Multiple equilibria and free energy for rotating, self-gravitating fluid bodies

Statistics – Computation

Scientific paper

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Computational Astrophysics, Cosmology, Galactic Evolution, Gravitational Effects, Rotating Bodies, Rotating Fluids, Computational Fluid Dynamics, Density Distribution, Equilibrium Equations, Free Energy, Spheroids

Scientific paper

The multiple equilibria of a rotating self-gravitating fluid body embedded in an external medium and condensed around a central mass seed are investigated. The body's density is approximated as constant on nested spheroids, and it is shown that there is a range of parameters for which three equilibrium configurations exist. It is argued that this is a generic result for axisymmetric bodies. To distinguish the 'preferred' equilibria, a free energy is defined, and it is proven that it never increases for isothermal bodies when internal temperature and external pressure are constant. Of the three equilibria states, the free energy is minimized by two: one compact and one diffuse.

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