BIFURCATION AND FISSION OF 3 DIMENSIONAL, RIGIDLY ROTATING AND SELF-GRAVITATING POLYTROPES
BIFURCATION AND FISSION OF 3 DIMENSIONAL, RIGIDLY ROTATING AND SELF-GRAVITATING POLYTROPES
复制标题
DOI：
10.1143/ptp.68.206
复制
发表时间：
1982-01-01
影响因子：
--
通讯作者：
ERIGUCHI, Y
中科院分区：
文献类型：
--
作者：
HACHISU, I;ERIGUCHI, Y
本文用解析延拓法给出了一种求解旋转多面体三维流体静力平衡结构的新方法。将椭圆型微分方程如Poisson方程转化为双曲型微分方程。因此，当柯西数据在中心区域给出时，我们可以直接从中心向外积分方程并获得结构。利用这种方法，研究了快速旋转多面体的分岔和裂变，以重新审视流行的分岔和裂变理论。具有x-y，y-zandz-x平面对称性和较小压缩率的多面体，即多变指数N =0，0.1、0.2、0.3、0.4和0.5。结果表明：1）所有这些多面体在每个分叉点都从类椭球分叉为类椭球。这些分叉发生在几乎相同的角动量（j=J/（4π GM 10/3ρc−1/3）1/2 <$0.07）。2)N = 0.1 <$0.5的类椭球序列终止于每个临界点，在该临界点处，在哑铃形出现之前，质量从赤道脱落，尽管3）哑铃形构型在不可压缩情况下（N=0.）从Jacobi序列分叉。
A new computational method for solving three dimensional hydrostatic equilibrium structures of rotating polytropes is formulated by using analytic continuation. An elliptic-type differential equation such as Poisson equation is transformed into a hyperbolic-type one. Therefore, when Cauchy data are given in the central region, we can integrate the equation directly outward from the center and obtain the structure. Using this method, bifurcation and fission of rapidly rotating polytropes are investigated in order to reexamine the prevailing bifurcation and fission theories. The polytropes withx-y, y-zandz-xplanes symmetry and with small compressibilities, i.e., polytropic indexesN=0., 0.1, 0.2, 0.3, 0.4 and 0.5 have been calculated. The results show the following: 1) All of these polytropes bifurcate from a spheroid-like shape to an ellipsoid-like one at each bifurfcation point. These bifurcations occur at much the same angular momentum (j=J/(4πGM10/3ρc−1/3)1/2≃0.07). 2) The ellipsoid-like sequences withN= 0.1 ∼ 0.5 terminate at each critical point where the mass sheds from the equator before the dumb-bell shape appears, though 3) the dumb-bell configuration bifurcates from the Jacobi sequence in the incompressible case (N=0.).