Magnetoatmospheric Oscillations in Flux Tubes

The present investigation is a continuation of earlier work by Hasan & Christensen-Dalsgaard (1992) and Banerjee, Hasan & Christensen-Dalsgaard (1995), who has examined the eeects of a weak vertical magnetic eld on the normal adiabatic modes of an isothermal atmosphere by combining a semi-analytic approach, based on asymp-totic dispersion relations, with numerical solutions. In the present study of the strong-eld case, we concentrate on the behaviour of the modes near the avoided crossings in the k ? ! diagram for zero gradient boundary conditions. It was predicted that due to strong mode coupling the eigenfrequencies in these regions become complex. We present here the consequences of mode coupling in such regions, which could be relevant for sunspots and more generally for stratiied ux tubes. 1 INTRODUCTION The detection of oscillations in magnetic elements has led to the development of several theoretical models to understand their physical nature. The bulk of the work in this area has focussed on oscillations in sunspots, particularly in the umbra where the magnetic eld can be regarded as almost vertical. Theoretical models for understanding umbral oscillations in the 3-min band fall into two distinct classes. In the rst one, the oscillations are considered to be fast modes trapped in a resonant cavity located in the photospheric layers of the umbra and below (Scheuer and Thomas 1981; Thomas and Scheuer 1982). The other model proposed by Zhugzhda et al. (1983, 1984) and Gurman and Leibacher (1984) treats the oscillations as resonantly trapped slow modes within a chromospheric cavity. However, more recent work by Hasan (1991) suggests that both types of cavities may exist simultaneously in the umbral atmosphere. Furthermore , it appears that there may be a strong coupling between the two cavities, especially for modes with horizontal wave numbers that undergo avoided crossings in the k?! diagram. This can have many important consequences, particularly as it can lead to a transfer of energy between the cavities.per II) made a detailed investigation of the nature of MAG oscillations in an isothermal medium. By using the weak eld approximation, it was possible to derive an analytic dispersion relation and thereby infer many useful properties of the waves. The interaction among various modes was studied and it was shown that this interaction becomes particularly important at the locations in the diagnostic diagram where the frequencies of diierent elementary modes coincide. These regions, referred to as avoided crossings, are …