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Register a new userCharged-Particle Thermonuclear Reaction Rates: I. Monte Carlo Method and Statistical Distributions
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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 miu and sigma. 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 series (Paper II). The nuclear physics input used to derive our reaction rates is presented in the third paper of this series (Paper III). In the fourth paper of this series (Paper IV) we compare our new reaction rates to previous results.
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The study of d+d reactions is of major interest since their reaction rates affect the predicted abundances of D, 3He, and 7Li. In particular, recent measurements of primordial D/H ratios call for reduced uncertainties in the theoretical abundances predicted by big bang nucleosynthesis (BBN). Different authors have studied reactions involved in BBN by incorporating new experimental data and a careful treatment of systematic and probabilistic uncertainties. To analyze the experimental data, Coc et al. (2015) used results of ab initio models for the theoretical calculation of the energy dependence of S-factors in conjunction with traditional statistical methods based on Chi-2 minimization. Bayesian methods have now spread to many scientific fields and provide numerous advantages in data analysis. Astrophysical S-factors and reaction rates using Bayesian statistics were calculated by Iliadis et al. (2016). Here we present a similar analysis for two d+d reactions, d(d,n)3He and d(d,p)3H, that has been translated into a total decrease of the predicted D/H value by 0.16%.
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.
It has been suggested that a $ u$p process can occur when hot, dense, and proton-rich matter is expanding within a strong flux of anti-neutrinos. In such an environment, proton-rich nuclides can be produced in sequences of proton captures and (n,p) reactions, where the free neutrons are created in situ by $overline{ u}_mathrm{e}+mathrm{p} rightarrow mathrm{n}+mathrm{e}^+$ reactions. The detailed hydrodynamic evolution determines where the nucleosynthesis path turns off from N = Z line and how far up the nuclear chart it runs. In this work, the uncertainties on the final isotopic abundances stemming from uncertainties in the nuclear reaction rates were investigated in a large-scale Monte Carlo approach, simultaneously varying ten thousand reactions. A large range of model conditions was investigated because a definitive astrophysical site for the $ u$p process has not yet been identified. The present parameter study provides, for each model, identification of the key nuclear reactions dominating the uncertainty for a given nuclide abundance. As all rates appearing in the $ u$p process involve unstable nuclei, and thus only theoretical rates are available, the final abundance uncertainties are larger than those for nucleosynthesis processes closer to stability. Nevertheless, most uncertainties remain below a factor of three in trajectories with robust nucleosynthesis. More extreme conditions allow production of heavier nuclides but show larger uncertainties because of the accumulation of the uncertainties in many rates and because the termination of nucleosynthesis is not at equilibrium conditions. It is also found that the solar ratio of the abundances of ${}^{92}$Mo and ${}^{94}$Mo could be reproduced within uncertainties.
Small-scale magnetic reconnection processes, in the form of nanoflares, have become increasingly hypothesized as important mechanisms for the heating of the solar atmosphere, for driving propagating disturbances along magnetic field lines in the Suns corona, and for instigating rapid jet-like bursts in the chromosphere. Unfortunately, the relatively weak signatures associated with nanoflares places them below the sensitivities of current observational instrumentation. Here, we employ Monte Carlo techniques to synthesize realistic nanoflare intensity time series from a dense grid of power-law indices and decay timescales. Employing statistical techniques, which examine the modeled intensity fluctuations with more than 10^7 discrete measurements, we show how it is possible to extract and quantify nanoflare characteristics throughout the solar atmosphere, even in the presence of significant photon noise. A comparison between the statistical parameters (derived through examination of the associated intensity fluctuation histograms) extracted from the Monte Carlo simulations and SDO/AIA 171{AA} and 94{AA} observations of active region NOAA 11366 reveals evidence for a flaring power-law index within the range of 1.82 - 1.90, combined with e-folding timescales of 385 +/- 26 s and 262 +/- 17 s for the SDO/AIA 171{AA} and 94{AA} channels, respectively. These results suggest that nanoflare activity is not the dominant heating source for the active region under investigation. This opens the door for future dedicated observational campaigns to not only unequivocally search for the presence of small-scale reconnection in solar and stellar environments, but also quantify key characteristics related to such nanoflare activity.
Thermonuclear supernovae originating from the explosion of a white dwarf accreting mass from a companion star have been suggested as a site for the production of $p$ nuclides. Such nuclei are produced during the explosion, in layers enriched with seed nuclei coming from prior strong $s$ processing. These seeds are transformed to proton-richer isotopes mainly by photodisintegration reactions. Several thousand trajectories from a 2D explosion model were used in a Monte Carlo approach. Temperature-dependent uncertainties were assigned individually to thousands of rates varied simultaneously in post-processing in an extended nuclear reaction network. The uncertainties in the final nuclear abundances originating from uncertainties in the astrophysical reaction rates were determined. In addition to the 35 classical $p$ nuclides, abundance uncertainties were also determined for the radioactive nuclides $^{92}$Nb, $^{97,98}$Tc, $^{146}$Sm, and for the abundance ratios $Y$(${}^{92}$Mo)/$Y$(${}^{94}$Mo), $Y$(${}^{92}$Nb)/$Y$(${}^{92}$Mo), $Y$(${}^{97}$Tc)/$Y$(${}^{98}$Ru), $Y$(${}^{98}$Tc)/$Y$(${}^{98}$Ru), and $Y$(${}^{146}$Sm)/$Y$(${}^{144}$Sm), important for Galactic Chemical Evolution studies. Uncertainties found were generally lower than a factor of two, although most nucleosynthesis flows mainly involve predicted rates with larger uncertainties. The main contribution to the total uncertainties comes from a group of trajectories with high peak density originating from the interior of the exploding white dwarf. The distinction between low-density and high-density trajectories allows more general conclusions to be drawn, also applicable to other simulations of white dwarf explosions.
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