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

¹ Shandong Key Laboratory of Space Environment and Exploration Technology, Institute of Space Sciences, Shandong University, Weihai 264209, China
² Center for Integrated Research on Space Science, Astronomy, and Physics, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao 266237, China

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 12 September 2025
Accepted: 4 February 2026

Abstract

Context. Little attention has been paid to group velocities of three-dimensional (3D) magnetohydrodynamic (MHD) waves in solar coronal seismology.

Aims. This study presents a comprehensive examination of 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.

Methods. We worked in linear, ideal, pressureless MHD, and took the equilibrium slab to be symmetrically structured only in one transverse direction. The dispersion relation was numerically solved, and the results were understood by making in-depth analytical progress. We addressed both the transverse fundamental and its first overtone.

Results. We developed a three-subgroup scheme for categorizing 3D kink modes on the plane spanned by the axial and out-of-plane wavenumbers. The group (v_gr) and phase velocities (v_ph) lie on the same side of the equilibrium magnetic field (B₀) for the B₀-same-side A and B₀-same-side F subgroups, which are further discriminated by the directional similarity of v_gr and B₀. The B₀-straddling subgroup is peculiar in that v_gr and v_ph lie astride B₀, a feature that cannot be found for waves in unbounded uniform media in pressureless MHD. This B₀-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 B₀ derive exclusively from B₀-straddling modes, and are confined to narrow sectors.

Conclusions. The directional information of impulsively excited 3D wavefronts carries rich seismic information, whose inversion requires a thorough understanding of the behavior of group velocities of 3D modes.