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

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.