J. Cooperstein

Electron Capture in Stellar Collapse

Abstract Electron-capture rates are calculated for the high-density regime of pre-supernova stellar collapse. The Gamow-Teller contribution arises from thermal unblocking and proceeds mainly through captures beneath the T = 0 energy threshold. Parity-forbidden (Δl = 1) processes also contribute, particularly the 2− unique forbidden transition. Both are quenched by the effective renormalization of the vector and axial vector charges by ground-state correlations and isobars. Special attention is paid to the temperature-induced unblocking of the GTs and the thermal redistribution of the forbidden-transition strength. A statistical treatment averages the contributions of nuclear species present in the mass range 60

Shock propagation in supernovae: Concept of net ram pressure

Abstract In this paper we discuss circumstances under which shock waves, formed in the collapse of large stars, will propagate outwards, blowing off the mantle and envelope of these stars. This is a mechanism for the formation of neutron stars. We introduce the concept of “net ram pressure”; in terms of this quantity our book-keeping is conveniently carried out. The formation of a “dense pack”, a region at the center of the collapsed stellar core at densities above nuclear matter density, is essential for successful shock formation and propagation. Effects of nuclear excited states and nuclear dissociation are conveniently expressed in terms of the net ram pressure. We construct pre-supernova cores of 1.25M⊙ and 1.35M⊙, and perform hydrodynamical calculations using them as input, which give marginally successful and unsuccessful results, respectively. Low entropy for the initial core and the thinning out of matter falling through the shock wave turn out to be essential for success.

A simplified equation of state near nuclear density

Abstract The equation of state near nuclear density influences shock formation in stellar collapse Supernovae. The drop in the adiabatic index below 4 3 in this region, due to the negative nuclear pressure, disturbs the homology of the inner core and decreases its size. The initial shock energy and formation dynamics are particularly sensitive to matter in this regime. Only matter at low entropies ( S ⩽ 1.5) in the unshocked inner core approaches nuclear densities. We derive a simple equation of state for this material and find that nuclear properties are close to those at S = 0. The entropy associated with the nuclear surface can be absorbed into an “effective mass” which decreases towards one with increasing density, giving an accurate accounting for the storage of entropy in the excitation of the large nuclei. Such thermal excitation drains energy with little contribution to the pressure and thus may have important effects on the launching of the shock. Two phase transitions are considered. The first, from the heavy nucleus to the “bubble” phase, occurs at half nuclear matter density and is accomplished by use of simple expressions for the energy and pressure that include effects of the transition implicitly. The second, that to uniform nuclear matter, is done by requiring continuity of the pressure and entropy at the transition. The density at which this transition takes place is calculated and is found to decrease with entropy in a simple manner. With the use of suitable approximations, the equation of state is presented in a non-iterative form easily adapted for use in full hydrodynamical calculations of the supernovae process. Comparison with more detailed equations of state is made and the simplified one is found to represent well all important features.

The equation of state in supernovae

Abstract A simple equation of state for supernova matter is based on the compressible liquid-drop model. The nuclei-bubbles and bubbles-nuclear matter phase transitions are handled smoothly and properties of the dense phase in the bubble regime are investigated. Using phenomenological values for the nuclear bulk compression modulus and surface energies, we find the dense phase expands to occupy most of the volume well before the overall density approaches saturation. Finite-temperature properties are modelled by use of a nucleon effective mass whose enhancement over the saturation value is taken as proportional to the surface and Coulomb energies. In the bubble region the adiabatic index decreases only slightly below the relativistic 4 3 value.

Collapse of 9 solar mass stars

General relativistic hydrodynamical calculations of the collapse of O + Ne + Mg cores of a 9 solar mass star are reported. Collapse is induced by rapid electron captures as the O + Ne + Mg is burned to nuclear statistical equilibrium. The high entropy in the core after burning leads to a large abundance of free protons which readily capture electrons. This leads to large neutrino losses and a correspondingly small infalling homologous core. The hydrodynamic shock thus forms at a small mass point. The shock stalls before reaching the edge of the O + Ne + Mg core and thereby fails to produce a successful supernova explosion by the direct mechanism. No enhancement in the shock energy due to nuclear burning is found. 16 references.

Collapsing white dwarfs

The results of the hydrodynamic collapse of an accreting C + O white dwarf are presented. Collapse is induced by electron captures in the iron core behind a conductive deflagration front. The shock wave produced by the hydrodynamic bounce of the iron core stalls at about 115 km, and thus a neutron star formed in such a model would be formed as an optically quiet event. 19 references.

Neutrino diffusion in stellar collapse

We consider the diffusion flows of neutrinos in stellar collapse. The neutrino energy and number fluxes are driven by the gradients of temperature and chemical potential, and are characterized by four Rosseland mean free paths. We derive exact expressions for these Rosseland means, taking scattering and stimulated absorption of the neutrinos into account separately as well as in combination. The Rosseland means for the combined opacities constitute new analytical results. These exact expressions represent an improvement over previously published prescriptions.

Flux-limited diffusion in hydrodynamics

The radiation transport equation, correct to order v/c, is used to derive a flux limiter valid in high-velocity hydrodynamic flows. In the limit v = 0 the widely used result of Levermore and Pomraning (LP) (1982) is recovered. In the case of homologous flow (v varies as R) the LP result remains valid, but in the presence of shock waves and other nonhomologous flows differences may be large. We calculate the Eddington factors, which are significantly altered, and discuss the importance of having them possess the correct form in the presence of a shock wave, e.g., on the neutrino transport during the formation of a supernova.