Magnetoacoustic surface gravity waves at a spherical interface

¹ Solar Physics and Space Plasma Research Centre (SP 2RC), Dept. of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK
e-mail: i.ballai@sheffield.ac.uk
² Eötvös University, Department of Astronomy, 1117 Budapest, 1/A Pázmány Péter, Budapest, Hungary

Received: 4 November 2010
Accepted: 20 December 2010

Abstract

Aims. The plasma structured by magnetic fields in the solar atmosphere is a perfect medium for the propagation of guided magnetic and magnetoacoustic waves. Geometrical restriction of wave propagation is known to confer a dispersive character for waves. In addition, waves propagating along discontinuities in the medium are known to remain localized. As an extension to theories of guided waves in magnetic slabs and cylinders under solar and stellar conditions, we aim to study the propagation of magnetoacoustic-gravity waves at a spherical interface in the low solar corona (considered here as a density discontinuity), modelling global waves recently observed in the corona in EUV wavelengths.

Methods. Using conservation laws at the interface we derive the dispersion relation in spherical geometry with a radially expanding magnetic field in the presence of gravitational stratification. The obtained dispersion relation describing fast magnetoacoustic-gravity surface waves is derived using an approximative method taking into account that propagation takes place near the solar surface.

Results. Theoretical results obtained in the present study are applied to investigate the propagation of EIT waves in the low corona. The frequency of waves is shown to increase with decreasing density contrast at the interface. We also show that, for a given azimuthal wavenumber, the magnetic field has a very small effect on the value of the frequency of waves. When plotted against the location of the interface (in the radial direction) the frequency varies inversely proportional to the distance, while for a fixed density ratio and location of the interface the frequency is obtained to be defined in a very narrow region.