EDP Sciences
Free access
Issue A&A
Volume 506, Number 2, November I 2009
Page(s) 885 - 893
Section The Sun
DOI http://dx.doi.org/10.1051/0004-6361/200912652
Published online 18 August 2009

A&A 506, 885-893 (2009)
DOI: 10.1051/0004-6361/200912652

On the vertical and horizontal transverse oscillations of curved coronal loops

M. S. Ruderman

Department of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
    e-mail: M.S.Ruderman@sheffield.ac.uk

Received 8 June 2009/ Accepted 10 August 2009

Abstract
Kink oscillations of curved coronal loops with the density varying along the loop are studied in the thin tube approximation. The equilibrium magnetic field is assumed to be potential, and the field potential and flux function are used as curvilinear coordinates. It is also assumed that the loop expansion is weak, and the solution to the problem is looked for in the form of power series with respect to the tube expansion parameter $\lambda$ $\ll$ 1. The main result of the study is that the eigenfrequencies of the vertical and horizontal tube oscillations are, in general, different, their difference being proportional to $\lambda$. As an example a simple equilibrium with the magnetic field magnitude exponentially decaying with the height is considered. The implication of the obtained results for the interpretation of observational data is discussed.


Key words: magnetohydrodynamics (MHD) -- waves -- Sun: oscillations -- Sun: corona



© ESO 2009

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Editor-in-Chief: T. Forveille
Letters Editor-in-Chief: J. Alves
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ISSN: 0004-6361 ; e-ISSN: 1432-0746
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Published by: EDP Sciences

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