Richard Longland

Charged-Particle Thermonuclear Reaction Rates: II. Tables and Graphs of Reaction Rates and Probability Density Functions

Abstract Numerical values of charged-particle thermonuclear reaction rates for nuclei in the A = 14 to 40 region are tabulated. The results are obtained using a method, based on Monte Carlo techniques, that has been described in the preceding paper of this issue (Paper I). We present a low rate, median rate and high rate which correspond to the 0.16, 0.50 and 0.84 quantiles, respectively, of the cumulative reaction rate distribution. The meaning of these quantities is in general different from the commonly reported, but statistically meaningless expressions, “lower limit”, “nominal value” and “upper limit” of the total reaction rate. In addition, we approximate the Monte Carlo probability density function of the total reaction rate by a lognormal distribution and tabulate the lognormal parameters μ and σ at each temperature. We also provide a quantitative measure (Anderson–Darling test statistic) for the reliability of the lognormal approximation. The user can implement the approximate lognormal reaction rate probability density functions directly in a stellar model code for studies of stellar energy generation and nucleosynthesis. For each reaction, the Monte Carlo reaction rate probability density functions, together with their lognormal approximations, are displayed graphically for selected temperatures in order to provide a visual impression. Our new reaction rates are appropriate for bare nuclei in the laboratory. The nuclear physics input used to derive our reaction rates is presented in the subsequent paper of this issue (Paper III). In the fourth paper of this issue (Paper IV) we compare our new reaction rates to previous results.

Charged-particle thermonuclear reaction rates: I. Monte Carlo method and statistical distributions

Abstract A method based on Monte Carlo techniques is presented for evaluating thermonuclear reaction rates. We begin by reviewing commonly applied procedures and point out that reaction rates that have been reported up to now in the literature have no rigorous statistical meaning. Subsequently, we associate each nuclear physics quantity entering in the calculation of reaction rates with a specific probability density function, including Gaussian, lognormal and chi-squared distributions. Based on these probability density functions the total reaction rate is randomly sampled many times until the required statistical precision is achieved. This procedure results in a median (Monte Carlo) rate which agrees under certain conditions with the commonly reported recommended “classical” rate. In addition, we present at each temperature a low rate and a high rate, corresponding to the 0.16 and 0.84 quantiles of the cumulative reaction rate distribution. These quantities are in general different from the statistically meaningless “minimum” (or “lower limit”) and “maximum” (or “upper limit”) reaction rates which are commonly reported. Furthermore, we approximate the output reaction rate probability density function by a lognormal distribution and present, at each temperature, the lognormal parameters μ and σ . The values of these quantities will be crucial for future Monte Carlo nucleosynthesis studies. Our new reaction rates, appropriate for bare nuclei in the laboratory , are tabulated in the second paper of this issue (Paper II). The nuclear physics input used to derive our reaction rates is presented in the third paper of this issue (Paper III). In the fourth paper of this issue (Paper IV) we compare our new reaction rates to previous results.

Direct measurement of the N-14(p, gamma) O-15 S-factor

The 14N(p,gamma)15O reaction regulates the rate of energy generation in the stellar CN cycle. Because discrepancies have been found in the analysis and interpretation of previous capture data, we have measured the 14N(p,gamma)15O excitation function for energies in the range E(lab)(p)=155-524 keV. Fits of these data using R-matrix theory yield a value for the S factor at zero energy of 1.68+/-0.09(stat)+/-0.16(syst) keV b, which is significantly smaller than the previous result. The corresponding reduction in the stellar reaction rate for 14N(p,gamma)15O has a number of interesting consequences, including an impact on estimates for the age of the Galaxy derived from globular clusters.

Charged-particle thermonuclear reaction rates: III. Nuclear physics input

Abstract The nuclear physics input used to compute the Monte Carlo reaction rates and probability density functions that are tabulated in the second paper of this issue (Paper II) is presented. Specifically, we publish the input files to the Monte Carlo reaction rate code RatesMC , which is based on the formalism presented in the first paper of this issue (Paper I). This data base contains overwhelmingly experimental nuclear physics information. The survey of literature for this review was concluded in November 2009.

Reaction rates for the s-process neutron source 22Ne + α

The 22Ne(α, n)25Mg reaction is an important source of neutrons for the s-process. In massive stars responsible for the weak component of the s-process, 22Ne(α, n)25Mg is the dominant source of neutrons, both during core helium burning and in carbon-shell burning. For the main s-process component produced in asymptotic giant branch (AGB) stars, the 13C(α, n)16O reaction is the dominant source of neutrons operating during the interpulse period, with the 22Ne + α source affecting mainly the s-process branchings during a thermal pulse. Rate uncertainties in the competing 22Ne(α, n)25Mg and 22Ne(α, γ)26Mg reactions result in large variations of s-process nucleosynthesis. Here, we present up-to-date and statistically rigorous 22Ne + α reaction rates using recent experimental results and Monte Carlo sampling. Our new rates are used in postprocessing nucleosynthesis calculations both for massive stars and AGB stars. We demonstrate that the nucleosynthesis uncertainties arising from the new rates are dramatically reduced in comparison to previously published results, but several ambiguities in the present data must still be addressed. Recommendations for further study to resolve these issues are provided.

New reaction rates for improved primordial D/H calculation and the cosmic evolution of deuterium

Primordial or big bang nucleosynthesis (BBN) is one of the three historically strong evidences for the big bang model. Standard BBN is now a parameter-free theory, since the baryonic density of the Universe has been deduced with an unprecedented precision from observations of the anisotropies of the cosmic microwave background radiation. There is a good agreement between the primordial abundances of He4, D, He3, and Li7 deduced from observations and from primordial nucleosynthesis calculations. However, the Li7 calculated abundance is significantly higher than the one deduced from spectroscopic observations and remains an open problem. In addition, recent deuterium observations have drastically reduced the uncertainty on D/H, to reach a value of 1.6%. It needs to be matched by BBN predictions whose precision is now limited by thermonuclear reaction rate uncertainties. This is especially important as many attempts to reconcile Li observations with models lead to an increased D prediction. Here, we reevaluate the d(p,γ)He3, d(d,n)He3, and d(d,p)H3 reaction rates that govern deuterium destruction, incorporating new experimental data and carefully accounting for systematic uncertainties. Contrary to previous evaluations, we use theoretical ab initio models for the energy dependence of the S factors. As a result, these rates increase at BBN temperatures, leading to a reduced value of D/H=(2.45±0.10)×10-5 (2σ), in agreement with observations.

Charged-Particle Thermonuclear Reaction Rates: IV. Comparison to Previous Work

Abstract We compare our Monte Carlo reaction rates (see Paper II of this issue) to previous results that were obtained by using the classical method of computing thermonuclear reaction rates. For each reaction, the comparison is presented using two types of graphs: the first shows the change in reaction rate uncertainties, while the second displays our new results normalized to the previously recommended reaction rate. We find that the rates have changed significantly for almost all reactions considered here. The changes are caused by (i) our new Monte Carlo method of computing reaction rates (see Paper I of this issue), and (ii) newly available nuclear physics information (see Paper III of this issue).

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 γ-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.

Lithium production in the merging of white dwarf stars

The origin of R Coronae Borealis stars has been elusive for over 200 years. Currently, two theories for their formation have been presented. These are the Final Flash scenario, in which a dying asymptotic giant branch (AGB) star throws o its atmosphere to reveal the hydrogen poor, heavily processed material underneath, and the double degenerate scenario, in which two white dwarfs merge to produce a new star with renewed vigour. Some theories predict that the temperatures reached during the latter scenario would destroy any lithium originally present in the white dwarfs. The observed lithium content of some R Coronae Borealis stars, therefore, is often interpreted as an indication that the Final Flash scenario best describes their formation. In this paper, it is shown that lithium production can, indeed, occur in the merging of a helium white dwarf with a carbon-oxygen white dwarf if their chemical composition, particularly that of 3 He, is fully considered. The production mechanism is described in detail, and the sensitivity of lithium production to the merger environment is investigated. Nucleosynthesis post-processing calculations of smoothed-particle hydrodynamics (SPH) tracer particles are performed to show that any lithium produced in these environments will be concentrated towards the cloud of material surrounding the R CrB star. Measurements of the lithium content of these clouds would, therefore, provide a valuable insight into the formation mechanism of R CrB stars.

Nuclear astrophysics in the laboratory and in the universe

Nuclear processes drive stellar evolution and so nuclear physics, stellar models and observations together allow us to describe the inner workings of stars and their life stories. This Information on nuclear reaction rates and nuclear properties are critical ingredients in addressing most questions in astrophysics and often the nuclear database is incomplete or lacking the needed precision. Direct measurements of astrophysically-interesting reactions are necessary and the experimental focus is on improving both sensitivity and precision. In the following, we review recent results and approaches taken at the Laboratory for Experimental Nuclear Astrophysics (LENA, http://research.physics.unc.edu/project/nuclearastro/Welcome.html).