Impulsively Generated Wave Trains in Coronal Structures: I. Effects of Transverse Structuring on Sausage Waves in Pressureless Tubes

TL;DR

This study analyzes how transverse density structuring affects sausage wave modes in coronal tubes, revealing diverse group speed behaviors that influence impulsively generated wave trains and their spectral signatures.

Contribution

It provides a comprehensive analytical and numerical analysis of sausage mode dispersive properties in pressureless tubes with various density profiles, highlighting their impact on wave train evolution.

Findings

Group speed curves vary with density contrast and profile steepness.

Morlet spectra of wave trains differ significantly from classical 'crazy tadpoles'.

Rich spectral features can help diagnose transverse density structures.

Abstract

The behavior of the axial group speeds of trapped sausage modes plays an important role in determining impulsively generated wave trains, which have often been invoked to account for quasi-periodic signals with quasi-periods of order seconds in a considerable number of coronal structures. We conduct a comprehensive eigenmode analysis, both analytically and numerically, on the dispersive properties of sausage modes in pressureless tubes with three families of continuous radial density profiles. We find a rich variety of the dependence on the axial wavenumber $k$ of the axial group speed $v_{\rm gr}$. Depending on the density contrast and profile steepness as well as on the detailed profile description, the $v_{\rm gr}-k$ curves either possess or do not possess cutoff wavenumbers, and they can behave in either a monotonical or non-monotonical manner. With time-dependent simulations, we further show that this rich variety of the group speed characteristics heavily influences the temporal evolution and Morlet spectra of impulsively generated wave trains. In particular, the Morlet spectra can look substantially different from "crazy tadpoles" found for the much-studied discontinuous density profiles. We conclude that it is necessary to re-examine available high-cadence data to look for the rich set of temporal and spectral features, which can be employed to discriminate between the unknown forms of the density distributions transverse to coronal structures.