Effects of the radiative interior on solar inertial modes

TL;DR

This study investigates how the radiative interior influences solar inertial modes, revealing minor frequency changes but significant mode penetration into the overshooting layer, and identifies Rossby modes in the radiative zone.

Contribution

It provides the first detailed analysis of the coupling between solar inertial modes and the radiative interior, highlighting the existence of mixed Rossby-inertial modes.

Findings

Including the radiative zone slightly alters mode frequencies and eigenfunctions.

Most modes penetrate into the overshooting layer, affecting their growth rates.

Rossby modes exist in the radiative zone and can form mixed modes with inertial modes.

Abstract

Solar inertial modes are believed to play important diagnostic and dynamical roles in the Sun's differentially rotating convection zone. However, the coupling of these modes to the radiative interior has not yet been discussed. We aim to understand the dependence of the modes on the uniformly rotating sub-adiabatic region below the convection zone and determine whether this leads to measurable changes at the surface. We used the Dedalus code to compute linear eigenmodes in the inertial frequency range in a setup that includes both the convection zone and the radiative interior down to $0.5R_\odot$. We imposed free-surface boundary conditions at both radial boundaries. For comparison, we also computed the eigenmodes in a setup restricted to the convection zone. We find that including the radiative zone only slightly modifies the frequencies and surface eigenfunctions, except for some modes with significant radial motion (high-frequency retrograde and prograde columnar modes). On the other hand, most modes penetrate significantly into the overshooting layer below the convection zone. This reduces their growth rates and distorts their eigenfunctions near the base of the convection zone. Furthermore, the uniformly rotating sub-adiabatic radiative zone supports oscillations due to Rossby modes of all possible spherical harmonics and radial nodes. In particular, when the nearest inertial mode in frequency space lies within around 10 nHz and shares the same north-south symmetry, these Rossby modes evolve into mixed modes characterized by significant motions within both the radiative and convection zones. However, such mixed modes have a high mode mass in the radiative interior and thus will be difficult to excite stochastically via convection.