Impact of Nuclear Reaction Rate Uncertainties on Type I X-ray Burst Nucleosynthesis: A Monte Carlo Study

TL;DR

This work systematically investigates how nuclear-reaction-rate uncertainties affect Type I X-ray burst nucleosynthesis by performing large-scale Monte Carlo simulations with both temperature-independent (REACLIB) and temperature-dependent (STARLIB) rate treatments. Using three representative XRB trajectories and a 686-nuclide network, the authors perturb 1,711 forward rates (and their inverses) across 100{,}000 trials, revealing that large perturbations can produce multi-peaked abundance distributions and non-linear coupling between reactions. The study confirms several previously identified key reactions while providing a more robust and comprehensive list of influential rates, and it demonstrates that temperature-dependent rate uncertainties yield more physically realistic abundance spreads and mass-range predictions. The findings underscore the importance of incorporating realistic, temperature-dependent rate uncertainties and suggest prioritizing measurements of reactions that consistently drive abundances across models; this has direct implications for experimental nuclear astrophysics and the interpretation of XRB observations.

Abstract

To investigate the impact of nuclear reaction rate uncertainties on type I X-ray burst nucleosynthesis, comprehensive Monte Carlo simulations are performed with temperature-independent and -dependent variations in reaction rates using the REACLIB and STARLIB libraries, respectively. A total of 1,711 $(p, γ)$, $(p, α)$, $(α, p)$, and $(α, γ)$ reactions are varied simultaneously, along with their inverse reactions, via detailed balance. For the first time, it is found that Monte Carlo sampling with larger perturbations to these reaction rates may lead to multi-peaked abundance distributions for some isotopes. These multi-peak structures arise not only from coupled reactions but also, in some cases, from single reactions. Our study also confirmed previously identified key reactions and provides more robust lists. These reactions deserve priority consideration in future study.

Figures (13)

• Figure 1: (Left) Time evolution of temperature for the XRB Models K04 (orange dashed line) Koike2004, S01 (blue solid line) Schatz2001, and S16 (green dot-dashed line) Cyburt2016. (Right) Same as left panel, but for temperature vs. density (in units of $10^6~\mathrm{g/cm^{3}}$). The peak temperature and initial metallicity for each model are listed as well.
• Figure 2: (Top) Standard normal distribution of reaction rate variation factor $p_i$. three points of $p_i = -0.5$, $1.2$, and $2.5$ are also drawn from left to right. (Bottom) The resulting reaction rates compared to the median for the $^{15}$O($\alpha$, $\gamma$)$^{19}$Ne reaction rate. In the bottom panel, these points are mapped to reaction rates according to Equation 4, and then compared with the median, corresponding to the red dot–dashed, blue dashed, and green solid lines, respectively.
• Figure 3: Effect of $^{69}$Se$(p, \gamma)^{70}$Br rate variations on the normalized abundance of $^{69}$Ge in Model K04. The reaction shows a strong negative correlation with $^{69}$Ge. Compared to $\sigma = 1.15$, the linear regression $R^2$ (black dashed line) and absolute Spearman correlation coefficient $|r_s|$ are smaller for $\sigma = 2.3$, while the corresponding abundance uncertainty is larger.
• Figure 4: Histogram of the logarithmic relative abundances of $^{55}$Co in Model K04. The green dashed lines indicate the 95% (2.5th–97.5th percentile) and 68% (16th–84th percentile) confidence intervals (C.I.s). in the top and bottom panels, respectively. The gray dot-dashed line in the bottom panel denotes the location of minimum probability density between the two peaks.
• Figure 5: Similar to Figure \ref{['fig:Ge69A']}, but for the correlations between the abundance of $^{55}$Co and the reactions (a) $^{55}$Ni$(p, \gamma)^{56}$Cu, (b) $^{56}$Cu$(p, \gamma)^{57}$Zn, (c) $^{59}$Cu$(p, \alpha)^{56}$Ni, and (d) $^{59}$Cu$(p, \gamma)^{60}$Zn in Model K04 with $\sigma = 2.3$. Gray dashed lines separate the primary (bottom) and secondary (top) clusters, corresponding to the minimum of the probability density of $^{55}$Co indicated by the gray dot-dashed line in Figure \ref{['fig:Co55A']}(b). Each cluster is analyzed individually, with the Spearman correlation coefficient ($r_s$) and sample counts reported at the bottom of each panel.