${}^{19}\mathrm{F}{(p,\gamma )}^{20}\mathrm{Ne}$ and ${}^{19}\mathrm{F}(p,\alpha ){}^{16}\mathrm{O}$ reaction rates and their effect on calcium production in Population III stars from hot CNO breakout

First generation, or Population III, stars have a different evolution than those of later generations owing to their initial primordial abundance composition. Most notably, the lack of carbon, oxygen, and nitrogen means that primordial massive stars must rely on the less efficient $p\text{−}p$ chains, thereby requiring the star to contract to reach temperatures high enough to eventually trigger $3\alpha$ reactions. Even small amounts of the ${}^{12}\mathrm{C}(\alpha ,\gamma ){}^{16}\mathrm{O}$ reactions begin feeding the CNO mass range and enable the CNO cycle to generate energy, but this occurs at higher temperature compared to later stellar generations. It is currently controversial if the observed enhanced abundances of Ca in the most metal-poor stars could be a result of the high temperature H-burning conditions in the first massive stars. The level of this enrichment depends on the hot breakout path from the CNO cycles via the ${}^{19}\mathrm{F}(p,\gamma ){}^{20}\mathrm{Ne}$ reaction. In this work, the rates of both the ${}^{19}\mathrm{F}(p,\gamma ){}^{20}\mathrm{Ne}$ and competing ${}^{19}\mathrm{F}(p,\alpha ){}^{16}\mathrm{O}$ reactions are re-evaluated using the phenomenological $R$-matrix approach, simultaneously considering several ${}^{19}\mathrm{F}(p,\gamma ){}^{20}\mathrm{Ne}$, ${}^{19}\mathrm{F}(p,\alpha ){}^{16}\mathrm{O}$, and ${}^{19}\mathrm{F}(p,p){}^{19}\mathrm{F}$ data sets, to better characterize the rate uncertainties. It is found that the rate uncertainty for ${}^{19}\mathrm{F}(p,\gamma ){}^{20}\mathrm{Ne}$ reaction is considerably larger than previously reported. This is the result of undetermined interferences between observed resonances, a possible threshold state, possible subthreshold states, direct capture, and background levels. Additional experimental measurements are therefore needed to determine if ${}^{19}\mathrm{F}(p,\gamma ){}^{20}\mathrm{Ne}$ CNO breakout is responsible for Ca enrichment in metal-poor stars. Astrophysically, the breakout reaction revision makes it less likely that Ca observed in the most Fe-poor stars can originate in hot CNO breakout H-burning nucleosynthtesis, thereby casting doubt on the prevailing faint supernova scenario to explain the abundances observed in these stars.

Figure 1

Level diagram of the ${}^{20}\mathrm{Ne}$ system, in the vicinity of the proton separation energy, showing the level properties relevant for the present $R$-matrix analysis of ${}^{19}\mathrm{F}+p$ reactions. Separation energies are indicated by the red dashed horizontal lines, while levels in ${}^{20}\mathrm{Ne}$ by black horizontal lines. Note that the lower part of the level diagram, below the real level at $E_x$ = 12.40 MeV, is not to scale.

Figure 2

Differential $S$ factors of the ${}^{19}\mathrm{F}(p,a_0){}^{16}\mathrm{O}$ data [24, 25, 45, 48].

Figure 3

Low-energy angular distributions for the ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}$ reaction [24, 25, 32, 35, 46, 47, 48, 49].

Figure 4

Lowest-energy angle integrated ${}^{19}\mathrm{F}(p,{\alpha }_1){}^{16}\mathrm{O}$ data of Devons et al. [50] and Caracciolo et al. [49]. The data of Devons et al. [50] has been renormalized as suggested in Lombardo et al. [44]. The $R$-matrix cross section (red line) has been convoluted with the energy resolution of the experiment.

Figure 5

Angular distributions of the ${}^{19}\mathrm{F}(p,{\alpha }_1){}^{16}\mathrm{O}$ reaction from Caracciolo et al. [49].

Figure 6

The $R$-matrix fit to the ${}^{19}\mathrm{F}(p,{\alpha }_2){}^{16}\mathrm{O}$ secondary $\gamma$-ray data of Lorenz-Wirzba [24] and Couture et al. [30] is shown by the red solid line. Additional data from Ott [26], which used substantially thicker targets, was not included in the fit, but calculations are shown (red dashed lines) comparing the $R$-matrix fit from this work convoluted with the experimental resolution.

Figure 7

Secondary on-resonance $\gamma$-ray angular distribution measurements for the ${}^{19}\mathrm{F}(p,{\alpha }_{(2,3,4)}){}^{16}\mathrm{O}$ reactions [38, 51]. The data of Devons et al. [51] are the sum of the three secondary $\gamma$-ray transitions while that of Keszthelyi et al. [38] are of only the ${}^{19}\mathrm{F}(p,{\alpha }_2){}^{16}\mathrm{O}$ reaction.

Figure 8

Secondary on-resonance $\gamma$-ray angular distribution measurements for the ${}^{19}\mathrm{F}(p,{\alpha }_{(2,4)}){}^{16}\mathrm{O}$ reactions at $E_p$ = 340 keV [52] and 484 keV [39]. The isotropic distributions of these isolated resonances provide accurate relative angular distribution calibrations for $\gamma$-ray detectors.

Figure 9

Differential cross-section measurement of the ${}^{19}\mathrm{F}(p,{\alpha }_2){}^{16}\mathrm{O}$ reaction though observation of the $\alpha$-particles. This thin target data set from Ott [26] is unique for this reaction, as all others have been made by measuring secondary $\gamma$ rays.

Figure 10

Sum of the ${}^{19}\mathrm{F}(p,{\alpha }_{(2,3,4)}){}^{16}\mathrm{O}$ reactions measured with a sodium iodide summing detector by Spyrou et al. [29]. The $R$-matrix cross section (red line) has been convoluted with the energy resolution of the experiment.

Figure 11

Experimental data for the ${}^{19}\mathrm{F}(p,{\alpha }_3){}^{16}\mathrm{O}$ reaction. The top panel displays the angle integrated data of Couture et al. [30] (circles) while the bottom panel shows the differential data of Lorenz-Wirzba [24] (squares) at ${\theta }_{\gamma }$ = ${45}^{\circ }$. The $R$-matrix cross section (red line) has been convoluted with the energy resolution of the experiment.

Figure 12

Experimental data for the ${}^{19}\mathrm{F}(p,{\alpha }_4\gamma ){}^{16}\mathrm{O}$ reaction. The top panel displays the angle integrated data of Couture et al. [30] (circles) while the bottom panel shows the differential data of Lorenz-Wirzba [24] (squares) at ${\theta }_{\gamma }$ = ${45}^{\circ }$. The $R$-matrix cross section (red line) has been convoluted with the energy resolution of the experiment.

Figure 13

The limited amount of proton scattering data from Webb et al. [53] and Caracciolo et al. [49]. The $R$-matrix cross section (red line) has been convoluted with the energy resolution of the experiment.

Figure 14

Only the ${}^{19}\mathrm{F}(p,{\gamma }_1){}^{20}\mathrm{Ne}$ data of Couture et al. [30] are available for the capture reaction. The $R$-matrix cross section (red line) has been convoluted with the energy resolution of the experiment.

Figure 15

Illustration of the inconsistencies between the low-energy data of Lorenz-Wirzba [24], the data of Lombardo et al. [32], and the THM measurements of LaCognata et al. [33].

Figure 16

Calculations of the ${}^{19}\mathrm{F}(p,{\alpha }_2){}^{16}\mathrm{O}S$ factor given different interference scenarios and partial width limits for the near-threshold state at 11 keV. These should be compared with the blue dashed line, which corresponds to the nearly constant ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}S$ factor.

Figure 17

Calculations of different interference scenarios given the width limitations of the near-threshold state at 11 keV.

Figure 18

Fractional contributions of the different final state contributions to the central value calculation of ${}^{19}\mathrm{F}(p,\alpha ){}^{16}\mathrm{O}$ reaction rate. Here the ${}^{19}\mathrm{F}(p,{\alpha }_0){}^{16}\mathrm{O}$ rate dominates around $T\approx$ 0.1 GK, as found in previous works (e.g., NACRE [20]).

Figure 19

Fractional contributions of the different final state contributions to the upper limit calculation of ${}^{19}\mathrm{F}(p,\alpha ){}^{16}\mathrm{O}$ reaction rate. In this case the interference of the threshold state and subthreshold resonances enhance the ${}^{19}\mathrm{F}(p,{\alpha }_2){}^{16}\mathrm{O}$ reaction, making it dominant at all temperatures.

Figure 20

Ratio of the present reaction ${}^{19}\mathrm{F}(p,\alpha ){}^{16}\mathrm{O}$ reaction rate to that of the NACRE compilation [20] (red solid line). The upper and lower uncertainty limits are indicated by the red dashed lines (this work) and the black dashed lines (NACRE [20]).

Figure 21

Ratio of the present reaction ${}^{19}\mathrm{F}(p,\gamma ){}^{20}\mathrm{Ne}$ reaction rate to that of the NACRE compilation [20] (red solid line). The upper and lower uncertainty limits are indicated by the red dashed lines (this work) and the black dashed lines (NACRE [20]).

Figure 22

Abundance chart showing the percent change of isotopes using updated ${}^{19}\mathrm{F}+p$ reaction rates, presented in this work, compared to rates from the NACRE compilation [20]. Orange colors indicate a reduction in the total mass fractions and blue indicates an increase.

Figure 23

Abundance evolution showing simulations with rates from this work (solid lines) and using rates from the NACRE compilation [20] for ${}^{19}\mathrm{F}+p$ reactions (dotted lines). Abundances are plotted as a function of the decreasing amount of H in the single-zone network simulation. Therefore time proceeds from left to right.

Figure 24

Mass fractions of Ca, and all isotopes with $Z$ $>9$ in a Pop III hydrogen burning single zone simulation, calculated using either the ${}^{19}\mathrm{F}+p$ reaction rates of this work (red) or those from the NACRE compilation [20] (blue). Bars indicate the variation of these abundances within the uncertainties.