Standing sausage modes in coronal loops with plasma flow

Abstract

Context. Magnetohydrodynamic waves are important for diagnosing the physical parameters of coronal plasmas. Field-aligned flows appear frequently in coronal loops. Aims. We examine the effects of transverse density and plasma flow structuring on standing sausage modes trapped in coronal loops, and examine their observational implications in the context of coronal seismology. Methods. We model coronal loops as straight cold cylinders with plasma flow embedded in a static corona. An eigen-value problem governing propagating sausage waves is formulated and its solutions are employed to construct standing modes. Two transverse profiles are distinguished, and are called profiles E and N. A parameter study is performed on the dependence of the maximum period P max and cutoff length-to-radius ratio (L/a) cutoff in the trapped regime on the density parameters (ρ 0 /ρ ∞ and profile steepness p) and the flow parameters (its magnitude U 0 and profile steepness u). Results. For either profile, introducing a flow reduces P max obtainable in the trapped regime relative to the static case. The value of P max is sensitive to p for profile N, but is insensitive to p for profile E. By far the most important effect a flow introduces is to reduce the capability for loops to trap standing sausage modes: (L/a) cutoff may be substantially reduced in the case with flow relative to the static one. In addition, (L/a) cutoff is smaller for a stronger flow, and for a steeper flow profile when the flow magnitude is fixed. Conclusions. If the density distribution can be described by profile N, then measuring the sausage mode period can help deduce the density profile steepness. However, this practice is not feasible if profile E more accurately describes the density distribution. Furthermore, even field-aligned flows with magnitudes substantially smaller than the ambient Alfvén speed can make coronal loops considerably less likely to support trapped standing sausage modes.

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

“…In the appendix to Li et al (2014), we have performed an extensive validation study of this code using available analytical solutions in the context of coronal seismology. The end result is that the dimensionless angular frequency ωR/v Ai can be formally expressed as…”

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“…Thus, for a given radius, the period of the trapped sausage mode waves increases with increasing loop length until the critical L/a ratio is reached and the mode becomes leaky (e.g. Gruszecki et al 2012;Li et al 2014). This could explain the increasing time scales measured early during the decay of the flare and the disappearance of the pulsations from AR11748 after 02:00 UT.…”

Magnetohydrodynamic Fast Sausage Waves in the Solar Corona

“…Such a symmetry is lost when v 0 does not vanish, thereby violating Feature 1 (see the appendix of Li et al 2013 for an illustration, also the introduction therein for early studies addressing non-zero v 0 ). Focusing on coronal FSMs, the available studies seem to pertain exclusively to a time-independent field-aligned flow in straight loops, although the transverse profiles were allowed to be either step (e.g., Yu et al 2016a) or continuous (e.g., Li et al 2014). Of interest were standing modes in loops of length L, for which the axial wavenumbers (k + and k − ) of the component running waves need to satisfy k + +k − = 2πn/L for the transverse displacements at the loop border to be identically zero on the bounding photospheres.…”