Title Page

Outline

1. Introduction

2. Physical Modeling

3. Numerical Results

4. Summary

2. PHYSICAL MODELING

2.1 Fizzlers

• Traditional Fizzler Scenario

  Gold (1974), Lightman & Shapiro (1976), Tohline (1984), Hayashi, Eriguchi, & Hashimoto (1998,1999); Aborted core collapse due to rotation with a subsequent quasistatic approach to neutron star densities driven by the gravitational radiation reaction (GRR) driven secular instability.

• Modified Fizzler Scenario
  Imamura & Durisen (2000), Imamura, Durisen, & Pickett (2002); Aborted collapse due to rotation with a subsequent quasistatic approach driven by deleptonization and cooling to dynamic barlike instability. instabilities may set in for T/|W| > 0.14 for large n polytropes). The evolution of the barlike instability is driven primarily by the Newtonian self-interaction torque but angular momentum is also shed to infinity through gravitational radiation from the bar. (see Centrella, New, Lowe, & Brown 2001, Ap. J., L93 for results suggesting that m=1 dynamic instabilities may set in for T/|W| > 0.14 for large n polytropes also negating the traditional fizzler scenario.)

2.2 Hydrodynamics Equations

2.2.1 Equations

We consider the standard inviscid, adiabatic Newtonian hydrodynamics equations and Poisson's equation.

2.2.2 Equation-of-State
We use the Lattimer & Swesty (LS) equation-of-state (EOS) for hot, dense material. The LS EOS is based on the liquid drop model for nuclear material. At high density, it is harder than the cold, beta-equilibrium EOS. It, however, is very soft at low density.

2.2.3 Gravitational Wave Radiation

2.2.4 Deleptonization and Cooling

2.3 Numerical Methodology

• Equilibrium Modeling -- Self-consistent field technique (Hachisu 1986, Imamura & Durisen 2000)

• Linear Modeling -- The initial value problem for the evolution of infinitesimal perturbations away from equilibrium is solved (Toman et al. 1998, Imamura, Durisen, & Pickett 2000, Imamura & Durisen 2000).

• Quasi-linear Modeling -- The linear eigenfunctions are used to model the early nonlinear behavior (Imamura, Durisen, & Pickett 2000, Imamura & Durisen 2000).

• Nonlinear Modeling -- Fully nonlinear hydro equations are solved. The spatial and temporal derivatives are second-order accurate. The fluxing is accomplished using the van Leer algorithm (Pickett, Durisen, & Davis 1996, Imamura, Durisen, & Pickett 2002).