Surface effects on the solar oscillation frequencies

Abstract

The solar p-mode frequencies and eigenfunctions are modified by four processes operative in the atmosphere and the subphotospheric layers which can be, to a good approximation, treated as surface phenomena; they are the imperfect reflection at the outer boundary, scattering by convective eddies, effects caused by abrupt hydrogen ionization and non-adiabatic processes which are important mainly in the region where the product of the pressure and sound velocity is comparable to or less than the radiative flux. Propagation of acoustic modes of short period or large horizontal wave number l greater than or equal to 800 critically depend on the atmospheric structure as well as the treatment of non-adiabatic effects. But the surface effects on low frequency modes can be, to sufficient accuracy, represented as a phase difference between the two solutions of the second order differntial equation describing the adiabatic modes in the Cowling approximation. Most of these effects are frequency-dependent only, since the radial wave number of the modes is large compared to their horizontal wave number. However, it is possible to isolate the l-dependent contribution, which becomes important when the magnitude of the (imaginary) Brunt-Vaisala frequency is comparable to the Lamb frequency.