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Keywords:

  • stars: evolution;
  • stars: late-type;
  • stars: oscillations

ABSTRACT

We calculated the populations of core-helium-burning (CHeB) stars and found that secondary red-clump (SRC) stars can form a SRC peak in the distributions of the frequency of maximum seismic amplitude (νmax) and mean large-frequency separation (Δν) of CHeB stars when metallicity Z≥ 0.02. The νmax and Δν of CHeB stars are dependent not only on He-core mass but also on H-shell burning. The SRC peak is composed of CHeB stars with mass roughly between the critical mass MHeF and MHeF+ 0.2, while He-core mass is between about 0.33 and 0.36 M. The location of the SRC peak can be affected by the mixing-length parameter α, metallicity Z and overshooting parameter δov. A decrease in α or increase in Z or δov leads to a movement of the SRC peak towards a lower frequency. The change in Z and α only slightly affects the value of MHeF, but the variation in δov can affect the value of MHeF significantly. Thus the SRC peak might aid in determining the value of MHeF and calibrating δov. In addition, the effects of convective acceleration of SRC stars and the decrease in the νmax of ‘semidegenerate’ stars with mass result in the appearance of a shoulder between about 40 and 50 μHz in the νmax distribution. However, the convective acceleration of stars with M < MHeF leads to a deficit in the νmax distribution between about 9 and 20 μHz. Moreover, the value of the parameter b of the relation between νmax and Δν for populations with M > MHeF is obviously larger than that for populations with M < MHeF.