Characteristics of solar-like oscillations of clusters simulated by stellar population synthesis

Using a stellar population-synthesis method, we studied the distributions of nu(max) and Delta nu of simulated clusters with various ages and metallicities. Except for the confirmed peak (RC peak) of Delta nu of red-clump (RC) stars, i.e. core helium-burning stars, one sees a gap and a main-sequence (MS) peak in the distributions of nu(max) and Delta nu of young clusters. The gap corresponds mainly to the Hertzsprung-gap phase of evolution. The RC peak is caused by the fact that the radii of many RC stars near the zero-age horizontal branch are concentrated in a certain range. The MS peak also results from the fact that many MS stars located in a certain mass range have an approximate radius in the early phase of the MS. The MS peak barely exists in the simulated clusters with age less than or similar to 1.0 Gyr. The location of the MS peak moves to a lower frequency with increasing age or metallicity, which may be applied to constrain the age and metallicity of young clusters. For simulated clusters with Z = 0.02, the frequency of the location of the dominant RC peak increases with age when age < 1.2 Gyr, and then decreases with age when age > 1.2 Gyr, but scarcely varies when age > 2.4 Gyr. This is relative to the degeneracy of the hydrogen-exhausted core at the time of helium ignition. In addition, the RC peak is not sensitive to the metallicity, especially for clusters with age > 2.4 Gyr. Asteroseismical observations of clusters with age less than or similar to 2.4 Gyr may aid in testing the theory of degeneracy of hydrogen-exhausted cores. Moreover, for clusters with 1.1 M-circle dot < M-hook < 1.3 M-circle dot there is a MS gap and a peak on the left of the MS gap in the distributions of nu(max) and Delta nu, which may be applied to constrain the central hydrogen abundance of stars in the MS gap and the peak.