Eigenoscillations of the differentially rotating Sun

Abstract

Retrograde waves with frequencies much lower than the rotation frequency become trapped in the solar radiative interior. The eigenfunctions of the compressible, nonadiabatic (ϵ-mechanism and radiative losses taken into account) Rossby-like modes are obtained by an asymptotic method assuming a very small latitudinal gradient of the rotation rate. An integral dispersion relation for the complex eigenfrequencies is derived as a solution of the boundary value problem. The discovered resonant cavity modes (called R-modes) are fundamentally different from the known r-modes: their frequencies are functions of the solar interior structure, and the reason for their existence is not related to geometrical effects. The most unstable R-modes are those with periods of ≈1–3 yr, 18–30 yr, and 1500–20 000 yr; these three separate period ranges are known from solar and geophysical data. The growing times of those modes which are unstable with respect to the ϵ-mechanism are ≈ $10^2, 10^3,$ and 105 years, respectively. The amplitudes of the R-modes are growing towards the center of the Sun. We discuss some prospects to develop the theory of R-modes as a driver of the dynamics in the convective zone which could explain, e.g., observed short-term fluctuations of rotation, a control of the solar magnetic cycle, and abrupt changes of terrestrial climate in the past