Eigenoscillations of the differentially rotating Sun - I. 22-year, 4000-year, and quasi-biennial modes

Retrograde waves with frequencies much lower than the rotation frequency become trapped in the solar radiative interior. The eigenfunctions of the compressible, nonadiabatic (-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 dierent from the knownr-modes: their frequencies are functions of the solar interior structure, and the reason for their existence is not related to geometrical eects. The most unstable R-modes are those with periods of1{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 -mechanism are 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.