Nonlinear multimode coupling of the solar gravity modes in a rotationally split multiplet.

Abstract

This dissertation explores some of the nonlinear properties of gravity-mode oscillations in the solar interior. In particular, it is concerned with the interactions amongst the nonradial modes of a single rotationally split multiplet. It investigates the multi-mode coupling of a large number (typically about 20) of the modes in a multiplet. Many internal resonances occur in a given problem, and the effects occur at third order. Motivation for this analysis arises both from general theoretical interest and from observed properties of the Sun that have recently become available. Observat ions of solar gravity-mode oscillation eigenfrequencies and eigenfunctions obtained at the Santa Catalina Laboratory for Experimental Relativity by Astrometry (SCLERA) show strong evidence of nonlinear effects (Hill 1986; Hill and Czarnowski 1986; Rabaey and Hill 1989; Rabaey 1989). This dissertation provides a general theoretical framework for investigating many problems of second- and third-order mode coupling in stellar systems. A multiple-scale perturbation technique is used. The formalism presents an alternative to that of Dziembowski (1982), and is more generally applicable. The theory provides a means to infer the core amplitudes of the gravity-modes exhibiting the nonlinear behavior in the SCLERA data. (These modes have a radial order of approximately 15 and an angular degree of about 30.) This is. a significant accomplishment because it bypasses the traditional extrapolation of measured surface amplitudes into the interior, which is a questionable procedure, in part because of the uncertainty regarding the surface boundary conditions in the Sun (Hill 1978). It is found that the relative radial displacement of these oscillations, δr/r, has a typical maximum amplitude in the interior of (6x10⁻⁴±30%). The maximum of the relative Lagrangian temperature variation, δT/T, is (7x 10⁻⁵). The potential implications of such interior amplitude determinations are briefly discussed. As a byproduct of the analysis, certain characteristics of the data used in conjunction with the theory allow the possibility of determining the linear damping time of these modes. As with the amplitudes, traditional approaches are bypassed, thus providing a novel and independent determination. Very preliminary results seem to indicate a typical damping time of about 40 years.