Inverse and Forward Helioseismology: Understanding the Interior Composition and Structure of the Present Sun

Abstract

Inverse and forward helioseismic approaches are reviewed. Chemical abundance profiles from a solar model generated by Takata and Shibahashi (1998) by inverse helioseismology are used in a forward approach. This forward model is referred to as the author’s ‘seismic’ solar model. This model is compared to a similarly calculated standard evolution solar model (ssm) and the author’s reference high-Z core (hzc) solar model. The degree l = 1 nonradial oscillation frequencies of the three models are compared, for orders n = 7 to 33. Relative to current observations, there is good agreement between the seismic model predictions and the five-minute-band frequency observations. In addition, there is good agreement between the hzc model frequencies and the seismic model frequencies. Further comparisons are made in terms of fractional differences and/or of ratios of seismic/ssm, hzc/ssm and seismic/hzc quantities such as (1) speed of sound, (2) density and (3) gamma functions, Γ1. From prior studies, the effective gamma, γe, defined by the relation, (γe − 1) = P/E, with P, the total pressure and E, the total energy, respectively, is used in the oscillation equations instead of the complete analytic form of the Γ1 function. It is shown that between the radius fractions x (= r/R) = 0.05 to 0.95, the fractional differences and ratios seismic/hzc yield good agreements for the speed of sound, density and gammal function. Since the hzc model is also consistent with two of the three operating solar neutrino experiments and has the bottom of the convection region at x = 0.6926 with a temperature over 2.4 × 106 K (hence consistent with the lithium problem without invoking ‘overshoot’), it is concluded that the current hzc model is closest to the structure of the real sun. Consequently, an astrophysical solution to the solar neutrino problem is possible as part of an answer to the question of how the real sun formed and evolved to its present state.