Standing Sausage Perturbations in Solar Coronal Slabs with Continuous Transverse Density Profiles: cutoff wavenumbers, evanescent eigenmodes, and oscillatory continuum

Abstract

The lack of observed sausage perturbations in solar active region loops is customarily attributed to the relevance of cutoff axial wavenumbers and the consequent absence of trapped modes (called ``evanescent eigenmodes'' here). However, some recent eigenvalue problem studies yield that cutoff wavenumbers may disappear for those equilibria where the external density varies sufficiently slowly, thereby casting doubt on the rarity of candidate sausage perturbations. We examine the responses of straight, transversely structured, coronal slabs to small-amplitude sausage-type perturbations that excite axial fundamentals by solving the pertinent initial value problem with eigensolutions for a closed domain. The density variation in the slab exterior is dictated by some steepness parameter $\mu$, and cutoff wavenumbers are theoretically expected to be present (absent) when $\mu \ge 2$ ($\mu <2$). However, our numerical results show no qualitative difference in the system evolution when $\mu$ varies, despite the differences in the modal behavior. Only oscillatory eigenmodes are permitted when $\mu \ge 2$. Our discrete eigenspectrum becomes increasingly closely spaced when the domain broadens, and an oscillatory continuum results for a truly open system. Oscillatory eigenmodes remain allowed and dominate the system evolution when $\mu <2$. We show that the irrelevance of cutoff wavenumbers does not mean that all fast waves are evanescent. Rather, it means that an increasing number of evanescent eigenmodes emerge when the domain size increases. We conclude that sausage perturbations remain difficult to detect even for the waveguide formulated here.

arXiv comment32 pages, 8 figures, accepted for publication in ApJ

References in corpus (28)

• MHD Waves and Coronal Seismology: an overview of recent results
• Modelling Quasi-Periodic Pulsations in Solar and Stellar Flares
• Observational Tests of Damping by Resonant Absorption in Coronal Loop Oscillations
• Alfven Waves in the Solar Atmosphere
• Quasi-periodic pulsations in solar and stellar flares: an overview of recent results
• Kink oscillations of coronal loops
• MHD Sausage Mode Oscillations in Coronal Loops
• MHD Waves in open coronal structures
• The behavior of transverse waves in nonuniform solar flux tubes. I. Comparison of ideal and resistive results
• Dynamics of coronal rain and descending plasma blobs in solar prominences: II. partially ionized case
• Magnetohydrodynamic Fast Sausage Waves in the Solar Corona
• Magnetohydrodynamic kink waves in nonuniform solar flux tubes: phase mixing and energy cascade to small scales
• Inferring flare loop parameters with measurements of standing sausage modes
• Standing Sausage Modes In Nonuniform Magnetic Tubes: An Inversion Scheme For Inferring Flare Loop Parameters
• Propagation and dispersion of sausage wave trains in magnetic flux tubes
• Propagation and dispersion of transverse wave trains in magnetic flux tubes
• Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads
• Impulsively Generated Wave Trains in Coronal Structures: I. Effects of Transverse Structuring on Sausage Waves in Pressureless Tubes
• Resonantly damped surface and body MHD waves in a solar coronal slab with oblique propagation
• Fast magnetoacoustic wave trains: from tadpoles to boomerangs
• Impulsively generated wave trains in coronal structures: II. Effects of transverse structuring on sausage waves in pressureless slabs
• Kink oscillations of flowing threads in solar prominences
• Resonant Damping of Kink Modes in Solar Coronal Slabs
• Damping of slow surface kink modes in solar photospheric waveguides modeled by one-dimensional inhomogeneities
• Standing Sausage Perturbations in solar coronal loops with diffuse boundaries: An initial-value-problem perspective
• Three-Dimensional Propagation of Kink Wave Trains in Solar Coronal Slabs
• Do Coronal Loops Oscillate in Isolation?
• Construction of coronal hole and active region magnetohydrostatic solutions in two dimensions: Force and energy balance

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