标题： 经典造父变星的一种湍流对流模型的启示 显示英文标题

标题： Implications of a turbulent convection model for classical Cepheids

摘要： 中间质量核心氦燃烧恒星演化轨迹中出现的蓝环对于解释造父变星的观测特性至关重要。 当仅使用经典的局部混合长度理论（MLT）时，无法始终再现较低质量造父变星的蓝环。 此外，经典模型与脉动和动力学质量测定相比存在质量差异问题。 这两个问题都可以通过对流的MLT经验扩展来解决。 我们使用了Kuhfuss湍流对流模型（TCM），该模型可以直接从TCM方程的解中解释过冲现象。 本研究的主要目的是测试将Kuhfuss TCM应用于中间质量核心氦燃烧恒星时的预测，并验证这些模型预测是否与造父变星的观测结果一致。 我们使用最先进的1D恒星演化代码GARSTEC，并结合Kuhfuss TCM的实现，计算了中间质量核心氦燃烧恒星的演化轨迹。 我们将这些轨迹与使用MLT计算的轨迹进行比较，包括和排除经验过冲，并与文献中获得的五个分离双星系统中的造父变星观测结果进行对比。 使用Kuhfuss TCM和带有经验过冲的MLT生成的恒星演化轨迹具有相似的外观。 从对流边界溢出混合以及造父变星蓝环的出现作为Kuhfuss TCM方程的自然解得到了实现。 此外，这些模型成功地再现了观测到的恒星参数，包括质量、光度、半径和有效温度。 总之，我们的TCM方法再现了造父变星的蓝环，并且与具有过冲的MLT模型一样很好地符合观测结果，但无需微调模型参数或假设。 显示英文摘要

摘要： The appearance of blue loops in the evolutionary tracks of intermediate-mass core He-burning stars is essential for explaining the observed characteristics of Cepheids. The blue loops for lower mass Cepheids cannot always be reproduced when only classical, local mixing length theory (MLT) is used. Additionally, classical models result in a mass discrepancy compared to pulsational and dynamical mass determinations. Both problems can be resolved through an ad-hoc extension of the MLT for convection. We use the non-local Kuhfuss turbulent convection model (TCM) which can explain overshooting directly from the solution of the TCM equations. The primary objective of this study is to test the predictions of the Kuhfuss TCM when applied to intermediate-mass core He-burning stars and validate the model predictions against observations of Cepheids. We used the state-of-the-art 1D stellar evolution code GARSTEC with the implementation of the Kuhfuss TCM and computed evolutionary tracks for intermediate-mass core He-burning stars. We compare these tracks with those computed with MLT including and excluding ad-hoc overshooting and with observations of five Cepheids in detached binary systems obtained from the literature. The stellar evolution tracks generated using the Kuhfuss TCM and MLT with ad-hoc overshooting exhibit similar appearances. Overshoot mixing from the convective boundaries and the occurrence of the Cepheid blue-loop have been achieved naturally as solutions to the Kuhfuss TCM equations. Furthermore, these models successfully reproduce observed stellar parameters including mass, luminosity, radius, and effective temperature. In conclusion, our TCM approach reproduces Cepheid blue loops and agrees with observations similarly well as MLT models with overshooting, however, without fine-tuning the model parameters or ad-hoc assumptions.