The influence of turbulence on the solar p-mode frequencies I. Free-mode approximation

The influence of turbulence on the frequencies of free acoustic modes in convection zones is considered. The frequencies are modified via the speed of sound by the turbulence-induced alterations of the effective pressure: (i) by the correlated fluctuations of temperature and density and (ii) the pressure part of the Reynolds stress. The two effects shift the frequency of low l p-modes in opposite directions. In addition, the correlation of the density fluctuations with the random velocity — the eddy-mass flow — is also relevant. It is, in a steady state, balanced by a vertical mean velocity. The balance results in a rather small net effect completely disappearing for highly nonradial oscillations. Both effects of the density fluctuations produce a redshift of the low l p-mode frequencies. The Reynolds stress, however, makes a blueshift of the frequencies relative to that computed for a laminar gas. This effect dominates for subsonic turbulences. The applied second-order correlation-approximation, however, only holds for the lowest frequencies, where the KORONAS (solar minimum) data are indicating a blueshift. Of particular importance for the present concept is the expected cycle-variations of the lineshifts, i.e. the consideration of the magnetic modification of the various contributions. Observations may show whether the suggested modifications of the solar oscillation theory are correct.