Title Page

Outline

1. Introduction

2. Physical Modeling

3. Numerical Results

4. Summary

3. NUMERICAL RESULTS

• General Fizzler Evolution
  Rotating core collapse is nonhomologous; the inner core collapses first while the outer core is essentially stationary. Collapse halts either when nuclear density is reached or centrifugal forces overcome gravity. The inner core rebounds dynamically and the outer core accretes onto the inner core. We assume that matter is not ejected and collapse leads to quasi-equilibrium fizzlers with M_core and J_core. Typical precollapse cores have M_core = 1.2-2.05 M_o, Y_e = 0.4-0.49, and S_b = 1.5 k.
  Iso-(Y_e,S_b,density) Fizzler Sequences

  

  
  

  • The above figure summarizes the equilibrium results. The loci are for n' = 0 (the specific angular momentum distribution of a Maclaurin spheroid) fizzlers with given central density and representative (Y_e,S_b/k). The curves have 10¹¹ g cm^-3 to 10¹⁴ g cm^-3, increasing in steps of factors of 10.

  • The dot-dashed lines which cut across the curves mark T/|W| = 0.27, the dynamic stability limit and the solid lines mark T/|W| = 0.14, the secular stability limit.

  • Defining the region above and to the left of the Y_e = 0.4, 10¹⁴ g cm^-3 sequence to be the fizzler regime leads to:
    
    

    Mass	J-Threshold
    1.2 M0	1049 g cm2 s-1
    1.6 Mo	2x1049 g cm2 s-1
    2 Mo	5x1049 g cm2 s-1

    
    
    

• Secular instability vs. Deleptonization and Cooling: The GRR time scales are longer than the deleptonization and cooling time scales and so, fizzler evolution is then driven by decreases in Y_e (deleptonization) and in S_b (cooling). This has two main consequences:
  • A fizzler which cools and deleptonizes at fixed M and J contracts to higher density.

  • As Y_e and S_b/k decrease, the stability limiting masses drop significantly and the deleptonizing fizzler is driven secularly to dynamic instability.