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Astron. Astrophys. 339, 225-238 (1998)

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The effect of delays on filament oscillations and stability

G.H.J. van den Oord, N.A.J. Schutgens and M. Kuperus

Sterrekundig Instituut, Utrecht University, P.O. Box 80.000, 3508 TA Utrecht, The Netherlands

Received 21 April 1998 / Accepted 17 July 1998


We discuss the linear response of a filament to perturbations, taking the finite communication time between the filament and the photosphere into account. The finite communication time introduces delays in the system. Recently Schutgens (1997a b) investigated the solutions of the delay equation for vertical perturbations. In this paper we expand his analysis by considering also horizontal and coupled oscillations. The latter occur in asymmetric coronal fields. We also discuss the effect of Alfvén wave emission on filament oscillations and show that wave emission is important for stabilizing filaments. We introduce a fairly straightforward method to study the solutions of delay equations as a function of the filament-photosphere communication time. A solution can be described by a linear combination of damped harmonic oscillations each characterized by a frequency, a damping/growth time and, accordingly, a quality factor. As a secondary result of our analysis we show that, within the context of line current models, Kippenhahn/Schlüter-type filament equilibria can never be stable in the horizontal and the vertical direction at the same time but we also demonstrate that Kuperus/Raadu-type equilibria can account for both an inverse or a normal polarity signature. The diagnostic value of our analysis for determining, e.g., the filament current from observations of oscillating filaments is discussed.

Key words: Sun: filaments – Sun: prominences – Sun: magnetic fields – Sun: oscillations – MHD – waves

Send offprint requests to: G.H.J. van den Oord

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© European Southern Observatory (ESO) 1998

Online publication: September 30, 1998