The equilibrium of a galactic bar

TL;DRAbstract

It is shown that, for values of the polytropic index not less than 0.5, every uniformly rotating, gaseous polytrope has an exact stellar-dynamical counterpart. Like gaseous polytropes, uniformly rotating polytropic stellar systems have axisymmetric configurations of equilibrium and, provided that the polytropic index is less than 0.808, nonaxisymmetric configurations of equilibrium as well. The axisymmetric and nonaxisymmetric configurations form linear sequences which correspond, respectively, to the Maclaurin and Jacobi sequences of uniformly rotating, homogeneous fluid ellipsoids. The distribution functions in these stellar systems are functions of Jacobi's integral alone; consequently, the systems exhibit no differential motions in their rotating frames of reference, and the distributions of the peculiar velocities of their stars are isotropic. The nonaxisymmetric configurations are counterexamples to the prevailing conjecture that stellar systems can be triaxial only if their dist

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