Resonant Damping of Kink Modes in Solar Coronal Slabs

TL;DR

This study analyzes how different transverse density profiles affect the resonant damping of kink modes in solar coronal slabs, providing analytical solutions and emphasizing the importance of profile specifics for wave damping.

Contribution

It derives a generalized dispersion relation for resonantly damped kink modes considering arbitrary density profiles in coronal slabs, highlighting the sensitivity of eigenfrequencies to profile variations.

Findings

Eigenfrequencies vary significantly with density profile choice.

Analytical solutions outperform numerical ones in validation.

Resonant absorption is crucial for oblique kink wave components.

Abstract

We examine resonantly damped kink modes in straight coronal slabs, paying special attention to the effects of the formulation for the transverse density distribution ("profile"). We work in the framework of pressure-less, gravity-free, resistive magnetohydrodynamics, and we adopt the dissipative-eigenmode perspective. The density profile is restricted to be one-dimensional, but nonetheless allowed to take a generic form characterized by a continuous transition layer connecting a uniform interior to a uniform exterior. A dispersion relation (DR) is derived in the thin-boundary limit, yielding analytical expressions for the eigenfrequencies that generalize known results in various aspects. We find that the analytical rather than the numerical solutions to the thin-boundary DR serve better the purpose for validating our self-consistent resistive solutions. More importantly, the eigenfrequencies are found to be sensitive to profile specifications, the ratio of the imaginary to the real part readily varying by a factor of two when one profile is used in place of another. Our eigenmode computations are also examined in the context of impulsively excited kink waves, suggesting the importance of resonant absorption for sufficiently oblique components when the spatial scale of the exciter is comparable to the slab half-width.