Thermonuclear detonations in collapsing white dwarf stars

Collapsing white dwarf stars (or degenerate cores) may occur in binary systems, in the formation of Type I supernovae or in the formation of pulsars. These collapsing configurations may explode their nuclear fuel (¹²C or¹⁶O) by the detonation wave mechanism. A combination of analytical and numerical models is used to investigate the formation of detonation waves. The tentative conclusion is that a detonation wave will form which will lead to the ignition of esentially all the fuel in such a collapsing star. This potentially explosive configuration will be strongly affected, however, by rapid beta processes which occur in the detonated matter and which should cause a fraction of the stellar mass to collapse toward a neutron star state. The nature and effect of such beta processes, which have not yet been incorporated in the dynamical calculations, are discussed.An appendix gives approximate expressions for the pressureP(,T) and the internal energy densityU(,T) for a degenerate relativistic electron gas and an analysis of the errors expected in making such approximations to the standard parametric form of the equation of state. These expressions are useful in analyzing shock waves in a degenerate electron gas.Supported in part by the National Science Foundation GP-15911, GP-9114, GP-19887] and the Office of Naval Research Nonr-220 (47)] at the California Institute of Technology, and National Science Foundation Grant GP-12455 at the University of Colorado.