Nonaxisymmetric dynamic instabilities of rotating polytropes. II. Torques,bars, and mode saturation with applications to protostars and fizzlers

Dynamic nonaxisymmetric instabilities in rapidly rotating stars and protost ars have a range of potential applications in astrophysics, including impli cations for binary formation during protostellar cloud collapse and for the possibility of aborted collapse to neutron star densities at late stages o f stellar evolution ("fizzlers"). We have recently presented detailed linea r analyses for polytropes of the most dynamically unstable global modes, th e barlike modes. These produce bar distortions in the regions near the rota tion axis but have trailing spiral arms toward the equator. In this paper, we use our linear eigenfunctions to predict the early nonlinear behavior of the dynamic instability and compare these "quasi-linear" predictions with several fully nonlinear hydrodynamics simulations. The comparisons demonstr ate that the nonlinear saturation of the barlike instability is due to the self-interaction gravitational torques between the growing central bar and the spiral arms, where angular momentum is transferred outward from bar to arms. We also find a previously unsuspected resonance condition that accura tely predicts the mass of the bar regions in our own simulations and in tho se published by other researchers. The quasi-linear theory makes other accu rate predictions about consequences of instability, including properties of possible end-state bars and increases in central density, which can be lar ge under some conditions. We discuss in some detail the application of our results to binary formation during protostellar collapse and to the formati on of massive rotating black holes.