A numerical study of the fission hypothesis for rotating polytropes

Conclusions

Our results show that n = 3/2 and n = 1/2 polytropes are dynamically unstable to non-axisymmetric perturbations if t ≳ 0.30, in rough agreement with linear theory. Instead of fission as the direct end product of dynamic instability in rapidly rotating, centrally condensed stars, it appears that a rapidly rotating star can, through gravitational torques, eject some high angular momentum material in its equatorial plane and settle down into a dynamically stable (lower t) configuration. The central object, at least in the detailed evolution described above, ends up as a stable traixial star! The assumption of reflection symmetry through the rotation axis needs to be relaxed before this evolutionary picture can be considered realistic and before meaningful comparisons can be made with the results of Lucy (1977) and Gingold and Monaghan (1978, 1979), who found “odd” modes to be of crucial importance.

We cannot escape mentioning that the ejected disk/ring of material in our models may have some connection with the formation of planetary systems.