Spatial damping of propagating sausage waves in coronal cylinders

¹ Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, and Institute of Space Sciences, Shandong University Weihai, Weihai, 264209 PR China
e-mail: bbl@sdu.edu.cn
² CAS Key Laboratory of Geospace Environment, University of Science & Technology of China, Chinese Academy of Sciences, Hefei 230026, PR China

Received: 30 May 2015
Accepted: 28 July 2015

Abstract

Context. Sausage modes are important in coronal seismology. Spatially damped propagating sausage waves were recently observed in the solar atmosphere.

Aims. We examine how wave leakage influences the spatial damping of sausage waves propagating along coronal structures modeled by a cylindrical density enhancement embedded in a uniform magnetic field.

Methods. Working in the framework of cold magnetohydrodynamics, we solve the dispersion relation (DR) governing sausage waves for complex-valued, longitudinal wavenumber k at given real angular frequencies ω. For validation purposes, we also provide analytical approximations to the DR in the low-frequency limit and in the vicinity of ω_c, the critical angular frequency separating trapped from leaky waves.

Results. In contrast to the standing case, propagating sausage waves are allowed for ω much lower than ω_c. However, while able to direct their energy upward, these low-frequency waves are subject to substantial spatial attenuation. The spatial damping length shows little dependence on the density contrast between the cylinder and its surroundings, and depends only weakly on frequency. This spatial damping length is of the order of the cylinder radius for ω ≲ 1.5v_Ai/a, where a and v_Ai are the cylinder radius and the Alfvén speed in the cylinder, respectively.

Conclusions. If a coronal cylinder is perturbed by symmetric boundary drivers (e.g., granular motions) with a broadband spectrum, wave leakage efficiently filters out the low-frequency components.