Ray Tracing of MHD Rossby Waves in the Solar Tachocline: Meridional Propagation and Implications for the Solar Magnetic Activity

Abstract

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Rossby waves have been recently recognised for their role in the large-scale spatio-temporal organisation of the solar magnetic activity. Here, we study the propagation of magnetohydrodynamic Rossby waves in a thin layer, representing the solar tachocline. We consider the waves embedded in a meridionally varying background state characterised by a mean zonal flow, which mimics the differential rotation profile of the Sun, and a toroidal magnetic field. Two anti-symmetric toroidal magnetic fields are utilised: one having a global structure with the maximum at around 50o and the other characterised by a narrow band centered at around 20o. We show that for a global structure toroidal magnetic field, the MHD Rossby modes undergo significant meridional propagation, either equatorward or poleward. In addition, the latitude where the waves exhibit a stationary behaviour is sensitive to the strength of the background magnetic field. On the other hand, a narrow band toroidal magnetic field is shown to work as a waveguide for the fast branch of MHD Rossby waves.

Keywords

• MHD Rossby waves
• solar tachocline
• solar differential rotation
• background toroidal magnetic field
• WKB (Liouville-Green) approximation