Convectively Coupled Equatorial Trapped Waves in Stars and Planets

In this paper, we have studied convectively coupled equatorially trapped waves in rotating stars, with and without magnetic fields. The equatorial trapped hydrodynamic and magnetohydrodynamic Poincaré, Rossby, mixed Rossby–Poincaré, and Kelvin waves were identified. The effects of stratification and nontraditional Coriolis force terms have been investigated. When the flow is strongly stratified, the wave frequencies of the convectively coupled model are almost the same as those of a shallow-water model. However, when the flow is weakly stratified, the wave frequencies are constrained by the buoyancy frequency. The nontraditional Coriolis terms affect the widths and phases of the equatorial waves. The width increases with an increasing nontraditional Coriolis parameter. Phase shift occurs when the nontraditional Coriolis parameter is included. The magnetic effect is significant when the magnetic field is strong. We have applied the model in the solar atmosphere and solar tachocline to explain the Rieger-type periodicities. For the solar atmosphere, when the magnetic effect is taken into account, we find that the magnetic field should be smaller than 5 G in the solar photosphere. Otherwise, the Rieger-type periodicities can only be attributed to long Rossby waves. For the solar tachocline, we find that magnetic field of the solar tachocline should be smaller than 50 kG to observe the 160 day Rieger period. In addition, we find that the effect of the nontraditional Coriolis terms is not obvious in the solar photosphere, but its effect on the tachocline is significant.