An asteroseismic signature of helium ionization

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 He I and He II ionization regions.That variation is probably best exhibited in the second frequency difference 2 ν n,l ≡ ν 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 2 ν 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 2 ν that reproduces the data.