Statistical Methods for Thermonuclear Reaction Rates and Nucleosynthesis Simulations

Rigorous statistical methods for estimating thermonuclear reaction rates and nucleosynthesis are becoming increasingly established in nuclear astrophysics. The main challenge being faced is that experimental reaction rates are highly complex quantities derived from a multitude of different measured nuclear parameters (e.g., astrophysical S-factors, resonance energies and strengths, particle and gamma-ray partial widths). We discuss the application of the Monte Carlo method to two distinct, but related, questions. First, given a set of measured nuclear parameters, how can one best estimate the resulting thermonuclear reaction rates and associated uncertainties? Second, given a set of appropriate reaction rates, how can one best estimate the abundances from nucleosynthesis (i.e., reaction network) calculations? The techniques described here provide probability density functions that can be used to derive statistically meaningful reaction rates and final abundances for any desired coverage probability. Examples are given for applications to s-process neutron sources, core-collapse supernovae, classical novae, and big bang nucleosynthesis.Comment: Accepted for publication in J. Phys. G Focus issue "Enhancing the interaction between nuclear experiment and theory through information and statistics

Properties of Carbon-Oxygen White Dwarfs From Monte Carlo Stellar Models

We investigate properties of carbon-oxygen white dwarfs with respect to the composite uncertainties in the reaction rates using the stellar evolution toolkit, Modules for Experiments in Stellar Astrophysics (MESA) and the probability density functions in the reaction rate library STARLIB. These are the first Monte Carlo stellar evolution studies that use complete stellar models. Focusing on 3 M$_{\odot}$ models evolved from the pre main-sequence to the first thermal pulse, we survey the remnant core mass, composition, and structure properties as a function of 26 STARLIB reaction rates covering hydrogen and helium burning using a Principal Component Analysis and Spearman Rank-Order Correlation. Relative to the arithmetic mean value, we find the width of the 95\% confidence interval to be $\Delta M_{{\rm 1TP}}$ $\approx$ 0.019 M$_{\odot}$ for the core mass at the first thermal pulse, $\Delta$$t_{\rm{1TP}}$ $\approx$ 12.50 Myr for the age, $\Delta \log(T_{{\rm c}}/{\rm K}) \approx$ 0.013 for the central temperature, $\Delta \log(\rho_{{\rm c}}/{\rm g \ cm}^{-3}) \approx$ 0.060 for the central density, $\Delta Y_{\rm{e,c}} \approx$ 2.6$\times$10$^{-5}$ for the central electron fraction, $\Delta X_{\rm c}(^{22}\rm{Ne}) \approx$ 5.8$\times$10$^{-4}$, $\Delta X_{\rm c}(^{12}\rm{C}) \approx$ 0.392, and $\Delta X_{\rm c}(^{16}\rm{O}) \approx$ 0.392. Uncertainties in the experimental $^{12}$C($\alpha,\gamma)^{16}\rm{O}$, triple-$\alpha$, and $^{14}$N($p,\gamma)^{15}\rm{O}$ reaction rates dominate these variations. We also consider a grid of 1 to 6 M$_{\odot}$ models evolved from the pre main-sequence to the final white dwarf to probe the sensitivity of the initial-final mass relation to experimental uncertainties in the hydrogen and helium reaction rates.Comment: Accepted for publication in The Astrophysical Journal; 19 Pages, 23 Figures, 5 Table

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

STARLIB: A Next-Generation Reaction-Rate Library for Nuclear Astrophysics

STARLIB is a next-generation, all-purpose nuclear reaction-rate library. For the first time, this library provides the rate probability density at all temperature grid points for convenient implementation in models of stellar phenomena. The recommended rate and its associated uncertainties are also included. Currently, uncertainties are absent from all other rate libraries, and, although estimates have been attempted in previous evaluations and compilations, these are generally not based on rigorous statistical definitions. A common standard for deriving uncertainties is clearly warranted. STARLIB represents a first step in addressing this deficiency by providing a tabular, up-to-date database that supplies not only the rate and its uncertainty but also its distribution. Because a majority of rates are lognormally distributed, this allows the construction of rate probability densities from the columns of STARLIB. This structure is based on a recently suggested Monte Carlo method to calculate reaction rates, where uncertainties are rigorously defined. In STARLIB, experimental rates are supplemented with: (i) theoretical TALYS rates for reactions for which no experimental input is available, and (ii) laboratory and theoretical weak rates. STARLIB includes all types of reactions of astrophysical interest to Z = 83, such as (p,g), (p,a), (a,n), and corresponding reverse rates. Strong rates account for thermal target excitations. Here, we summarize our Monte Carlo formalism, introduce the library, compare methods of correcting rates for stellar environments, and discuss how to implement our library in Monte Carlo nucleosynthesis studies. We also present a method for accessing STARLIB on the Internet and outline updated Monte Carlo-based rates.Comment: Accepted for publication in the Astrophysical Journal Supplement Series; 96 pages, 22 figure

The Effects of the pep Nuclear Reaction and Other Improvements in the Nuclear Reaction Rate Library on Simulations of the Classical Nova Outburst

We have continued our studies of the Classical Nova outburst by evolving TNRs on 1.25Msun and 1.35Msun WDs (ONeMg composition) under conditions which produce mass ejection and a rapid increase in the emitted light, by examining the effects of changes in the nuclear reaction rates on both the observable features and the nucleosynthesis during the outburst. In order to improve our calculations over previous work, we have incorporated a modern nuclear reaction network into our hydrodynamic computer code. We find that the updates in the nuclear reaction rate libraries change the amount of ejected mass, peak luminosity, and the resulting nucleosynthesis. In addition, as a result of our improvements, we discovered that the pep reaction was not included in our previous studies of CN explosions. Although the energy production from this reaction is not important in the Sun, the densities in WD envelopes can exceed $10^4$ gm cm$^{-3}$ and the presence of this reaction increases the energy generation during the time that the p-p chain is operating. The effect of the increased energy generation is to reduce the evolution time to the peak of the TNR and, thereby, the accreted mass as compared to the evolutionary sequences done without this reaction included. As expected from our previous work, the reduction in accreted mass has important consequences on the characteristics of the resulting TNR and is discussed in this paper.Comment: Accepted to the Astrophysical Journa

Theoretical Studies of Accretion of Matter onto White Dwarfs and the Single Degenerate Scenario for Supernovae of Type Ia

We present a brief summary of the Single Degenerate Scenario for the progenitors of Type Ia Supernovae in which it is assumed that a low mass carbon-oxygen white dwarf is growing in mass as a result of accretion from a secondary star in a close binary system. Recent hydrodynamic simulations of accretion of solar material onto white dwarfs without mixing always produce a thermonuclear runaway and steady burning does not occur. For a broad range in WD mass (0.4 Solar masses to 1.35 Solar Masses), the maximum ejected material occurs for the 1.25 Solar Mass sequences and then decreases as the white dwarf mass decreases. Therefore, the white dwarfs are growing in mass as a consequence of the accretion of solar material and as long as there is no mixing of accreted material with core material. In contrast, a thermonuclear runaway in the accreted hydrogen-rich layers on the low luminosity WDs in close binary systems where mixing of core matter with accreted material has occurred is the outburst mechanism for Classical, Recurrent, and Symbiotic novae. The differences in characteristics of these systems is likely the WD mass and mass accretion rate. The high levels of enrichment of CN ejecta in elements ranging from carbon to sulfur confirm that there is dredge-up of matter from the core of the WD and enable them to contribute to the chemical enrichment of the interstellar medium. Therefore, studies of CNe can lead to an improved understanding of Galactic nucleosynthesis, some sources of pre-solar grains, and the Extragalactic distance scale. The characteristics of the outburst depend on the white dwarf mass, luminosity, mass accretion rate, and the chemical composition of both the accreting material and WD material. The properties of the outburst also depends on when, how, and if the accreted layers are mixed with the WD core and the mixing mechanism is still unknown.Comment: 25 Pages, Bulletin of the Astronomical Society of India (BASI) in pres

Primordial Nucleosynthesis

Primordial nucleosynthesis, or Big-Bang Nucleosynthesis (BBN), is one of the three evidences for the Big-Bang model, together with the expansion of the Universe and the Cosmic Microwave Background. There is a good global agreement over a range of nine orders of magnitude between abundances of 4He, D, 3He and 7Li deduced from observations, and calculated in primordial nucleosynthesis. This comparison was used to determine the baryonic density of the Universe. For this purpose, it is now superseded by the analysis of the Cosmic Microwave Background (CMB) radiation anisotropies. However, there remain, a yet unexplained, discrepancy of a factor 3-5, between the calculated and observed lithium primordial abundances, that has not been reduced, neither by recent nuclear physics experiments, nor by new observations. We review here the nuclear physics aspects of BBN for the production of 4He, D, 3He and 7Li, but also 6Li, 9Be, 11B and up to CNO isotopes. These are, for instance, important for the initial composition of the matter at the origin of the first stars. Big-Bang nucleosynthesis, that has been used, to first constrain the baryonic density, and the number of neutrino families, remains, a valuable tool to probe the physics of the early Universe, like variation of "constants" or alternative theories of gravity.Comment: Invited Plenary Talk given at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS

Hydrodynamic Studies of the Evolution of Recurrent, Symbiotic, and Dwarf Novae: The White Dwarf Components are Growing in Mass

Symbiotic binaries are systems containing white dwarfs (WDs) and red giants. Symbiotic novae are those systems in which thermonuclear eruptions occur on the WD components. These are to be distinguished from events driven by accretion disk instabilities analogous to dwarf novae eruptions in cataclysmic variable outbursts. Another class of symbiotic systems are those in which the WD is extremely luminous and it seems likely that quiescent nuclear burning is ongoing on the accreting WD. A fundamental question is the secular evolution of the WD. Do the repeated outbursts or quiescent burning in these accreting systems cause the WD to gain or lose mass? If it is gaining mass, can it eventually reach the Chandrasekhar Limit and become a supernova (a SN Ia if it can hide the hydrogen and helium in the system)? In order to better understand these systems, we have begun a new study of the evolution of Thermonuclear Runaways (TNRs) in the accreted envelopes of WDs using a variety of initial WD masses, luminosities and mass accretion rates. We use our 1-D hydro code, NOVA, which includes the new convective algorithm of Arnett, Meakin and Young, the Hix and Thielemann nuclear reaction solver, the Iliadis reaction rate library, the Timmes equation of state, and the OPAL opacities. We assume a solar composition (Lodders abundance distribution) and do not allow any mixing of accreted material with core material. This assumption strongly influences our results. We report here (1) that the WD grows in mass for all simulations so that canonical `steady burning' does not occur, and (2) that only a small fraction of the accreted matter is ejected in some (but not all) simulations. We also find that the accreting systems, before thermonuclear runaway, are too cool to be seen in X-ray searches for SN Ia progenitors

The 25Mg(p,g)Al reaction at low astrophysical energies

In the present work we report on a new measurement of resonance strengths in the reaction 25Mg(p,gamma)26Al at E_cm= 92 and 189 keV. This study was performed at the LUNA facility in the Gran Sasso underground laboratory using a 4pi BGO summing crystal. For the first time the 92 keV resonance was directly observed and a resonance strength omega-gamma=(2.9+/-0.6)x10E-10 eV was determined. Additionally, the gamma-ray branchings and strength of the 189 keV resonance were studied with a high resolution HPGe detector yielding an omega-gamma value in agreement with the BGO measurement, but 20% larger compared to previous works.Comment: 6 pages, 4 figures, accepted for publication in Physics Letters

Production of 26Al in stellar hydrogen-burning environments: spectroscopic properties of states in 27Si

Model predictions of the amount of the radioisotope 26Al produced in hydrogen-burning environments require reliable estimates of the thermonuclear rates for the 26gAl(p,{\gamma})27Si and 26mAl(p,{\gamma})27Si reactions. These rates depend upon the spectroscopic properties of states in 27Si within about 1 MeV of the 26gAl+p threshold (Sp = 7463 keV). We have studied the 28Si(3He,{\alpha})27Si reaction at 25 MeV using a high-resolution quadrupole-dipole-dipole-dipole magnetic spectrograph. For the first time with a transfer reaction, we have constrained J{\pi} values for states in 27Si over Ex = 7.0 - 8.1 MeV through angular distribution measurements. Aside from a few important cases, we generally confirm the energies and spin-parity assignments reported in a recent {\gamma}-ray spectroscopy study. The magnitudes of neutron spectroscopic factors determined from shell-model calculations are in reasonable agreement with our experimental values extracted using this reaction.Comment: accepted for publication in Phys. Rev.