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 $\gamma$ is a superposition of two decaying periodic functions of frequency $\nu$, 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 $\Delta_2\nu_{n,l}\equiv\nu_{n-1,l}-2\nu{n,l}+\nu_{n+1,l}$. We show how an analytic approximation to the variation of $\gamma$ leads to a simple representation of this oscillatory contribution to $\Delta_2\nu$ which can be used to characterize the $\gamma$ 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 $\gamma$, not merely to find a formula for $\Delta_2\nu$ that reproduces the data.