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  Δ₂ν _{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 Δ₂ν 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 Δ₂ν that reproduces the data.