An asteroseismic signature of helium ionization

Abstract

We investigate the influence of the ionization of helium on the low-degree acoustic oscillation frequencies in model solar-type stars. The signature in the oscillation frequencies characterizing the ionization-induced depression of the first adiabatic exponent $γ$ is a superposition of two decaying periodic functions of frequency $ν$, with `frequencies' that are approximately twice the acoustic depths of the centres of the Helium I and Helium II ionization regions. That variation is probably best exhibited in the second frequency difference $Δ_2ν_{n,l}\equivν_{n-1,l}-2ν{n,l}+ν_{n+1,l}$. We show how an analytic approximation to the variation of $γ$ leads to a simple representation of this oscillatory contribution to $Δ_2ν$ which can be used to characterize the $γ$ variation, our intention being to use it as a seismic diagnostic of the helium abundance of the star. We emphasize that the objective is to characterize $γ$, not merely to find a formula for $Δ_2ν$ that reproduces the data.