Sausage and kink oscillations in incompressible annular magnetic cylinders

Solar Physics & Space Plasma Research Centre (SPRC), Dept. of Applied Maths, The University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK e-mail: [robertus;b.carter]@sheffield.ac.uk

Received: 24 January 2007
Accepted: 30 July 2007

Abstract

Aims.The propagation of MHD waves in a structured magnetic flux tube embedded within a straight magnetic environment is studied analytically. The motivation for this analysis comes from the observations of damped loop oscillations indicating the possibility that only part of the loop is homogeneous in the radial direction and from the observation of two simultaneous waves with different speeds in the same magnetic loop in the solar atmosphere.

Methods.The general dispersion relation of longitudinal wave propagation is derived for a flux tube configuration consisting of a core, annulus and external region each with straight distinct magnetic field. Modes of oscillation are examined from the general dispersion relation that is suitable for obtaining information not just on oscillations but also on some instability properties of this complex tube structure. Specific attention is given to the modification of the phase speeds and oscillation periods caused by the annulus structure, compared to a single monolithic tube.

Results.It is shown that two purely surface modes arise. The relative change in periods due to the additional annulus layer is shown to be rather significant (up to in some cases). In particular we found that in photospheric type annular tubes, periods are less than their counterparts in a monolithic loop while for a dense flux tube in the majority of cases the period was greater than the period of the counterpart monolithic flux tube. Both short and long wavelength approximations are considered for both the symmetrical (sausage) and kink modes.

Conclusions.Annular structuring of a magnetic flux tube will reduce or increase periods of the allowed oscillations depending on the type of flux tube considered (either as a magnetic or as a density enhancement). The results are relevant to further our knowledge of solar magneto-seismology. In particular, the obtained results for the kink oscillations may be applicable from photosphere to corona, while the case for the sausage mode is more relevant in the lower part of the solar atmosphere.