Assessing and Improving Helioseismological Inferences of Solar Structure

P.B. Stark, Principal Investigator

Abstract:
Acoustic vibrations of the Sun contain information about the distributions of soundspeed, material density, and angular velocity within the Sun. Current methods for imaging these properties of the solar interior from helioseismic eigenfrequencies produce images that might resemble the Sun, but the formal uncertainties of the techniques do not accurately quantify possible differences between the models and the truth. Nor can the methods incorporate physical constraints that might reduce the uncertainty.

The effects of data errors, modeling algorithms, and theoretical approximations on the reliability of the images are largely unexplored; published uncertainties approximate the variability of the estimation method conditional on a particular parametric representation of the solar property, and a host of other assumptions, without regard for possible biases.

The proposed research is to develop and apply methods to study both the variability and the bias of estimates of the distribution of soundspeed in the solar interior and the distribution of angular velocity in the solar interior, under less restrictive assumptions, incorporating prior physical constraints such as bounds on energy or rotationally-induced oblateness to control the bias.

Shorter, but still conservative, confidence intervals for solar properties can be found by using unusual functionals for measuring fit to the data, rather than conventional $l_p$ misfit norms such as the common sum of squared residuals. Such alternatives will be explored and applied to find simultaneous confidence envelopes for the distribution of soundspeed in the solar interior, incorporating uncertainties due to surface effects and to neglected higher-order terms in the asymptotics, and to make direct inferences about spatial variations in the distribution of angular velocity within the Sun from the splitting of normal mode frequencies. A fringe benefit of the new misfit measures will be ``teleological'' data compression techniques that enhance the ability to image the solar interior from normal mode data.

Complete text of proposal, in LaTex or postscript.