The Dominance of Dynamic Barlike Instabilities in the Evolution of a Massive Stellar Core Collapse That “Fizzles”

Abstract

Core collapse in a massive rotating star may halt at subnuclear density if the core contains angular momentum J>~1049 g cm2 s-1. An aborted collapse can lead to the formation of a rapidly rotating equilibrium object, which, because of its high electron fraction, Ye>0.4, and high entropy per baryon, Sb/k~1-2, is secularly and 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 spin up, driving it toward instability points of the barlike modes. Using linear stability analyses to study the latter case, we find that the stability properties of fizzlers are similar to those of Maclaurin spheroids and polytropes 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 instabilities set in at T/|W|~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|~0.038, compared with T/|W|~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 stability limits occur at roughly constant mass over the range of typical fizzler central densities. Deleptonization and cooling decrease the limiting masses on timescales shorter than the growth time for secular instability. Consequently, unless an evolving fizzler reaches neutron star densities first, it will always encounter dynamic barlike instabilities before secular instabilities have time to grow. Quasi-linear analysis shows that the angular momentum loss during the early nonlinear evolution of the dynamic barlike instability is dominated by Newtonian self-interaction gravitational torques rather than by the emission of gravitational wave (GW) radiation. GW emission 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 predictions of GW production by barlike instabilities.