Bifurcation and Fission of Three Dimensional, Rigidly Rotating and Self-Gravitating Polytropes

Details Bifurcation and Fission of Three Dimensional, Rigidly Rotating and Self-Gravitating Polytropes Bifurcation and Fission of Three Dimensional, Rigidly Rotating and Self-Gravitating Polytropes

Jul 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982pthph..68..206h&link_type=abstract

Progress of Theoretical Physics, Vol. 68, No. 1, pp. 206-221

Physics

24

Scientific paper

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 with x-y, y-z and z-x planes symmetry and with small compressibilities, i.e., polytropic indexes N=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/(4 π GM10/3 ρc-1/3)1/2 ≃ 0.07). 2) The ellipsoid-like sequences with N= 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.).

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