波江座α的快速自转多方球模型

A Polytropic Model of Rapidly Rotating α Eri

波江座α是一颗具有代表性并被比较充分观测的快速自转恒星。以该星为例,建立了一种可以利用有限的观测数据有效反演此类恒星椭球形状及其内部结构的并行数值方法。求解此问题的经典近似方法 (一般)只对慢速旋转的恒星有效,需要对旋转角速度作小扰动假设;而该方法为严格数值求解恒星的旋转多方球模型,对快速旋转的情形仍然保持有效。该方法采用的大规模并行有限元方法,对超级计算设备的性能与计算方法实现的效率都有很高的需求。计算表明,如果有限元网格包含数千万单元水平,则经过充分内存优化的代码在上海超级计算中心曙光5000A超级计算机上运行需要不少于1024核的资源。

We present a three-dimensional numerical method for calculating the non-spherical shape and internal structure of a model of a rapidly rotating gaseous body with a polytropic index unity. The calculation is based on a finite element method and accounts for the full effects of rotation. We apply it to a model of a rapidly rotating, highly flattened star （α Eridani）. The distributions of density and pressure are determined via a hybrid inverse approach by adjusting a priori unknown coefficient in the equation of state （EOS） until the model mass matches the observed mass of the star. The numerical method, implemented as a 3D finite element scheme, relies on massively parallel computing facilities. On the Dawning 5000A machine in Shanghai Supercomputer Center （SSC）, we utilized typically 1024 cores to carry out our calculations effectively. The model and numerical method are both ready to be generalized to include various physical features and processes such as differential rotation, tidal effects and more realistic EOS of gaseous configurations.