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

Abstract

On the one hand, several types of global-scale inertial modes of oscillation have been observed on the Sun. They include the equatorial Rossby modes, critical-latitude modes, and high-latitude modes. On the other hand, the columnar convective modes (predicted by simulations; also known as banana cells or thermal Rossby waves) remain elusive. 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. We solve numerically for the eigenmodes of a rotating compressible fluid inside a spherical shell. We identify modes in the inertial frequency range including the columnar convective modes, as well as modes of mixed character. The corresponding mode dispersion relations and eigenfunctions are computed for azimuthal orders $m\le 16$. The three main results are as follows. Firstly, we find that, for $m\gtrsim 5$, 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 $\gtrsim 10^{12}$ cm${}^2$ s${}^{-1}$. Secondly, we find mixed modes, i.e. modes that share properties of the equatorial Rossby modes with one radial node ($n=1$) and the columnar convective modes. 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 (baroclinally unstable mode). 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.

24 pages, 29 figures, submitted to Astronomy & Astrophysics on 20 Jan 2022

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• Doppler velocity of $m=1$ high-latitude inertial mode over the last five sunspot cycles
• Viscous inertial modes on a differentially rotating sphere: Comparison with solar observations
• Interaction of solar inertial modes with turbulent convection. A 2D model for the excitation of linearly stable modes
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• Radial Trapping of Thermal Rossby Waves within the Convection Zones of Low-Mass Stars
• Oscillations of the solar photospheric magnetic field caused by the m = 1 high-latitude inertial mode
• A Possible Mechanism to Explain the Prograde Equatorial Jet of a Jupiter-like Gaseous Giant
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• Towards inertial-mode helioseismology: Direct sensing of solar rotation at 75 deg latitude and 0.8 Rsun