利用湍流模型研究新的化学组成下的太阳内部结构

The study of modeling solar structure is basic and important for astrophysics. The latest observation of the solar chemical composition results in remarkable distinctions between the standard solar model and the helioseismic inversions. These distinctions are the main problem of modeling sun at present, indicate that there are some physical processes that are not correctly taken into account. We apply for the NSFC to aim at that problem. The main problem of the standard solar model with new composition is that the base of the convection zone is too shallow to fit the helioseismic inversion. This leads to He abundance at the surface and the sound speed structure showing large biases in comparison with the helioseismic inversion. The convective overshoot modifies the temperature gradient and leads to chemical mixing in the overshoot region below the base of the solar convection zone. These effects are similar to the convection. Taking into account the overshoot is equivalent to enlarger the convection zone. The overshoot with proper intensity may result in the equivalent depth of the convection being in consistent with the helioseismic inversion, then the solar model could be improved. Recently, the helioseismic investigation suggested that the convective overshoot only described by turbulent convection models(TCMs) are favored. Therefore we should use the TCM to deal with the overshoot. The overshoot based on TCMs is significantly different from the classical overshoot model, since TCMs self-consistently describe the turbulent heat transport in the overshoot region. The numerical calculation of TCMs in stellar evolutionary models is the main difficulty in the application of TCMs. In our previous work, we developed an practicable code. However, the code is not stable enough, and takes very long time. We plan to use self-adjusting relaxations and GPU to improve the code.

使用新的太阳化学组成测定结果后，标准太阳模型与日震学反演之间出现了较大的差异，这成为当前太阳模型研究的难题之一，暗示了某些物理过程未能被正确的考虑。本研究项目针对研究这一问题而申请。新化学组成下的标准太阳模型存在的主要问题是对流区的深度太浅，这导致表面He丰度偏低和声速结构不符合日震学反演等问题。我们认为，如果使用湍流模型来描述对流超射，并在太阳结构中考虑对流超射的传热传质效果，即相当于增大对流区，若对流超射的传热传质的强度合适，使得太阳模型的等效对流区深度达到日震学反演的结果，则可能起到改善作用。湍流模型描述的对流超射图景与经典的超射模型有很大区别，不同之处在于它能够自洽的考虑超射的传能。当前日震学研究表明只有用湍流模型描述超射才能与日震学观测符合。在本申请项目中，我们还计划发展一套稳定高效的数值计算程序，用于包含湍流模型的恒星结构演化模型的计算。

本项目主要研究了恒星湍流模型的计算以及将其用于改善太阳结构模型等问题。我们对恒星湍流模型的计算过程进行了多方面探索，确定了将湍流模型方程和恒星演化方程之间的迭代量设置为温度梯度与其局地解的比值，并以渐近解为湍流模型方程的猜测值和使用自适应方法调整松弛因子，终于保证了稳定高效的数值求解湍流模型和恒星演化联立方程组。以此为基础，我们开发出一套恒星演化程序YNEV，可将湍流模型用于计算恒星内部对流，并与恒星结构演化方程一起求解。以此程序作为研究平台，可进一步研究各种质量恒星在不同演化状态下的内部湍动对流的物理性质。我们对太阳模型进行了大参数范围的计算，发现只有当太阳对流区底部湍流动能流为-14%倍太阳光度左右时，太阳模型与日震学反演才能符合，这为湍流模型的发展和改进提供了线索。我们还将湍流模型简化为一个线性模型，此线性模型计算简单，对于推广湍流模型在恒星演化中的应用提供了很大的便利。此外，我们还高精度的计算了电子屏蔽情况下微观扩散方程中抵抗系数，纠正了前人计算的错误，此结果可广泛用于恒星内部元素微观扩散过程的计算。

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