Nonasymptotic helioseismic inversion for solar structure

Abstract

A nonasymptotic technique based on the variational formulation of the equations of stellar oscillations is used for helioseismic inversion. This method can give the difference in sound speed and density between two solar models or between a solar model and the Sun using the corresponding frequency differences. Tests using pairs of known solar models show that this technique is capable of reproducing the sound speed to an accuracy of better than 0.1% for r<0.97 R_⊙, while the density can be determined to an accuracy of better than 0.5% in most of the radiative interior. Using the observed frequencies of solar oscillations it is found that the sound speed and density in a solar model with gravitational settling of helium and heavy elements is very close to that in the Sun, the maximum difference being 0.5% for the sound speed and 1.5% for density. It is possible to use this technique to obtain the adiabatic index Γ₁ inside the Sun, which can be employed as a probe for the equation of state in stellar interiors. The relative sound speed difference between the reference solar model and the Sun just below the He II ionization zone indicates that the adiabatic index of the solar material in this region is smaller than that in the model. The inverted density profile is found to be stable against convection in the solar core, while the depth of the surface convection zone is found to be approximately 0.29 R_⊙.