Inverse problem with continuous parameters for solar oscillations.

Abstract

Solar seismology is a relatively new field in solar astrophysics. It provides us a way of "looking" into the deep interior of the Sun. The goal of solar seismology is to derive information about the internal structure of the Sun from the observed properties of solar oscillations. This is called the inverse problem of solar seismology. This project is to explore a new set of methods and algorithms to solve the inverse problem. The continuous orthonormalization (CON) method and the adjoint method adapted by Rosenwald can be used to compute the eigenfrequency sensitivities to the solar structure parameters in a very efficient way. In this work, the computational algorithm for using these methods has been modified and improved. Continuous parametrization for the internal structure of the Sun is introduced. The solar interior is subdivided into sections, and polynomial fits are applied to the solar structure parameters in each section. The eigenfrequency sensitivities to these polynomial coefficients--the continuous parameters--are computed. These sensitivities can be used to predict the change in solar eigenfrequencies when the structure parameters are perturbed (with the necessary physical constraints satisfied). The inverse problem for the solar internal structure is formulated by using these sensitivities. The generalized inverse technique is used to solve the nonlinear inverse problem in an iterative process. Observed data of low-degree g-modes have been used for a preliminary inversion. The nonlinearity of the solar seismic inverse problem is demonstrated. A nonlinear inversion process has been successfully performed and the results analysed. The inversion results indicate that the standard solar model is a good approximation of the real Sun. Only relatively small perturbations to the model are needed to explain the frequency deviations between observation and theory.