Silicon Burning II: Quasi-Equilibrium and Explosive Burning

Having examined the application of quasi-equilibrium to hydrostatic silicon burning in Paper I of this series, Hix & Thielemann (1996), we now turn our attention to explosive silicon burning. Previous authors have shown that for material which is heated to high temperature by a passing shock and then cooled by adiabatic expansion, the results can be divided into three broad categories; \emph{incomplete burning}, \emph{normal freezeout} and \emph{$\alpha$-rich freezeout}, with the outcome depending on the temperature, density and cooling timescale. In all three cases, we find that the important abundances obey quasi-equilibrium for temperatures greater than approximately 3 GK, with relatively little nucleosynthesis occurring following the breakdown of quasi-equilibrium. We will show that quasi-equilibrium provides better abundance estimates than global nuclear statistical equilibrium, even for normal freezeout and particularly for $\alpha$-rich freezeout. We will also examine the accuracy with which the final nuclear abundances can be estimated from quasi-equilibrium.Comment: 27 pages, including 15 inline figures. LaTeX 2e with aaspp4 and graphicx packages. Accepted to Ap

Computational Methods for Nucleosynthesis and Nuclear Energy Generation

This review concentrates on the two principle methods used to evolve nuclear abundances within astrophysical simulations, evolution via rate equations and via equilibria. Because in general the rate equations in nucleosynthetic applications form an extraordinarily stiff system, implicit methods have proven mandatory, leading to the need to solve moderately sized matrix equations. Efforts to improve the performance of such rate equation methods are focused on efficient solution of these matrix equations, by making best use of the sparseness of these matrices. Recent work to produce hybrid schemes which use local equilibria to reduce the computational cost of the rate equations is also discussed. Such schemes offer significant improvements in the speed of reaction networks and are accurate under circumstances where calculations with complete equilibrium fail.Comment: LaTeX2e with graphicx, 40 Pages with 5 embedded figures. To be published in Computational Astrophysics, The Journal of Computational and Applied Mathematics, eds. H. Riffert, K. Werne

Silicon Burning I: Neutronization and the Physics of Quasi-Equilibrium

As the ultimate stage of stellar nucleosynthesis, and the source of the iron peak nuclei, silicon burning is important to our understanding of the evolution of massive stars and supernovae. Our reexamination of silicon burning, using results gleaned from simulation work done with a large nuclear network (299 nuclei and more than 3000 reactions) and from independent calculations of equilibrium abundance distributions, offers new insights into the quasi-equilibrium mechanism and the approach to nuclear statistical equilibrium. We find that the degree to which the matter has been neutronized is of great importance, not only to the final products but also to the rate of energy generation and the membership of the quasi-equilibrium groups. A small increase in the global neutronization results in much larger free neutron fluences, increasing the abundances of more neutron-rich nuclei. As a result, incomplete silicon burning results in neutron richness among the isotopes of the iron peak much larger than the global neutronization would indicate. Finally, we briefly discuss the limitations and pitfalls of models for silicon burning currently employed within hydrodynamic models. In a forthcoming paper we will present a new approximation to the full nuclear network which preserves the most important features of the large nuclear network calculations at a significant improvement in computational speed. Such improved methods are ideally suited for hydrodynamic calculations which involve the production of iron peak nuclei, where the larger network calculation proves unmanageable.Comment: 44 pages of TeX with 25 Postscript figures, uses psfig.sty, To appear in the The Astrophysical Journal, April 1 1996. Complete PostScript version of the paper is also available from http://tycho.as.utexas.edu/~raph/Publications.htm

Nuclear Structure Studies at ISOLDE and their Impact on the Astrophysical r-Process

The focus of the present review is the production of the heaviest elements in nature via the r-process. A correct understanding and modeling requires the knowledge of nuclear properties far from stability and a detailed prescription of the astrophysical environment. Experiments at CERN/ISOLDE have played a pioneering role in exploring the characteristics of nuclear structure in terms of masses and beta-decay properties. Initial examinations paid attention to far unstable nuclei with magic neutron numbers related to r-process peaks, while present activities are centered on the evolution of shell effects with the distance from the valley of stability. We first show in site-independent applications the effect of both types of nuclear properties on r-process abundances. Then, we explore the results of calculations related to two different `realistic' astrophysical sites, (i) the supernova neutrino wind and (ii) neutron star mergers. We close with a list of remaining theoretical and experimental challenges needed to overcome for a full understanding of the nature of the r-process, and the role CERN/ISOLDE can play in this process.Comment: LATEX, 38 pages, 16 figures, submitted to Hyperfine Interaction

Simulation of the Spherically Symmetric Stellar Core Collapse, Bounce, and Postbounce Evolution of a 13 Solar Mass Star with Boltzmann Neutrino Transport, and Its Implications for the Supernova Mechanism

With exact three-flavor Boltzmann neutrino transport, we simulate the stellar core collapse, bounce, and postbounce evolution of a 13 solar mass star in spherical symmetry, the Newtonian limit, without invoking convection. In the absence of convection, prior spherically symmetric models, which implemented approximations to Boltzmann transport, failed to produce explosions. We are motivated to consider exact transport to determine if these failures were due to the transport approximations made and to answer remaining fundamental questions in supernova theory. The model presented here is the first in a sequence of models beginning with different progenitors. In this model, a supernova explosion is not obtained. We discuss the ramifications of our results for the supernova mechanism.Comment: 5 pages, 3 figures, Submitted to Physical Review Letter