Standing MHD Waves in a Magnetic Slab Embedded in an Asymmetric Plasma Environment: Slow Surface Waves

Abstract

Abstract The field of solar magnetoseismology (SMS) is heavily reliant upon our understanding of magnetohydrodynamic (MHD) waves that occur in many solar features. Building on previous studies of propagating MHD waves in a magnetic slab embedded in a nonmagnetic asymmetric environment, in this study we assume a line-tying boundary condition and use analytical techniques to derive the dispersion relation for linear standing MHD oscillations. The slab is first assumed thin, with arbitrary asymmetry, in order to derive the frequencies of the standing harmonic modes for both slow quasi-sausage and slow quasi-kink waves. Besides this, the asymmetry is assumed to be weak in order to determine the frequency dependence on the width of the slab and the asymmetry of the system, to leading order. For both the quasi-sausage and quasi-kink modes, the derived eigenfrequencies show that the dependence on the asymmetry in the system is much weaker than the dependence on the width of the slab. Using the eigenfrequencies, other observable quantities are derived (such as, e.g., the frequency ratio) providing an opportunity to use SMS to infer background diagnostics of the system.