The detectability of signatures of rapid variation in low-degree stellar p-mode oscillation frequencies

Regions of rapid variation in stellar interiors introduce characteristic periodic signatures into the frequencies of their p-mode oscillations. These signatures have previously been isolated in solar data and have been used to estimate the level of convective overshoot and the envelope helium abundance in the Sun. Precise asteroseismic data are now becoming available for a number of distant Sun-like stars, and the techniques developed for low-degree solar data can be used in the stellar case. In this paper, we address the observational duration required to isolate and examine these rapid-variation signatures through the use of low-degree solar data as a Sun-like stellar analog. We also outline the difficulties involved and bias introduced when using a limited number of poorly constrained mode frequencies. The signature resulting from the region of the second ionization of helium is found to be detectable in spectra of shorter duration than those required to isolate the smaller amplitude signature arising from the base of the convective envelope. Observations of just 84 days may be sufficient to extract reliable information on the acoustic depth and extent of the He II ionization zone, although longer observations are required to obtain sufficient precision to estimate the envelope helium abundance. The acoustic radius of the base of the convective envelope and the amplitude of the signature are reliably isolated in spectra of at least 182 days.