SIMBAD references

Using a stellar population-synthesis method, we studied the distributions of ν_max and Δν of simulated clusters with various ages and metallicities. Except for the confirmed peak (RC peak) of Δν 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 ν_max and Δν 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 ≲ 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 ≲ 2.4 Gyr may aid in testing the theory of degeneracy of hydrogen-exhausted cores. Moreover, for clusters with 1.1 M_☉< M_hook< 1.3 M_☉ there is a MS gap and a peak on the left of the MS gap in the distributions of ν_max and Δν, which may be applied to constrain the central hydrogen abundance of stars in the MS gap and the peak.