A THREE-DIMENSIONAL NUMERICAL SOLUTION FOR THE SHAPE OF A ROTATIONALLY DISTORTED POLYTROPE OF INDEX UNITY
A THREE-DIMENSIONAL NUMERICAL SOLUTION FOR THE SHAPE OF A ROTATIONALLY DISTORTED POLYTROPE OF INDEX UNITY
复制标题
DOI：
10.1088/0004-637x/763/2/116
复制
发表时间：
2013-01
期刊：
影响因子：
--
通讯作者：
D. Kong;Keke Zhang;G. Schubert;J. Anderson
中科院分区：
文献类型：
--
作者：
D. Kong;Keke Zhang;G. Schubert;J. Anderson
本文提出了一种新的三维数值方法，用于计算具有多方统一指数的快速旋转气体体模型的非球形形状和内部结构。计算是基于有限元法，并考虑到旋转的全部影响。在验证了数值方法对渐近解的rasekhar是有效的，只有一个缓慢旋转的气体体，我们将其应用到模型的木星和快速旋转，高度扁平的星星（波江座α）。在木星的情况下，密度和压力的二维分布确定通过混合逆方法通过调整状态方程中的先验未知系数，直到模型形状匹配观测到的木星的形状。在得到二维密度分布后，我们从充分考虑旋转引起的形状变化的非球形模型中计算纬向重力系数和总质量。我们的非球形模型具有多方统一指数，能够以约4%的精度给出木星的已知质量，并以优于2%的精度给出木星的纬向引力系数J2，考虑到模型中只有一个参数，这是一个合理的结果。对于波江座α星，我们根据观测得到的星星的自转速率和大小，采用类似的混合逆方法计算了它的旋转畸变形状和内部结构。我们的星星模型非常接近于观测到的扁率。
We present a new 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 of unity. The calculation is based on a finite-element method and accounts for the full effects of rotation. After validating the numerical approach against the asymptotic solution of Chandrasekhar that is valid only for a slowly rotating gaseous body, we apply it to models of Jupiter and a rapidly rotating, highly flattened star (α Eridani). In the case of Jupiter, the two-dimensional distributions of density and pressure are determined via a hybrid inverse approach by adjusting an a priori unknown coefficient in the equation of state until the model shape matches the observed shape of Jupiter. After obtaining the two-dimensional distribution of density, we then compute the zonal gravity coefficients and the total mass from the non-spherical model that takes full account of rotation-induced shape change. Our non-spherical model with a polytropic index of unity is able to produce the known mass of Jupiter with about 4% accuracy and the zonal gravitational coefficient J 2 of Jupiter with better than 2% accuracy, a reasonable result considering that there is only one parameter in the model. For α Eridani, we calculate its rotationally distorted shape and internal structure based on the observationally deduced rotation rate and size of the star by using a similar hybrid inverse approach. Our model of the star closely approximates the observed flattening.