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HELIOSEISMIC CONSTRAINTS ON THE STRUCTURE OF THE PRESENT SUN

Given the chemical composition (essentially the hydrogen abundance), mass and the physics of the interior, the structure of a star is uniquely determined. The usual method for the determination of the hydrogen-abundance profile of the present Sun is via evolutionary calculations. But the existing uncertainties in the physics and evolutionary history suggest considering a more extended set of possible solar models. Here, we examine models with solar values of radius, luminosity and mass, but with arbitrary profiles of the hydrogen abundance in the core. Of course, the profiles X(m/M) must satisfy some (rather weak) restrictions, so that the solar values (determined by fitting) can be attained. We assume the hypothesis that within fixed physics (opacity, thermodynamics, nuclear reactions) there is for all solar models a rigorous relation between the surface helium abundance and the entropy of the adiabatic part of the convective zone. We verify this hypothesis with models using somewhat simplified physics (Christensen-Dalsgaard 1988), and with six evolutionary models computed by Christensen-Dalsgaard (1992). The relation mainly depends on the opacity in the radiative zone between the lower boundary of convection and the region of nuclear reactions. We discuss the possibility of an agreement between these relations and the helioseismic determination of the surface helium abundance.