Frequency dependence of the large frequency separation of solar-like   oscillators: Influence of the Helium second-ionization zone
  The large frequency separation between modes of the same degree and consecutive orders in a star is approximately proportional to the square root of its mean density. To determine the large frequency separation as accurately as possible a mean large frequency separation computed over several orders is often used. It is, however, known that the large frequency separation varies with frequency in a second order effect. From observations it has been shown that this frequency dependence is more important for main-sequence stars than it is for red-giant stars. Here we use YREC models to verify and explain this observational result. We find that for stars with R > 8 Rsun the effect of the Helium second ionisation zone is relatively small. For these stars the deep location of the He II zone induces a frequency modulation covering only a few large separations, while the amplitude of the modulation is low due to the relatively weak and extended He II layer, causing a shallow wide depression in the first adiabatic exponent. For less evolved stars the He II zone is located closer to the surface, and it is more confined, i.e. a deep narrow depression in the first adiabatic exponent. This causes frequency modulations with relatively high amplitudes covering up to about 20 large separations, inducing a relatively large frequency modulation. Additionally, we find that for less evolved stars the He II zone is stronger and more localised for more massive stars and for stars with low metallicities further increasing the amplitude of the frequency modulation. 
S. Hekker, Sarbani Basu, Y. Elsworth, W.J. Chaplin
astro-ph.SR