The equilibrium of a galactic bar
Abstract
It is shown that, for values of the polytropic index not less than 0.5, every uniformly rotating, gaseous polytrope has an exact stellardynamical 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 distribution functions depend on three isolating integrals of the motion.
 Publication:

The Astrophysical Journal
 Pub Date:
 September 1980
 DOI:
 10.1086/158253
 Bibcode:
 1980ApJ...240..478V
 Keywords:

 Barred Galaxies;
 Galactic Rotation;
 Galactic Structure;
 Polytropic Processes;
 Star Clusters;
 Stellar Motions;
 Stellar Systems;
 Astronomical Models;
 Body Kinematics;
 Elliptical Galaxies;
 Astrophysics