High Resolution Study of ${}^{40}\mathrm{Ca}$ to Constrain Potassium Nucleosynthesis in NGC 2419

The globular cluster NGC 2419 was the first to exhibit a Mg-K anticorrelation, linked to hydrogen burning at temperatures between 80–260 MK. However, the key K-destroying reaction, ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{Ca}$, has a large rate uncertainty in this range. We significantly constrain this rate with a high resolution ${}^{39}\mathrm{K}({}^3\mathrm{He},d){}^{40}\mathrm{Ca}$ study. We resolve the ${\mathrm{E}}_{\mathrm{r}}^{\mathrm{c}.\mathrm{m}.}=154\mathrm{keV}$ resonance in ${}^{39}\mathrm{K}+p$ for the first time, increasing the previous rate by up to a factor 13 and reducing its $1\sigma$ width by up to a factor of 42. Reaction network calculations for NGC 2419 suggest that this could lower temperatures needed to reproduce the Mg-K anticorrelation.

Figure 1

Energy-calibrated focal-plane position spectrum gated on deuterons from the ${}^{39}\mathrm{K}({}^3\mathrm{He},d){}^{40}\mathrm{Ca}$ reaction at ${\theta }_{\mathrm{lab}}=5°$ with a 21 MeV ${}^3\mathrm{He}$ beam. The unbound ${}^{40}\mathrm{Ca}$ states populated in the present experiment are labeled with their ENSDF [31] energies in keV. This spectrum was collected using about 230 pnA of ${{}^3\mathrm{He}}^{++}$ for 4.6 h.

Figure 2

Differential cross sections of unbound ${}^{40}\mathrm{Ca}$ states below 8935 keV observed in the present experiment. The left panel shows the $l=1$ distributions, while the right panel shows all other distributions. The experimental data were normalized to the Si detector telescope yield, as described in the text. The zero-range DWBA model curves were computed using the nuclear reaction code, FRESCO [25, 26]. Error bars represent statistical uncertainties only.

Figure 3

Comparison between the ${}^{39}\mathrm{K}(p,\gamma ){}^{40}\mathrm{Ca}$ reaction rate using the proton partial widths and resonance energies of the present experiment (solid line, blue band) and the most recent evaluation of Longland et al. [11] (dotted line, gray band). The reaction rate ratio is taken with respect to the median, recommended rate of Ref. [11] for both calculations. The $1\sigma$ uncertainty bands are shown.