Theory of solar oscillations in the inertial frequency range: Linear modes of the convection zone

¹ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
e-mail: bekki@mps.mpg.de
² Institut für Astrophysik, Georg-August-Universtät Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
³ Center for Space Science, NYUAD Institute, New York University Abu Dhabi, Abu Dhabi, UAE

Received: 20 January 2022
Accepted: 9 March 2022

Abstract

Context. Several types of global-scale inertial modes of oscillation have been observed on the Sun. These include the equatorial Rossby modes, critical-latitude modes, and high-latitude modes. However, the columnar convective modes (predicted by simulations and also known as banana cells or thermal Rossby waves) remain elusive.

Aims. We aim to investigate the influence of turbulent diffusivities, non-adiabatic stratification, differential rotation, and a latitudinal entropy gradient on the linear global modes of the rotating solar convection zone.

Methods. We numerically solved for the eigenmodes of a rotating compressible fluid inside a spherical shell. The model takes into account the solar stratification, turbulent diffusivities, differential rotation (determined by helioseismology), and the latitudinal entropy gradient. As a starting point, we restricted ourselves to a superadiabaticity and turbulent diffusivities that are uniform in space. We identified modes in the inertial frequency range, including the columnar convective modes as well as modes of a mixed character. The corresponding mode dispersion relations and eigenfunctions are computed for azimuthal orders of m ≤ 16.

Results. The three main results are as follows. Firstly, we find that, for m ≳ 5, the radial dependence of the equatorial Rossby modes with no radial node (n = 0) is radically changed from the traditional expectation (r^m) for turbulent diffusivities ≳10¹² cm² s⁻¹. Secondly, we find mixed modes, namely, modes that share properties of the equatorial Rossby modes with one radial node (n = 1) and the columnar convective modes, which are not substantially affected by turbulent diffusion. Thirdly, we show that the m = 1 high-latitude mode in the model is consistent with the solar observations when the latitudinal entropy gradient corresponding to a thermal wind balance is included (baroclinically unstable mode).

Conclusions. To our knowledge, this work is the first realistic eigenvalue calculation of the global modes of the rotating solar convection zone. This calculation reveals a rich spectrum of modes in the inertial frequency range, which can be directly compared to the observations. In turn, the observed modes can inform us about the solar convection zone.