Impacts of the $^{16}$O($^{16}$O, n)$^{31}$S reaction rate on the evolution and nucleosynthesis in Pop III massive stars

TL;DR

This study systematically tests how the branching $^{16}$O($^{16}$O, n)$^{31}$S rate influences the evolution and nucleosynthesis of a $15\,M_\odot$ Population III star by varying the rate by factors of $0.1$, $1$, and $10$ using MESA with a 161-nuclide network. The results show that higher rates induce earlier O-burning ignition at lower $T$ and $\rho$, extend the core O-burning lifetime, and strengthen shell O burning, which yields a less compact OSi core and a smaller mass cut. Nucleosynthesis is notably affected: neutron-rich isotopes, especially $^{31}$P and $^{39}$K, are enhanced, with $^{39}$K yields increasing by up to $6.4\times$, producing $[K/Ca]\approx 0.29$ and $[K/Fe]\approx 0.22$ for $f_{16O}=10$, consistent with extremely metal-poor star observations within $2\sigma$. These findings offer a potential solution to potassium underproduction and motivate precise measurements of the oxygen fusion rate, while highlighting the need to couple these yields with explosion physics for robust Galactic chemical evolution predictions.

Abstract

We first present a systematic investigation into the effect of the $^{16}$O($^{16}$O, n)$^{31}$S reaction rate on the evolution and nucleosynthesis of Population III (Pop III) stars. We simulate the evolution of a 15 M$_\odot$ Pop III star from the zero-age main sequence through to core collapse, while varying the $^{16}$O($^{16}$O, n)$^{31}$S reaction rate by factors of 0.1, 1, and 10. Our results demonstrate that increasing this reaction rate prompts earlier onset and extended duration of core oxygen burning at lower temperatures and densities. A higher reaction rate also increases neutron excess in OSi-rich layers, thereby promoting the synthesis of neutron-rich isotopes, particularly $^{31}$P and $^{39}$K. Most notably, the K yield is enhanced by a factor of 6.4. For a tenfold enhancement of the $^{16}$O($^{16}$O, n)$^{31}$S rate, the predicted [K/Ca] and [K/Fe] values from presupernova models reach 0.29 and 0.22 dex, respectively-values that are consistent with the most recent observational data for extremely metal-poor stars. These findings hold promise as a potential new solution to the problem of potassium underproduction and offer a valuable theoretical reference and motivation for subsequent measurements of oxygen fusion reaction rate.

Figures (8)

• Figure 1: The branching ratios of the three branching reactions as a function of temperature in JINA REACLIB. The blue and orange regions represent the temperature range of hydrostatic burning and explosive burning.
• Figure 2: The time evolution of temperature, and the mass fractions of $^{16}$O, $^{28}$Si, and $^{31}$P at the center. The time $t=0$ is defined at O ignition for each model, where the energy generation rate of $^{16}$O+$^{16}$O reaction equals the energy loss rate of neutrinos.
• Figure 3: The Kippenhahn diagram of the star with $M {\rm (ZAMS)}$ = 15 M$_{\odot}$. The inner part of $M_r = 0 - 4$ M$_{\odot}$ is shown. The blue and grey regions represent the convection and overshooting. The blue, orange, green, and black dashed lines show the variation of CO core mass, O core mass, Si core mass, and Fe core mass. The boundaries of these cores are defined where $X$($^{4}$He), $X$($^{12}$C), $X$($^{16}$O), and $X$($^{28}$Si) decrease down to 10$^{-4}$.
• Figure 4: The time evolution of compactness parameter, $\xi_{2.5}$, for $f_{\rm 16O}$ = 0.1, 1, and 10.
• Figure 5: The mass distribution of log ($V/U$) at $t=t_{\rm final}$. The mass coordinates of the peaks indicate $M(V/U_{\rm max})$. Both the peak values and their mass coordinates are listed in Table \ref{['tab:data']}.