Forbidden electron capture on $^{24}$Na and $^{27}$Al in degenerate oxygen-neon cores

TL;DR

This study investigates forbidden electron capture transitions in $^{24}$Na and $^{27}$Al within degenerate oxygen-neon stellar cores, revealing their significant impact on core evolution and thresholds for electron capture reactions.

Contribution

The paper provides detailed formalism and shell model calculations for forbidden transitions in $^{24}$Na and $^{27}$Al, and assesses their astrophysical impact using stellar evolution models.

Findings

Forbidden transitions lower threshold densities for electron capture.

$^{24}$Na capture occurs immediately after $^{24}$Mg capture in models.

Impact on overall evolution is uncertain due to convective instabilities.

Abstract

Stars with an initial mass of $\sim 7$-11 solar masses form degenerate oxygen-neon cores following carbon burning. Electron captures in such cores can trigger runaway oxygen burning, resulting in either a collapse or a thermonuclear explosion. We provide a detailed description of the formalism used in previous work and apply it to two further forbidden transitions that are relevant to degenerate oxygen-neon cores: the $4^+_\text{g.s.}\rightarrow{}2^+_1$ transition in $^{24}\text{Na}(e^-,\nu_e)^{24}\text{Ne}$ and the ${5/2^+_{\text{g.s.}} \rightarrow{} 1/2^+_{\text{g.s.}}}$ transition in $^{27}\text{Al}(e^-,\nu_e)^{27}\text{Mg}$. The relevant nuclear matrix elements are determined through shell model calculations and constraints from CVC theory. We then investigate the astrophysical impact using the stellar evolution code MESA and through timescale arguments. In the relevant temperature range, the forbidden transitions substantially reduce the threshold densities for $^{24}\text{Na}(e^-,\nu_e)^{24}\text{Ne}$ and $^{27}\text{Al}(e^-,\nu_e)^{27}\text{Mg}$. In the MESA models, $^{24}\text{Na}(e^-,\nu_e)^{24}\text{Ne}$ now occurs immediately following the onset of $^{24}\text{Mg}(e^-,\nu_e)^{24}\text{Na}$. The impact on the overall evolution is uncertain: this is due to known difficulties in accounting for convective instabilities triggered by the $A=24$ electron captures. The transition between $^{27}\text{Al}$ and $^{27}\text{Mg}$ may have a minor effect on the early evolution but is unlikely to affect the outcome. The studied transitions should be included when calculating weak interaction rates between $^{24}$Na and $^{24}$Ne for temperatures $\log_{10}(T[\text{K}])\lesssim8.5$ and between $^{27}$Al and $^{27}$Mg for $\log_{10}(T[\text{K}])\lesssim8.8$.