Asteroseismology of 16 Kepler Solar-like Stars: Stellar Parameters and the Effects of Element Diffusion

Abstract

Element diffusion has small but significant effects on the structure of the stellar interior. It is interesting to investigate the effects of element diffusion using asteroseismology. We have constructed two grids of stellar models, one with diffusion and one without, for solar-like stars with masses between 0.9 and 1.4 solar masses, and varied initial helium abundance and metallicity. The oscillation frequencies of all stellar models have also been calculated. Piecewise Hermite cubic polynomials are adopted to interpolate stellar p-mode frequencies at an arbitrary age on a stellar evolutionary track. We have investigated 16 Kepler solar-like stars by comparing the model frequencies with observations. The suggested ranges of stellar parameters and some global variables are obtained. For all stars, the best model reproduces the observational frequencies with a χ 2 of the order of unity. It has been found that element diffusion is important in modeling solar-like stars. Without diffusion, the best value of the initial helium abundance is below the primordial helium abundance from Big Bang nucleosynthesis. When diffusion is taken into account, the required initial helium abundance increases to be higher than the primordial abundance. Diffusion also generally improves the frequency fitting results by reducing the minimum of χ 2. Investigation of the second difference of the oscillation frequencies on KIC 8694723 and KIC 10454113 indicates that the current model of element diffusion may underestimate the strength of settling.