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

Abstract

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.

A Synchronized Two-Dimensional $\alpha $–$\Omega $ Model of the Solar Dynamo

“…Invoking the equally rough estimate from renormalization theory (Moffatt and Dormy, 2019 ) (and even when realistically assuming to be one or two orders of magnitude smaller than ), a tidally generated -value of a few decimeters per second seems not out of reach. Indeed, it was recently shown (Horstmann et al., 2023 ) that (magneto–)Rossby waves (Marquez-Artavia, Jones, and Tobias, 2017 ; Zaqarashvili, 2018 ; Dikpati et al., 2020 ) under the influence of a realistic tidal forcing are capable of acquiring velocity scales of up to 1 m s −1 . Therefore, it appears that the “astrological homeopathy” (Charbonneau, 2022 ) of tidal forcing may well be suited to generate an -effect in the tachocline region that is strong enough to entrain the entire solar dynamo.…”

Equatorially trapped Rossby waves in radiative stars

“…It is also suggested that the Rossby waves may lead to intermediate periodicity in solar activity (Dikpati et al 2020; Gurgenashvili et al 2016; Gurgenashvili et al 2017; Zaqarashvili et al 2010). Theoretical description of Rossby waves in the solar interior and tachocline is also significantly developed in recent years (Bekki et al 2022; Damiani et al 2020; Dikpati et al 2018; Dikpati et al 2022; Gachechiladze et al 2019; Gizon et al 2020; Horstmann et al 2023; Zaqarashvili 2018; Zaqarashvili et al 2007).…”