Context. The binary fraction among extreme horizontal branch (EHB) stars in Galactic globular clusters (GCs) is an order of magnitude lower than the binary fraction among their counterparts, field hot subdwarfs. This casts serious doubt on their formation channels. Aims. In this Letter, I explain the difference between the field and the cluster EHB stars with the binary model of Han et al. (2002, MNRAS, 336, 449; 2003, MNRAS, 341, 669) for the formation of EHB stars. Methods. With the binary population synthesis code of Han et al. (2002, 2003), I follow the evolution of simple stellar populations resulting from single star bursts (note that Han et al. 2002, 2003, adopted a constant star formation rate over the last 15 Gyr for the production of field EHB stars), and obtain EHB stars at different stellar population ages. Results. I found that the binary fraction among EHB stars decreases with the stellar population age. The fraction of EHB binaries with orbital periods P < 5d is similar to 2.5% for a stellar population of 10Gyr from the standard simulation set. Conclusions. The binary model of Han et al. (2002, 2003) is able to explain the lack of EHB binaries in globular clusters. I also propose that the precise determination of the physical parameters of close EHB binaries in GCs can lead to the strictest constraint on common-envelope ejection efficiency.

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