Impact of Nuclear Reaction Rates on Calcium Production in Population III Stars: A Global Analysis

TL;DR

The study addresses how nuclear reaction-rate uncertainties shape calcium production in Population III stars by integrating a $137$-species network into 1D multi-zone stellar models and performing sensitivity analyses on $(p,\gamma)$ and $(p,\alpha)$ reactions. It identifies 13 key reactions and propagates uncertainties through two Monte Carlo rate-sets (STARLIB vs updated data), using Spearman correlations and SHAP to interpret the complex network effects. Updated rates yield Ca abundances and [Ca/Mg] comparable to the iron-poor star SMSS0313-6708 within the 68% confidence interval, with 40 $M_{\odot}$ models providing better agreement than 20 $M_{\odot}$, especially when including the $^{19}$F$(p,\gamma)^{20}$Ne rate from recent measurements. The work demonstrates a direct, in-situ Monte Carlo approach to nucleosynthesis uncertainties and highlights the pivotal role of $^{18}$F and $^{19}$F proton-capture channels in enabling CNO breakout toward Ca, offering concrete guidance for future experimental efforts to constrain early-universe calcium production.

Abstract

We investigate the sensitivity of calcium production to nuclear reaction rates of a 40 solar-mass Population III star using 1D multi-zone stellar models. A comprehensive nuclear reaction network was constructed, and all $(p,γ)$ and $(p,α)$ reaction rates were individually varied by a factor of 10 up and down, identifying 13 preliminary key reactions for calcium production. To propagate the reaction rate uncertainties on calcium production, two sets of Monte Carlo simulations were performed for these key reactions: one adopting STARLIB reaction rates and the other incorporating updated rates from recent experimental data and evaluations. Our results show that Monte Carlo simulations using the updated rates show good agreement with the observed calcium abundance of the extremely iron-poor star SMSS J031300.36-670839.3 within the 68% confidence interval predicted by the models. In contrast, the observed calcium abundance lies marginally outside the 68% C.I. when using the STARLIB rates. Spearman rank-order correlation analysis and SHAP values show that the $(p,γ)$ and $(p,α)$ reactions of F18 and F19 exhibit strong coupled effects on calcium production. These reaction-rate uncertainties need to be reduced to constrain the stellar model predictions. Our study provides insights for future nuclear physics experiments aimed at reducing reaction rate uncertainties in the nucleosynthesis of Population III Stars. Additionally, comparisons between 20 solar-mass and 40 solar-mass Population III stellar models confirm that the latter, with updated reaction rates, is more capable of reproducing the observed Ca abundance and [Ca/Mg] ratio.

Figures (22)

• Figure 1: (Color online) HRD of the baseline 40 M$_{\odot}$ stellar model from the PMS until the Pre-SN. The star symbol denotes the beginning of the stellar model, the triangle indicates the ZAMS, the circle denotes the TAMS, and the diamond represents core Ne-depletion. Ages at these stages are annotated. The subsequent evolution after core Ne-depletion until the Pre-SN shows only minor changes in luminosity and is therefore not depicted.
• Figure 2: (Color online) The evolution of the central temperature (orange) and density (blue) up to the TAMS for the baseline model. The gray dotted line represents the ZAMS, at which temperature and density reach the peaks.
• Figure 3: (Color online) Central mass fraction of main isotopes as a function of time up to the TAMS for the baseline model. The gray dotted line represents the ZAMS.
• Figure 4: (Color online) The luminosities of the $p-p$ chain reactions (orange solid line), the CNO reactions (green dashed line), and the $3\alpha$ process (blue dot-dashed line) as functions of time up to the TAMS for the baseline model. The gray dotted line represents the ZAMS, around which CNO reactions overtake $p-p$ chain reactions as the dominant luminosity source.
• Figure 5: (Color online) Kippenhahn diagram for the baseline 40 M$_{\odot}$ stellar model. The horizontal axis shows the time left until the Pre-SN, while the vertical axis denotes the mass coordinate. The green, cyan, and red-hatched areas correspond to convective, overshoot, and semi-convective regions, respectively. The blue dotted line indicates the H-depleted core, or He core, where the H mass fraction is below 0.01, and the He mass fraction is above 0.01. The red dotted line indicates the He-depleted core, or CO core, where the He mass fraction is below 0.01. The blue color scale shows the ${}^{40}\mathrm{Ca}$ mass fraction. The vertical gray dashed line represents the TAMS, while the dot-dashed line represents core Ne-depletion.