Seismology of the Solar f-Mode. I. Basic Signatures of Shearing Velocity Fields

The observed frequencies of the solar f-mode show systematic shifts from the (parabolic) dispersion relation characteristic of a pure surface mode, owing to the perturbing effects of such phenomena in the outer layers of the Sun as velocity fields, magnetic fields, and temperature gradients/discontinuities. These frequency shifts thus provide a good diagnostic probe of these phenomena. In this paper, we wish to focus our attention on the possible influence of shearing velocity fields on the f-mode frequencies. We show here that velocity fields of a wide class leave a signature on the frequency-shift profile which is consistent with observations, including the characteristic change of sign (crossover) in δω at a spherical harmonic degree of approximately 800. We demonstrate that quantitative fits to the observed frequency shifts are possible with parameters which are characteristic of the underlying motions of the solar convection zone. However, the simultaneous effects of other phenomena, e.g., chromospheric magnetic fields, should also be taken into account.