Measuring the helium abundance in the solar envelope: the role of the equation of state

Abstract

Variations in the adiabatic index of stellar material in the second helium ionization zone enable one to infer the helium abundance in the solar envelope, using the observed frequencies of solar oscillations. Three techniques based on the differential asymptotic method for sound speed inversion are considered. With the help of the signature of helium abundance on various tracers of ionization, it is possible to estimate the helium abundance. Using several test models, the systematic errors in these techniques are estimated. All these techniques are found to be sensitive to the equation of state. The magnetohydrodynamic (MHD) equation of state is found to be close to that of solar material. Using reference models employing MHD equation of state we find the solar helium abundance Y=0.252±0.003.