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

Atypical Thermonuclear Supernovae from Tidally Crushed White Dwarfs

Suggestive evidence has accumulated that intermediate mass black holes (IMBH) exist in some globular clusters. As stars diffuse in the cluster, some will inevitable wander sufficiently close to the hole that they suffer tidal disruption. An attractive feature of the IMBH hypothesis is its potential to disrupt not only solar-type stars but also compact white dwarf stars. Attention is given to the fate of white dwarfs that approach the hole close enough to be disrupted and compressed to such extent that explosive nuclear burning may be triggered. Precise modeling of the dynamics of the encounter coupled with a nuclear network allow for a realistic determination of the explosive energy release, and it is argued that ignition is a natural outcome for white dwarfs of all varieties passing well within the tidal radius. Although event rates are estimated to be significantly less than the rate of normal Type Ia supernovae, such encounters may be frequent enough in globular clusters harboring an IMBH to warrant a search for this new class of supernova.Comment: 13 pages, 4 figures, ApJ, accepte

The Effects of Changes in Reaction Rates on Simulations of Nova Explosions

Classical novae participate in the cycle of Galactic chemical evolution in which grains and metal enriched gas in their ejecta, supplementing those of supernovae, AGB stars, and Wolf-Rayet stars, are a source of heavy elements for the ISM. Once in the diffuse gas, this material is mixed with the existing gases and then incorporated into young stars and planetary systems during star formation. Infrared observations have confirmed the presence of carbon, SiC, hydrocarbons, and oxygen-rich silicate grains in nova ejecta, suggesting that some fraction of the pre-solar grains identified in meteoritic material come from novae. The mean mass returned by a nova outburst to the ISM probably exceeds ~2 x 10^{-4} Solar Masses. Using the observed nova rate of 35 per year in our Galaxy, it follows that novae introduce more than ~7 x 10^{-3} Solar Masses per year of processed matter into the ISM. Novae are expected to be the major source of 15N and 17O in the Galaxy and to contribute to the abundances of other isotopes in this atomic mass range. Here, we report on how changes in the nuclear reaction rates affect the properties of the outburst and alter the predictions of the contributions of novae to Galactic chemical evolution. We also discuss the necessity of including the pep reaction in studies of thermonuclear runaways in material accreted onto white dwarfs.Comment: 9 pages, 2 figures, as it appeared in the Proceedings of the Tours 2006 Symposium on Nuclear Physic

Neutrinos, Fission Cycling, and the r-process

It has long been suggested that fission cycling may play an important role in the r-process. Fission cycling can only occur in a very neutron rich environment. In traditional calculations of the neutrino driven wind of the core-collapse supernova, the environment is not sufficiently neutron rich to produce the r-process elements. However, we show that with a reduction of the electron neutrino flux coming from the supernova, fission cycling does occur and furthermore it produces an abundance pattern which is consistent with observed r-process abundance pattern in halo stars. Such a reduction can be caused by active-sterile neutrino oscillations or other new physics.Comment: Typos corrected. Presented at NIC-IX, International Symposium on Nuclear Astrophysics - Nuclei in the Cosmos - IX, CERN, Geneva, Switzerland, 25-30 June, 200

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

Ascertaining the Core Collapse Supernova Mechanism: An Emerging Picture?

Here we present the results from two sets of simulations, in two and three spatial dimensions. In two dimensions, the simulations include multifrequency flux-limited diffusion neutrino transport in the "ray-by-ray-plus" approximation, two-dimensional self gravity in the Newtonian limit, and nuclear burning through a 14-isotope alpha network. The three-dimensional simulations are model simulations constructed to reflect the post stellar core bounce conditions during neutrino shock reheating at the onset of explosion. They are hydrodynamics-only models that focus on critical aspects of the shock stability and dynamics and their impact on the supernova mechanism and explosion. In two dimensions, we obtain explosions (although in one case weak) for two progenitors (11 and 15 Solar mass models). Moreover, in both cases the explosion is initiated when the inner edge of the oxygen layer accretes through the shock. Thus, the shock is not revived while in the iron core, as previously discussed in the literature. The three-dimensional studies of the development of the stationary accretion shock instability (SASI) demonstrate the fundamentally new dynamics allowed when simulations are performed in three spatial dimensions. The predominant l=1 SASI mode gives way to a stable m=1 mode, which in turn has significant ramifications for the distribution of angular momentum in the region between the shock and proto-neutron star and, ultimately, for the spin of the remnant neutron star. Moreover, the three-dimensional simulations make clear, given the increased number of degrees of freedom, that two-dimensional models are severely limited by artificially imposed symmetries.Comment: 9 pages, 3 figure