Characteristics of solar-like oscillations of secondary red clump stars

We calculated the populations of core-helium-burning (CHeB) stars and found that the secondary red clump (SRC) stars can form an SRC peak in the distributions of the frequency of maximum seismic amplitude ($\nu_{max}$) and mean large-frequency separation ($\Delta\nu$) of CHeB stars when metallicity $Z \geq$ 0.02. The $\nu_{max}$ and $\Delta\nu$ of CHeB stars are dependent not only on He core mass but on H-shell burning. The SRC peak is composed of the CHeB stars with mass roughly between the critical mass M_{Hef} and M_{Hef}+0.2 while He core mass is between about 0.33 and 0.36 M_{sun}. The location of the SRC peak can be affected by the mixing-length parameter $\alpha$, metallicity $Z$, and overshooting parameter $\delta_{ov}$. A decrease in $\alpha$ or increase in $Z$ or $\delta_{ov}$ leads to a movement of the SRC peak towards a lower frequency. However, the change in $Z$ and $\alpha$ only slightly affects the value of M_{Hef} but the variation in $\delta_{ov}$ can significantly affects the value of M_{Hef}. Thus the SRC peak might aid in determining the value of M_{Hef} and calibrating $\delta_{ov}$. In addition, the effects of convective acceleration of SRC stars and the $\nu_{max}$ of `semi-degenerate' stars decreasing with mass result in the appearance of a shoulder between about 40 and 50 $\mu$hz in the \dnu{} distribution. However, the convective acceleration of stars with M < M_{Hef} leads to the deficit in the $\nu_{max}$ distribution between about 9 and 20 $\mu$hz{}. Moreover, the value of the parameter $b$ of the relation between $\nu_{max}$ and $\Delta\nu$ for the populations with M > M_{Hef} is obviously larger than that for the populations with $M <$ \dmhef{}.