Solar oscillations - A method for deriving nonlinear effects

The frequencies of solar oscillations are so closely spaced that nonlinear interactions among modes are probable. The rate of interaction is proportional to an integral involving the eigenfunctions of the interacting modes, which usually are known only numerically. An approximation in which the eigenfunctions are strictly sinusoidal functions of a suitably defined radial variable, and the numerical details of stellar structure are banished to a coefficient in the integrand, are here explored. The physical assumptions are the same as in the asymptotic approximation of p- or g-modes. This method should allow a general investigation as to likely nonlinear interactions and which modes may participate in such interactions. The coupling of two p-modes by possible large-scale internal magnetic fields is introduced as an anisotropic pressure response to a displacement. Pairs of modes differing in frequency by less than the fraction magnetic/thermal pressure are strongly coupled, and energy appears to oscillate slowly between the two associated spherical harmonics. Potentially, upper limits may be derived for internal magnetic fields.