios only depend on the ratio of the filament half-width to its half-length. Once this ratio is measured, with a given uncertainty, Pouget et al. (2006) assume that their 16-h long observation has allowed them to observe the six modes of interest, since the slowest mode is expected at a period of 5 h, for standard prominence parameters.
The inversion method first assigns a possible triplet of measured frequencies to the 3 odd fundamental frequencies (odd Alfvén, slow sausage, and fast sausage modes). The coherence of each choice is examined against two tests. The first requires to find three corresponding even frequencies, with the condition that the even/odd frequency ratios are consistent with the measured half-width to half-length ratio. The second involves the inferred values for the density, temperature, magnetic field inclination angle, and magnetic field strength to be consistent with typical values reported in the literature. For each test, if the test was negative, the full triplet was changed and the series started again. On the contrary, if the tests succeeded, Pouget et al. (2006) considered that the six fundamental modes were identified.
The three filament observations led to coherent diagnostics and a single possible set of frequencies was found for each observation. The importance of this study is its ability to simultaneously determine the values of the inclination angle, temperature, and Alfvén speed for the same prominence. The drawback is that the modeling, as in Régnier et al. (2001), does not permit to capture the highly inhomogeneous nature of prominences.
Living Rev. Solar Phys. 9, (2012), 2
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