Helioseismic calibration of the equation of state and chemical composition in the solar convective envelope

Abstract

Accurate and precise measurements of solar p-mode frequencies allow sensitive diagnostics of the adiabatic exponent Γ1 = (∂ln p/∂ln ρ)S as a function of depth in the adiabatically stratified part of the solar convective envelope. The profile of the adiabatic exponent contains information about the chemical composition of the partially ionized solar plasma, and allows the accuracy of different versions of the equation of state to be assessed. We address the diagnostic potential of solar p-mode frequencies inferred from Doppler velocity measurements in the SOHO MDI ‘medium-l’ program, the almost uninterrupted measurements covering 15 years of SOHO’s operational lifetime, by examining their agreement with the seismic stratification of solar envelope models constructed with various modern versions of the equation of state (two versions of OPAL, and two versions of the SAHA-S equation of state). We use two diagnostic techniques, which complement each other: (i) direct calibration using grids of envelope models that differ in chemical composition (parametrized by the helium abundance Y and the heavy element abundance Z) and in the specific entropy in the adiabatically stratified part of the solar convective envelope; and (ii) a constrained structural helioseismic inversion. The best agreement with seismic data is provided by the recently developed SAHA-S3 equation of state. The maximum-likelihood estimates of the composition parameters Y and Z depend on the particular version of the equation of state, and may also be distorted by systematic errors in solar frequency measurements. The estimates obtained in this study are in the range of Y = 0.240–0.255 and Z = 0.008–0.013. All our results provide strong evidence in favour of low Z values, as reported from recent spectroscopic measurements.