Eigenoscillations of the Differentially Rotating Sun: I. 22-year, 4000-year, and quasi-biennial modes

Abstract

Retrograde waves with frequencies much lower than the rotation frequency become trapped in the solar radiative interior. The eigenfunctions of the compressible, nonadiabatic, Rossby-like modes ($\epsilon$-mechanism and radiative losses taken into account) are obtained by an asymptotic method assuming a very small latitudinal gradient of rotation, without an arbitrary choice of other free parameters. 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--20000 yrs; 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 $\epsilon$-mechanism are $\approx 10^2, 10^3,$ and $10^5$ 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.