Effect of Nonlinear Interactions on pMode Frequencies and Line Widths
Abstract
We calculate the effect of nonlinear interactions among solar acoustic modes upon the modal frequencies and energy loss rates (or line widths). The frequency shift for a radial pmode of frequency 3 mHz is found to be about 0.5 microHz. The magnitude of nonlinear frequency shift increases more rapidly with frequency than the inverse mode mass (mode mass is defined as the ratio of energy in the mode to its surface velocity amplitude squared). This frequency shift is primarily due to nonresonant threemode interactions and is dominated by high l surface gravity waves (fmodes) and pmodes. The line width of a radial pmode of frequency 3 mHz, due to resonant nonlinear interactions, is about 0.3 microHz. This result is consistent with that of Kumar and Goldreich (1989). We also find, in agreement with these authors, that the most important nonlinear interactions of trapped pmodes involve fmodes and highfrequency pmodes (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 saturate the overstable solar pmodes at their small observed amplitudes. Both the nonlinear frequency shifts and line widths, at a fixed frequency, are proportional to the inverse of mode mass which for modes of degree greater than about 100 is approximately l^{0.8}. Therefore, the frequency of an fmode of l = 1000, due to nonlinear interactions, is decreased by approximately 0.4%.
 Publication:

The Astrophysical Journal
 Pub Date:
 May 1994
 DOI:
 10.1086/174159
 Bibcode:
 1994ApJ...427..483K
 Keywords:

 Energy Spectra;
 Gravitational Fields;
 Hamiltonian Functions;
 Mathematical Models;
 Stellar Models;
 Chromosphere;
 Frequency Shift;
 Solar Granulation;
 Stellar Magnitude;
 Astrophysics;
 SUN: OSCILLATIONS