Random damping and frequency reduction of the solar f-mode

We present observations showing that the frequency of the high-degree f-mode is significantly lower than the frequency given by the simple dispersion relation, ω² = gk, and that the line width grows with the wavenumber k. We attempt to explain that this behavior is the result of the interaction with granulation, which we model as a random flow. Because the f-mode spends more time propagating against the flow than with the flow, its effective speed and, consequently, frequency are reduced. Additionally, an eddy viscosity introduces the negative imaginary part of frequency. This negative imaginary part represents the damping of the coherent field due to scattering. The line width is proportional to the magnitude of the imaginary part of the frequency. We apply an analytical perturbation technique and numerical methods to estimate the line width and the frequency shift, and we show that the results are consistent with the properties of the f-mode obtained from the high-resolution Michelson Doppler Imager data from the Solar and Heliospheric Observatory.