EFFECT OF NONLINEAR-INTERACTIONS ON P-MODE FREQUENCIES AND LINE WIDTHS

We calculate the effect of nonlinear interactions among solar acoustic modes upon the modal frequencies and energy loss rates (or line width s). The frequency shift for a radial p-mode of frequency 3 mHz is foun d to be about -0.5 muHz. The magnitude of nonlinear frequency shift in creases more rapidly with frequency than the inverse mode mass (mode m ass is defined as the ratio of energy in the mode to its surface veloc ity amplitude squared). This frequency shift is primarily due to nonre sonant three-mode interactions and is dominated by high l surface grav ity waves (f-modes) and p-modes. The line width of a radial p-mode of frequency 3 mHz, due to resonant nonlinear interactions, is about 0.3 muHz. This result is consistent with that of Kumar & Goldreich (1989). We also find, in agreement with these authors, that the most importan t nonlinear interactions of trapped p-modes involve f-modes and high-f requency p-modes (frequency greater than about 5 mHz) which propagate in the solar photosphere. Thus, using the arguments advanced by Kumar & Goldreich (1989), we conclude that nonlinear couplings cannot satura te the overstable solar p-modes at their small observed amplitudes. Bo th the nonlinear frequency shifts and line widths, at a fixed frequenc y, are proportional to the inverse of mode mass which for modes of deg ree greater than about 100 is approximately l0.8. Therefore, the frequ ency of an f-mode of l = 1000, due to nonlinear interactions, is decre ased by approximately 0.4%.