Coupling of Solar Oscillations in Quasi-Degenerate Perturbation Theory
Abstract
We investigate the coupling of the solar p-modes, caused by a stationary poloidal velocity field in the solar convection zone, via quasi-degenerate perturbation theory, as suggested by Lavely and Ritzwoller (Phil. Trans. R. Soc. Lond. A (1992) 339, 431-496). As a consequence of the Wigner-Eckhart theorem oscillations couple if they satisfy several selection rules. The result is the lifting of the degeneracy. But in contrast to the rotational splitting, coupling between different multiplets is possible leading to asymmetric frequency multiplets. For illustration we examine the effect of sectoral velocity fields, similar to giant convective cells. We find an approximate solution of the general equations for the coupling of two p-modes with a degree l <= 12. The individual frequency shifts scale with the frequency itself, with the square of the velocity, and with the inverse difference of the squared frequencies of the two involved modes. The relative deviation of this estimate from the exact result is less than 10 %. Finally, we show that the splittings are up to ~100 nHz for a velocity with amplitude 100 m/s. Hence, large scale poloidal velocity fields lead to an additional line broadening and to an asymmetric line profile in the power spectra.
- Publication:
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Astronomische Gesellschaft Abstract Series
- Pub Date:
- 1999
- Bibcode:
- 1999AGAb...15...92R
- Keywords:
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- Solar Oscillations: Solar Convective Zone