Quasi-Equilibrium Figures for an Inhomogeneous Fluid Mass, of Riemann Type

Details Quasi-Equilibrium Figures for an Inhomogeneous Fluid Mass, of Riemann Type Quasi-Equilibrium Figures for an Inhomogeneous Fluid Mass, of Riemann Type

Oct 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995rmxaa..31..101c&link_type=abstract

Revista Mexicana de Astronomia y Astrofisica, 31, 101

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Stars: Rotation

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We establish both, numerically and analytically, the non-existence of exact equilibrium figures for a self-gravitating heterogeneous mass of an incompressible fluid, made up of two confocal ellipsoids in which Riemann or Dedekind conditions prevail. The body, therefore, can be either rotating as a solid or else be static, but in both cases the fluid circulates internally with uniform vorticity. On the other hand, if a discontinuity in the vorticity applies at the boundary between the two ellipsoids, then an approximate (quasi-equilibrium) solution is numerically tractable. This solution appears as a series of spheroids, the internal one being able to evolve into an ellipsoid, in roughly the same way as the homogeneous spheroids do. However, this evolution is never reached by the external mass whose surface of zero pressure, instead, becomes nearly spherical. The case which admits no solution at all is that of common vorticity, here worked out by means of a simple algebraic manipulation of Hamy's theorem.
Because both, a numerical error, and our recent awareness of this theorem, which rules out the existence of figures for a rotating model made up of n confocal layers, we published a result asserting the existence of Jacobi-type figures for n = 2, and we reconsider also here this result.

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