| 其他摘要 | The red giant binary is a system which consists of a red giant (RG) star and a companion star. Because the radius of RG stars dramatically expand during evolution, in many cases they will fill their Roche lobes and transfer their masses to the companion stars. Then the binaries will have stable Roche-lobe overflow (RLOF) or common envelope (CE) evolution. Afterwards, the binaries can contain a lot of peculiar stars, such as extremely low mass white dwarfs (WDs), subdwarf B (sdB) stars, blue stragglers and so on.Therefore, studying the binary evolution of RG stars is important for understanding the binary interactions and the formation of some peculiar stars. In a binary system with a RG donor star, which has a degenerate core, after stable RLOF it leaves behind a He WD which follows the mass-orbital period relation.This relation is important for the studies of long orbital period blue stragglers, sdB stars and millisecond pulsars.Several factors, e.g. metallicity, opacity, mixing length, or convective overshooting, can influence this relation, but the influence of mass-transfer schemes on this relation has not been studied. We compute the evolution of a grid of low mass binaries which initiate mass transfer on the RG branches (RGBs) with different mass-transfer schemes, and get the relations between the masses of WD or sdB stars and orbital periods at the end of mass transfer.In one of the schemes, it is assumed that mass transfer only occurs when the donor star’s radius is just larger than its Roche lobe radius ("classical" scheme). In another mass-transfer scheme, Kolb & Ritter (1990) consider the existence of stellar atmosphere beyond the photospheric radius. In this case, the mass transfer can also occur when the donor’s radius is smaller than its Roche-lobe radius ("Kolb" scheme). We find that the mass-transfer scheme has a significant influence on the evolution of RG binaries. For binaries with the same initial parameters, at the end of mass transfer, the final donor masses are smaller and orbital periods are larger in the models with the "Kolb" scheme, compared with the models with the "classical" scheme, especially when the mass transfer initiates near the tip of the RGB. As a result, the mass-orbital period relations derived by the two different mass-transfer schemes are quite different. For the same donor mass at the end of mass transfer, the orbital period from the "Kolb" scheme is larger than the one from the "classical" scheme. The difference between orbital periods (donor masses) from the two different mass-transfer schemes can be up to 500 days (0.04 M⊙ ) for a fixed final donor mass (orbital period). So if we get the WD masses from the orbital periods, the mass transfer-schemes should also take into account. For a low mass binary, the primary forms a He WD through the above channel. The secondary evolves to the RGB with a degenerate core and forms a sdB star via CE ejection if the secondary is massive enough. We find a He WD mass-orbital period relation for these sdB + He WD binaries which is similar to the above mass-orbital period relation with a semi-analytic method for the first time. In order to confirm this relation, we compute the evolution of a grid of binaries to model the formation of sdB + He WD binaries, and the results are consistent with the semi-analytic method. Moreover, we compare this relation with the observations and find that our results are in broad agreement with the observations. This relation is important for studying the CE ejection and binary evolution. Due to the uncertainties of orbital inclinations in the observations, it is hard to get the WD masses of sdB + He WD binaries. With this relation, if the orbital periods can be determined from observations, the WD masses can be inferred and then the inclination angle can be constrained with the binary mass function. In addition, we can also use this relation to constrain the CE ejection efficiency. By comparing this relation with observations, we find that a relative large CE ejection efficiency is favored. If both the WD and sdB star masses can be determined, the critical mass ratios of dynamically unstable mass transfer for RG binaries can also be constrained. |
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