Statistical framework for nuclear parameter uncertainties in nucleosynthesis modeling of r- and i-process

TL;DR

This work develops a coherent statistical framework, BFMC, to quantify and propagate nuclear parameter uncertainties in nucleosynthesis modeling of the i-process and r-process. By anchoring parameter spaces to experimental data via backward sampling and propagating them forward, the authors demonstrate that parameter uncertainties can rival model uncertainties in shaping final abundances, and that correlations among masses (via $S_n$ and $Q_\beta$) crucially affect r-process predictions. Key findings include the substantial impact of specific neutron-capture rates (notably $^{217}$Bi$(n,\gamma)^{218}$Bi) on actinide production in the i-process, and the mitigating effect of correlated $S_n$ uncertainties on NSM r-process abundance spreads, particularly beyond the second peak. The work highlights the practical importance of targeted experimental measurements of rates and masses to tighten predictions for stellar evolution and the origin of heavy elements, and provides a robust methodology for disciplined uncertainty quantification in nuclear astrophysics, grounded in experimental constraints.

Abstract

Propagating nuclear uncertainties to nucleosynthesis simulations is key to understand the impact of theoretical uncertainties on the predictions, especially for processes far from the stability region, where nuclear properties are scarcely known. While systematic (model) uncertainties have been thoroughly studied, the statistical (parameter) ones have been more rarely explored, as constraining them is more challenging. We present here a methodology to determine coherently parameter uncertainties by anchoring the theoretical uncertainties to the experimentally known nuclear properties through the use of the Backward Forward Monte Carlo method. We use this methodology for two nucleosynthesis processes: the intermediate neutron capture process (i-process) and the rapid neutron capture process (r-process). We determine coherently for the i-process the uncertainties from the (n,$γ$) rates while we explore the impact of nuclear mass uncertainties for the r-process. The effect of parameter uncertainties on the final nucleosynthesis is in the same order as model uncertainties, suggesting the crucial need for more experimental constraints on key nuclei of interest. We show how key nuclear properties, such as relevant (n,$γ$) rates impacting the i-process tracers, could enhance tremendously the prediction of stellar evolution models by experimentally constraining them.

Figures (8)

• Figure 1: Parameter uncertainties affecting neutron capture rates using Model A (upper panel) or B (lower panel) for an i-process nuclear network. See text for more details.
• Figure 2: Illustration of the parameter uncertainties on neutron capture rates obtained by their maximum-to-minimum ratios with Model A vs those of Model B. Each point is color-coded by the nuclear mass number $A$ of the target nucleus.
• Figure 3: Impact of the neutron capture rates parameter uncertainties on the i-process nucleosynthesis during the early AGB phase of a low-mass low-metallicity star.
• Figure 4: Primary (blue) and secondary (black) i-process paths (starting from $^{56}$Fe) in a 1 $M_{\odot}$ AGB model at [Fe/H] $=-2.5$, taken at the base of the convective TP during peak neutron density. A path is marked as secondary if it carries at least 30% of the total flux. The color of each nucleus gives its mass fraction at this time.
• Figure 5: Impact of the $^{217}$Bi(n,$\gamma$)$^{218}$Bi rate parameter uncertainty on the i-process nucleosynthesis during the early AGB phase of a low mass low metallicity star.