Recommendations for Monte Carlo nucleosynthesis sampling (Research Note)

Context: Recent reaction rate evaluations include reaction rate uncertainties that have been determined in a statistically meaningful manner. Furthermore, reaction rate probability density distributions have been determined and published in the form of lognormal parameters with the specific goal of pursuing Monte Carlo nucleosynthesis studies. Aims: To test and assess different methods of randomly sampling over reaction rate probability densities and to determine the most accurate method for estimating elemental abundance uncertainties. Methods: Experimental Monte Carlo reaction rates are first computed for the 22Ne+alpha, 20Ne(p,g)21Na, 25Mg(p,g)26Al, and 18F(p,alpha)15O reactions, which are used to calculate reference nucleosynthesis yields for 16 nuclei affected by nucleosynthesis in massive stars and classical novae. Five different methods of randomly sampling over these reaction rate probability distributions are then developed, tested, and compared with the reference nucleosynthesis yields. Results: Given that the reaction rate probability density distributions can be described accurately with a lognormal distribution, Monte Carlo nucleosynthesis variations arising from the parametrised estimates for the reaction rate variations agree remarkably well with those obtained from the true rate samples. Most significantly, the most simple parametrisation agrees within just a few percent, meaning that Monte Carlo nucleosynthesis studies can be performed reliably using lognormal parametrisations of reaction rate probability density functions.Comment: 6 pages, 3 figures. Accepted to Astronomy & Astrophysics as a Research Not

Performance Improvements for Nuclear Reaction Network Integration

Aims: The aim of this work is to compare the performance of three reaction network integration methods used in stellar nucleosynthesis calculations. These are the Gear's backward differentiation method, Wagoner's method (a 2nd-order Runge-Kutta method), and the Bader-Deuflehard semi-implicit multi-step method. Methods: To investigate the efficiency of each of the integration methods considered here, a test suite of temperature and density versus time profiles is used. This suite provides a range of situations ranging from constant temperature and density to the dramatically varying conditions present in white dwarf mergers, novae, and x-ray bursts. Some of these profiles are obtained separately from full hydrodynamic calculations. The integration efficiencies are investigated with respect to input parameters that constrain the desired accuracy and precision. Results: Gear's backward differentiation method is found to improve accuracy, performance, and stability in integrating nuclear reaction networks. For temperature-density profiles that vary strongly with time, it is found to outperform the Bader-Deuflehard method (although that method is very powerful for more smoothly varying profiles). Wagoner's method, while relatively fast for many scenarios, exhibits hard-to-predict inaccuracies for some choices of integration parameters owing to its lack of error estimations.Comment: 13 pages, 12 figures, accepted to Astronomy and Astrophysics (section 15) - corrected units in Figs. 6-1

Mean proton and alpha-particle reduced widths of the Porter-Thomas distribution and astrophysical applications

The Porter-Thomas distribution is a key prediction of the Gaussian orthogonal ensemble in random matrix theory. It is routinely used to provide a measure for the number of levels that are missing in a given resonance analysis. The Porter-Thomas distribution is also of crucial importance for estimates of thermonuclear reaction rates where the contributions of certain unobserved resonances to the total reaction rate need to be taken into account. In order to estimate such contributions by randomly sampling over the Porter-Thomas distribution, the mean value of the reduced width must be known. We present mean reduced width values for protons and α particles of compound nuclei in the A = 28–67 mass range. The values are extracted from charged-particle elastic scattering and reaction data that weremeasured at the riangle Universities Nuclear Laboratory over several decades. Our new values differ significantly from those previously reported that were based on a preliminary analysis of a smaller data set. As an example for the application of our results, we present new thermonuclear rates for the 40Ca(α,γ)44Ti reaction, which is important for 44Ti production in core-collapse supernovae, and compare with previously reported results.Peer ReviewedPostprint (published version

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

Thermal Equilibration of 176-Lu via K-Mixing

In astrophysical environments, the long-lived (\T_1/2 = 37.6 Gy) ground state of 176-Lu can communicate with a short-lived (T_1/2 = 3.664 h) isomeric level through thermal excitations. Thus, the lifetime of 176-Lu in an astrophysical environment can be quite different than in the laboratory. We examine the possibility that the rate of equilibration can be enhanced via K-mixing of two levels near E_x = 725 keV and estimate the relevant gamma-decay rates. We use this result to illustrate the effect of K-mixing on the effective stellar half-life. We also present a network calculation that includes the equilibrating transitions allowed by K-mixing. Even a small amount of K-mixing will ensure that 176-Lu reaches at least a quasi-equilibrium during an s-process triggered by the 22-Ne neutron source.Comment: 9 pages, 6 figure