Three-dimensional kink modes in solar coronal slabs: group velocities and their implications for impulsively excited waves

Abstract

Little attention has been paid to group velocities of three-dimensional (3D) MHD waves in solar coronal seismology. This study aims to present a rather comprehensive examination on the group velocities of trapped 3D kink modes in coronal slabs, emphasizing the connection of mode analysis to both mode characterization and impulsively excited 3D kink waves. We work in linear, ideal, pressureless MHD, and take the equilibrium slab to be symmetrically structured only in one transverse direction. The dispersion relation is numerically solved, with the results understood by making in-depth analytical progress. We address both the transverse fundamental and its first overtone. We develop a three-subgroup scheme for categorizing 3D kink modes on the plane spanned by the axial and out-of-plane wavenumbers. The group ($\vec{v}_{\rm gr}$) and phase velocities ($\vec{v}_{\rm ph}$) sit on the same side of the equilibrium magnetic field ($\vec{B}_0$) for the ``$\vec{B}_0$-same-side A'' and ``$\vec{B}_0$-same-side F'' subgroups, which are further discriminated by the directional similarity of $\vec{v}_{\rm gr}$ and $\vec{B}_0$. The ``$\vec{B}_0$-straddling'' subgroup is peculiar in that $\vec{v}_{\rm gr}$ and $\vec{v}_{\rm ph}$ lie astride $\vec{B}_0$, a feature that cannot be found for waves in unbounded uniform media in pressureless MHD. This ``$\vec{B}_0$-straddling'' subgroup pertains to both the fundamental and its overtones. We further place our results in the context of impulsive waves, employing the method of stationary phase to predict the large-time wavefront morphology in the plane of symmetry of the equilibrium slab. Wavefronts directed toward $\vec{B}_0$ derive exclusively from ``$\vec{B}_0$-straddling'' modes, and are confined to narrow sectors.