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

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, there are 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 radius of many RC stars near the zero-age horizontal branch concentrates in a certain range. The MS peak also results from the fact that many MS stars which are located in a certain mass range have an approximate radius in the early phase of 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 the 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 it 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 the clusters with age > 2.4 Gyr. Asteroseismical observation for clusters with age < 2.4 Gyr may aid in testing the theory of the degeneracy of the hydrogen-exhausted core. Moreover, for the clusters with 1.1 M{\odot} < M_hook < 1.3 M{\odot}, there are a MS gap and a peak on the left of the MS gap in the distributions ofν_max and Δν, which may be applied to constrain the central hydrogen abundance of stars in the MS gap and the peak.