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 He I and He II ionization regions. That variation is probably best exhibited in the second frequency difference Delta(2)nu(n, l) equivalent to 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.