Implications for Type Ia Supernova Nucleosynthesis from an Experimentally Constrained $^{16}$O$(p,α)^{13}$N Reaction Rate

Abstract

The $^{16}$O$(p,α)^{13}$N reaction plays a key role in shaping the $α$-particle abundance during explosive oxygen burning in Type Ia supernovae. By enhancing $α$-production, this reaction directly affects the calcium-to-sulphur (Ca/S) and argon-to-sulphur (Ar/S) ratios, which serves as a tracer of progenitor metallicity. However, recent work suggests that the rate must be enhanced by a factor of up to seven over the standard value to explain observed Ca/S ratios across a range of progenitor metallicities. To explore this impact, available experimental cross-section data for the $^{16}$O$(p,α)^{13}$N reaction have been compiled and critically evaluated. Significant discrepancies are identified in the low-energy region ($E_{\mathrm{cm}}$ = 5.7--7.0 MeV), primarily due to limitations of the activation method. To resolve this, the first direct measurement at astrophysical energies has been performed using the MUSIC active-target detector. The new $^{16}$O$(p,α)^{13}$N thermonuclear reaction rate is found to be approximately 1.5 times higher than the REACLIB rate in the temperature range T = 3--4 GK, with more constrained uncertainties that resolve the previously large spread among existing data. The suggested factor of seven enhancement is excluded and these results indicate that this reaction alone cannot fully explain the variation in the Ca/S and Ar/S ratios observed across different progenitor metallicities. Therefore, future work should focus on reducing the uncertainties in other key oxygen-burning reactions, particularly $^{16}$O+$^{16}$O and $^{12}$C+$^{16}$O. Further reducing the constraints on the $^{16}$O$(p,α)^{13}$N rate is also needed to fully determine to whether a nuclear physics solution to this discrepancy is possible.

Figures (6)

• Figure 1: Experimental cross section data for the $\mathrm{^{16}O}(p,\alpha)\mathrm{^{13}N}$ reaction, plotted as a function of incident proton energy in the laboratory frame. The data were extracted from the EXFOR database zerkin2018experimental and include five datasets: mccamis1973total, gruhle1977reactions, SAJJAD1986Cyclotron, NERO, and whitehead1958activation. The solid line represents the recommended cross section evaluation using Padé approximant fits from Hermanne2021.
• Figure 2: Experimental $\Delta E$ traces recorded with MUSIC for events originating from strip 2. The $^{16}$O beam was normalised to 6 a.u. (black). Elastic scattering events $^{16}$O$(p,p')$ appear with higher $\Delta E$ (blue). $(p,\alpha)$ events corresponding to $^{13}$N production are seen with lower $\Delta E$ (red). The lowest traces (grey) are attributed to recoiling $^{12}$C nuclei from collisions of $^{16}$O with $^{12}$C in the methane gas.
• Figure 3: Two-dimensional energy loss ($\Delta E$) plot showing events assigned to strip 2 of the MUSIC detector. The vertical axis shows the average energy loss over anode strips 3–6, while the horizontal axis shows the average energy loss over strips 3–10. Distinct event populations corresponding to the unreacted ($^{16}$O) beam, inelastic scattering events $(p,p')$, $(p,\alpha)$ events producing $^{13}$N, and recoiling $^{12}$C nuclei are visible.
• Figure 4: Measured cross section values of the $\mathrm{^{16}O}(p,\alpha)\mathrm{^{13}N}$ reaction obtained with the MUSIC detector (present work), compared with previously published data from gruhle1977reactions, NERO, SAJJAD1986Cyclotron, and mccamis1973total, after applying energy loss corrections. The results are also compared with the $\mathcal{R}$-matrix calculation of Meyer2020EvaluationGrains and the Padé evaluation of Hermanne2021. Error bars include both statistical and systematic uncertainties. The downward arrow at $E_{\mathrm{cm}} = 5.78$ MeV shows the upper limit from strip 6 analysis.
• Figure 5: Ratio of the new reaction rate (blue line) to the CF88 rate (black dotted dashed line) as a function of temperature ($T = 2.5$–5 GK), relevant for explosive oxygen burning in Type Ia supernovae. The comparison includes the rate of Meyer2020EvaluationGrains as provided in the latest STARLIB sallaska2013starlib and the IAEA evaluation of Hermanne2021. Shaded bands indicate the one sigma uncertainty of each dataset.