Tidally Forced Planetary Waves in the Tachocline of Solar-like Stars

Can atmospheric waves in planet-hosting solar-like stars substantially resonate to tidal forcing, perhaps at a level of impacting the space weather or even being dynamo-relevant? In particular, low-frequency Rossby waves, which have been detected in the solar near-surface layers, are predestined to respond to sunspot cycle-scale perturbations. In this paper, we seek to address these questions as we formulate a forced wave model for the tachocline layer, which is widely considered as the birthplace of several magnetohydrodynamic planetary waves, i.e., Rossby, inertia-gravity (Poincaré), Kelvin, Alfvén, and gravity waves. The tachocline is modeled as a shallow plasma atmosphere with an effective free surface on top that we describe within the Cartesian β-plane approximation. As a novelty to former studies, we equip the governing equations with a conservative tidal potential and a linear friction law to account for viscous dissipation. We combine the linearized governing equations into one decoupled wave equation, which facilitates an easily approachable analysis. Analytical results are presented and discussed within several interesting free, damped, and forced wave limits for both midlatitude and equatorially trapped waves. For the idealized case of a single tide-generating body following a circular orbit, we derive an explicit analytic solution that we apply to our Sun for estimating leading-order responses to Jupiter. Our analysis reveals that Rossby waves resonating to low-frequency perturbations can potentially reach considerable velocity amplitudes on the order of 101–102 cm s−1, which, however, strongly rely on the yet unknown frictional damping parameter.