The linear and nonlinear dynamic stability of rotating N = 3/2 polytropes

A three-dimensional hydrodynamic computer program has been used to study the growth of nonaxisymmetric structure in rapidly rotating, n = 3/2 polytropes whose initial axisymmetric equilibria were constructed with the Ostriker-Mark, self-consistent field method. Differentially rotating models were studied, whose initial ratios t of rotational to gravitational potential energy were t = 0.28, 0.30, 0.33, and 0.35. An open, two-armed, trailing spiral pattern, rather than a coherent bar mode, has been found to grow dynamically in all models with t at least 0.30. The results of the investigation support the reliability of both the tensor virial equation (TVE) analysis of such systems and the computer simulation itself. The 3D code can be used with confidence to study the dynamical growth of nonaxisymmetric structure into the nonlinear amplitude regime.