5.6 Damping by wave leakage

The solutions obtained for the oscillations of prominence line current models (van den Oord and Kuperus, 1992Jump To The Next Citation Point; Schutgens, 1997aJump To The Next Citation Point,bJump To The Next Citation Point; van den Oord et al., 1998Jump To The Next Citation Point) mentioned in Section 4.3 suggest the existence of time amplification and damping of the studied oscillations. While the amplification should be linked to a prominence destabilization, the attenuation seems to be very efficient for many of the considered parameter values, and the ratio of the damping time to the period is between 1 and 10 (i.e., in agreement with observations). This indicates that the oscillations are efficiently damped (Figure 62View Imagea). On the other hand, in the prominence model used by Schutgens and Tóth (1999Jump To The Next Citation Point) vertical oscillations are very efficiently attenuated for all the parameters considered and the same happens with horizontal oscillations (Figure 62View Imageb) for coronal densities above ≃ 5 × 10–13 kg m–3. These constraining properties of damped horizontal and vertical oscillations could be used for prominence seismology.

However, the exact nature of the damping mechanism should be pointed out, and Schutgens and Tóth (1999Jump To The Next Citation Point) suggest that the damping of oscillations is due to the emission of waves by the prominence, i.e., wave leakage. The damping of horizontal motions is attributed to the emission of slow waves, whereas fast waves are invoked as the cause of the damping of vertical motions. Taking into account that the main difference between this work and those of van den Oord and Kuperus (1992), Schutgens (1997a,bJump To The Next Citation Point), and van den Oord et al. (1998) lies essentially in the cross section of the filament, it seems that the physics involved should be the same, so wave leakage should be the mechanism responsible for the accounted damping. However, in Schutgens and Tóth (1999Jump To The Next Citation Point), the plasma-β in the prominence ranges from β > 1 in its central part to β < 0.1 at its boundary. Hence, waves emitted by the prominence into the corona propagate in a β ≪ 1 environment in which magnetic field lines are closed. Under these conditions, slow modes propagate along magnetic field lines and are unable to transfer energy from the prominence into the corona and so wave leakage in the system studied by Schutgens and Tóth (1999Jump To The Next Citation Point) is only possible by fast waves. Then, it is hard to understand how the prominence oscillations can be damped by the emission of slow waves in this particular model, in which the dense, cool plasma is only allowed to emit fast waves. It must be mentioned, however, that the plasma-β in the corona increases with the distance from the filament, which implies that the emitted fast waves can transform into slow waves when they traverse the β ≃ 1 region. This effect has been explored by McLaughlin and Hood (2006) and McDougall and Hood (2007); see also references therein for similar studies.

View Image

Figure 62: Attenuation of prominence oscillations by wave leakage. (a) Quality factor (Q ≡ πτ ∕P 0 d) of stable IP (solid curves) and NP (dashed curves) prominence oscillations as a function of the coronal Alfvén speed. (b) Quality factor of the horizontally (squares) and vertically (diamonds) polarized stable oscillations versus the coronal density (from Schutgens, 1997b and Schutgens and Tóth, 1999).

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