Fast Standing Modes in Transversely Nonuniform Solar Coronal Slabs: Effects of a Finite Plasma Beta

TL;DR

This study investigates how finite plasma beta influences the dispersive properties of fast standing modes in nonuniform solar coronal slabs, finding it has minimal effect on key parameters when normalized appropriately.

Contribution

It derives a generic dispersion relation for fast waves in coronal slabs with arbitrary transverse profiles and assesses the impact of finite plasma beta on mode properties.

Findings

Finite plasma beta has marginal influence on periods and damping times when normalized.

Transverse profile details significantly affect mode characteristics.

Cold slab theory can be used with proper profile considerations.

Abstract

We examine the dispersive properties of linear fast standing modes in transversely nonuniform solar coronal slabs with finite gas pressure, or, equivalently, finite plasma beta. We derive a generic dispersion relation governing fast waves in coronal slabs for which the continuous transverse distributions of the physical parameters comprise a uniform core, a uniform external medium, and a transition layer (TL) in between. The profiles in the TL are allowed to be essentially arbitrary. Restricting ourselves to the first several branches of fast modes, which are of most interest from the observational standpoint, we find that a finite plasma beta plays an at most marginal role in influencing the periods ($P$), damping times ($\tau$), and critical longitudinal wavenumbers ($k_{\rm c}$), when both $P$ and $\tau$ are measured in units of the transverse fast time. However, these parameters are in general significantly affected by how the TL profiles are described. We conclude that, for typical coronal structures, the dispersive properties of the first several branches of fast standing modes can be evaluated with the much simpler theory for cold slabs provided that the transverse profiles are properly addressed and the transverse Alfv\'en time in cold MHD is replaced with the transverse fast time.