Collapse of rotating stellar cores equilibria between white dwarf and neutron star densities

At the end of its normal nuclear burning stage of evolution, the white dwarf--like core of a nonrotating massive star will collapse dynamically to neutron star densities because the effective adiabatic exponent GAMMA of matter at intermediate densities is less than 4/3. If the core is rotating such that the ratio β of rotational to gravitational energy in the core is greater than some minimum value β/sub min/, the collapse will not proceed all the way to neutron star densities. Instead of rotating equilibrium at intermediate density will form. These structures have previously been termed ''fizzlers'' by Shapiro and Lightman. The limiting value β/sub min/ is sensitive to the size of the adiabatic exponent GAMMA. A simple model presented here provides a quantitative relation between GAMMA and β/sub min/. The model also predicts what β will be in the core after it has settled to its intermediate-density equilibrium. Using a realistic representation of GAMMA during core collapse, we find that for a wide range of initial β, the final β has a value approx.0.15-0.20. Thus the endpoint of collapse is a dynamically stable, axisymmetric equilibrium. Further contraction of these objects will occur only on a (nondynamical) time scale that is governed by the rate at which they lose angular momentum. Magnetic dipole radiation or gravitational radiation should cause these ''fizzlers'' to evolve slowly toward a neutron star structure that is spinning with a period approx.1 ms