报告题目：快速旋转天体的自洽多方气体模型与旋转椭球近似Self-consistent internal structure of a rotating polytrope and its comparison with an approximation by oblate spheroidal equidensity surfaces

　　报 告 人：孔大力博士（上海天文台/University of Exeter)

　　摘    要：气态大行星和某些组分复杂的恒星内部状态可以近似为指数为1的多方球。由于天体的形状和内部结构直接影响和控制其重要的内部流体动力学过程与外部引力场特征，因此快速自转条件下多方球的流体静力学平衡与内部结构是一个受到持续关注的经典天体物理问题。自20世纪30年代钱德拉塞卡首先研究慢旋转条件下Lane-Emden方程近似解至今，已有数类出发点各异的方法被用于求解旋转多方球问题上，它们存在各自不同的近似简化或缺陷。P. H. Roberts在20世纪60年代初期提出了一类具有代表性的旋转椭球近似方法：在假设内部等密度面均为旋转椭球形状的前提下，通过总能量变分方法得到旋转多方球的流体静力学平衡解。该方法具有方便理论分析研究的巨大优势，但其椭球形状假设直至今日仍然受到持续的质疑与批评。我们通过三维自洽有限元方法首次在没有任何特殊假设的条件下求解指数为1的旋转多方球问题，得到多方球准确的形状和内部结构。我们也首次通过扁椭球波动函数构造的格林函数方法解析求解了仅假设外表面为旋转椭球形状时指数为1的旋转多方球问题。通过比较自洽数值解、外表面旋转椭球近似下的解析解和Roberts的完全旋转椭球假设条件下的解，我们首次支持了Roberts假设对类似木星参数的天体的适用和有效近似程度。

　　In an important paper, P.H. Roberts (1963, ApJ, 138, 809) studied the hydrostatic equilibrium of an isolated, self-gravitating, rapidly rotating polytropic gaseous body based on a controversial assumption/approximation that all (outer and internal) equidensity surfaces are in the shape of oblate spheroids whose eccentricities are a function of the equatorial radius and whose axes of symmetry are parallel to the rotation axis. We compute, for the first time, the three-dimensional, finite-element, fully self-consistent, continuous solution for a rapidly rotating polytropic gaseous body without making any prior assumptions about either its outer shape or internal structure. Upon partially relaxing the Roberts' approximation by assuming that only the outer surface is in the shape of an oblate spheroid, we also derive an exact analytic solution based on the Green’s function using spheroidal wave functions without making any prior assumptions about its internal structure. It is found that all equidensity surfaces of the fully self-consistent solution differ only slightly from the oblate spheroidal shape. It is also found that the characteristic difference between the fully self-consistent solution and the outer-spheroidal-shape solution is insignificantly small. Our results suggest that the Roberts' assumption of spheroidal equidensity surfaces represents a reasonably accurate approximation for rotating polytropic gaseous bodies with Jupiter-like parameters.

　　时间及地点：6月12日（周五）上午10:30，南京大学天文楼212报告厅

欢迎各位老师、同学参加！

　　                                     南京大学天文与空间科学学院