EDP Sciences
Free access
Volume 415, Number 2, February IV 2004
Page(s) 751 - 754
Section The Sun
DOI http://dx.doi.org/10.1051/0004-6361:20035820

A&A 415, 751-754 (2004)
DOI: 10.1051/0004-6361:20035820

Research Note

Tube waves: Exact and approximate

M. Stix

Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, 79104 Freiburg, Germany
(Received 8 December 2003 / Accepted 15 December 2003)

This note deals with magnetohydrodynamic body waves in a magnetic cylinder. It is shown that the solution obtained by the thin-tube expansion is, term by term, identical to the Taylor expansion of the exact solution. Each level of approximation adds a pair of modes, a slow and a fast one, and corrects the frequencies and eigenfunctions of the previous approximation. All eigenfrequencies, approximate and exact, can be read off from a single graph. All slow modes have phase velocities between the tube speed  $c_{\rm T}$ and $\sqrt{2}\,c_{\rm T}$, all fast modes have phase velocities above $\sqrt{2}\,c_{\rm T}$.

Key words: magnetohydrodynamics (MHD) -- waves -- methods: analytical -- Sun: magnetic fields

© ESO 2004