| 其他摘要 | In the stellar structure and evolution, the extension of convective regions and the associated mixing processes are still not fully understood. The size and extent of the convective core affect the amount of nuclear fuel available in the center of the star, as well as the chemical composition of the star, and ultimately its luminosity and lifetime. Handling convective overshooting using a fully hydrodynamical approach is a very complicated process, with different physical quantities having different overshooting distances. Observational studies, as well as theoretical and computational models, continue to help us understand and refine these important physical processes, improving our understanding of the internal structure of stars. With the increasing amount of observational data, we have effective means of verifying the complex turbulent convective motions within the interiors of stars. For core He-burning stars, there are considerable uncertainty regarding mixing in convective core and overshooting beyond it. Different approaches, such as convective overshooting, semi-convection, etc., have been adopted in stellar models, leading to different stellar structures and scenarios for stellar evolution. The 𝑘−𝜔 model is a stellar convection model that is based fully on fluid dynamics equations and turbulence theory. It can not only handle convective unstable zone but also the overshooting regions.We incorporated the 𝑘 − 𝜔 model into the Modules of Experiments in Stellar Astrophysics (MESA) to investigate overshooting mixing in the evolution of hot subdwarf B (sdB) stars. Our results show that the development of the convective core can be divided into three stages. When the radiative temperature gradient ∇rad decreases monotonically outward, the mass of the convective core increases monotonically, and the overshoot mixing shows an exponential decay similar to that in Herwig (2000). When the minimum value of the radiative temperature gradient ∇rad near the convective boundary is less than the adiabatic temperature gradient ∇ad, the convective core splits repeatedly, forming two convective regions. When the central helium abundance decreases to about 𝑌c ≈ 0.45, the mass at the boundary of convective shell 𝑀sc can reach about 0.2 𝑀⊙. This is close to the central convective core mass of younger sdB stars (0.22 ∼ 0.28 𝑀⊙) derived by asteroseismology analysis. In the final stage of helium burning when 𝑌c < 0.2, the convective core undergoes two to three ”core breathing pulses” injecting additional helium into the convective core and extending the lifetime of the sdB star. Finally, the mass of the central mixing region 𝑀mixed can raise to 0.303 𝑀⊙. Our g-mode sdB model has a high oxygen abundance, with a central oxygen content of about 80 per cent. Oxygen-rich white dwarfs deduced from asteroseismology can serve as evidence for the existence of breathing pulses.Massive stars have a large convective core in their center, which plays a significant role in validating convective overshooting. At the same time, stellar wind mass loss and rotational induced mixing also have important effects on the evolution of massive stars. To study the processes of overshoot mixing and rotational mixing outside the convective core of massive stars, we calculated both rotating and non-rotating stellar models with initial masses ranging from 25 to 120 𝑀⊙ at 𝑍 = 0.02. The rotating models have a uniform initial rotation rate of 𝑣ini/𝑣crit = 0.4 at zero-age main sequence (ZAMS). All models evolve from ZAMS until the end of central carbon burning.Stellar models that use the 𝑘 − 𝜔 model provide a larger convective core and a extend main-sequence width. The shrinking of the MS width occurs for stars with 𝑀ini ≥ 60 𝑀⊙, and the most massive stars (𝑀ini ≥ 100 𝑀⊙) can evolve to higher temperature at the late MS stage. For non-rotating models, there are a significant increase in surface nitrogen abundance when hydrogen burning products in the overshoot- ing region are exposed to the surface by stellar wind. However, the rotating models with rotational mixing display a wide range of intermediate nitrogen enrichment in the early MS. Meanwhile, the rotational mixing reduced the minimum initial mass of the Wolf-Rayet (WR) stars to about 36 𝑀⊙. The final mass range for the rotating and non-rotating WR models is 9.5 − 17.5 𝑀⊙ and 10 − 23 𝑀⊙, respectively. In rotating models, the C/N ratio slowly decreases to below 0.1 outside the convective core, creating a wider and smoother chemical elements transition region. In addition, the transitional WNC star lifetime is 1 − 4 × 104 yr, about one order of magnitude longer than that of non-rotating models. Therefore, the rotating models have a higher proportion of WNC stars, with a WNC/WR ratio of 0.059 and 0.004 for rotating and non-rotating models, respectively. The mass range of WNC stars is determined by internal mixing processes and the maximum con- vective core mass in core He-burning phase, and is about 15 − 36 𝑀⊙. Both rotating and non-rotating single star evolutionary calculations predict the formation of advanced WR stars (WNC, WC and WO stars) with a luminosity of log 𝐿/𝐿⊙ > 5.3. But simple unified mass-loss rates for stellar winds cannot explain the formation of observed low-luminosity (and thus low-mass) WNC and WC stars. |
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