Solar acoustic oscillations in a random density field

The influence of a space-dependent random mass density field on the develop ment of solar p-modes is investigated using analytical and numerical means. Using a perturbative approach, which is valid for a weak random field and small amplitude waves, we derive a linear dispersion relation whose solutio ns correspond to attenuated oscillations. The real part of the frequency of these oscillations exceeds the one of waves propagating in a medium withou t random density. We give an interpretation of the "unphysical" nature of t he frequency shift and of the amplitude attenuation which is similar to Lan dau damping. The analytical findings are compared with the results of the n umerical solution of a model wave equation. We find that, for weak random f ields and for wavelengths which are a few times the correlation length of t he random density fluctuations, numerical results agree with the analytical theory. Two practical formulas for deriving the correlation spectrum of th e random density field from observations are also given.