The dominance of dynamic barlike instabilities in the evolution of a massive stellar core collapse that "fizzles"

Core collapse in a massive rotating star may halt at subnuclear density if the core contains angular momentum J greater than or similar to 10(49) g cm (2) s(-1). An aborted collapse can lead to the formation of a rapidly rotat ing equilibrium object, which, because of its high electron fraction, Y-e > 0.4, and high entropy per baryon, S-b/k approximate to 1-2, is secularly a nd dynamically stable. The further evolution of such a "fizzler" is driven by deleptonization and cooling of the hot, dense material. These processes cause the fizzler both to contract toward neutron star densities and to spi n up, driving it toward instability points of the barlike modes. Using line ar stability analyses to study the latter case, we find that the stability properties of fizzlers are similar to those of Maclaurin spheroids and poly tropes despite the nonpolytropic nature and extreme compressibility of the fizzler equation of state. For fizzlers with the specific angular momentum distribution of the Maclaurin spheroids, secular and dynamic barlike instab ilities set in at T/\W\ approximate to 0.14 and 0.27, respectively, where T is the rotational kinetic energy and W is the gravitational energy of the fizzler, the same limits as found for Maclaurin spheroids. For fizzlers in which angular momentum is more concentrated toward the equator, the secular stability limits drop dramatically. For the most extreme angular momentum distribution we consider, the secular stability limit for the barlike modes falls to T/\W\ approximate to 0.038, compared with T/\W\ approximate to 0. 09-0.10 for the most extreme polytropic cases known previously (Imamura et al.). For fixed equation-of-state parameters, the secular and dynamic stabi lity limits occur at roughly constant mass over the range of typical fizzle r central densities. Deleptonization and cooling decrease the limiting mass es on timescales shorter than the growth time for secular instability. Cons equently, unless an evolving fizzler reaches neutron star densities first, it will always encounter dynamic barlike instabilities before secular insta bilities have time to grow. Quasi-linear analysis shows that the angular mo mentum loss during the early nonlinear evolution of the dynamic barlike ins tability is dominated by Newtonian self-interaction gravitational torques r ather than by the emission of gravitational wave (GW) radiation. GW emissio n may dominate after the initial dynamic evolutionary phase ends. Nonlinear hydrodynamics simulations with a proper equation of state will be required to determine the ultimate outcome of such evolutions and to refine predict ions of GW production by barlike instabilities.