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New Constraints on Sodium Production in Globular Clusters From the $^{23}$Na$(^3$He$, \textbf{d})^{24}$Mg Reaction
Nuclear Experiment · Submitted 10 Mar 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is found that while the astrophysical conditions still dominate the total uncertainty, intra-model variations on sodium production from the $^{23}$Na$(p, \gamma)$ and $^{23}$Na$(p, \alpha)$ reaction channels are a lingering source of uncertainty.
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The abstract, sentence by sentence
The star to star anticorrelation of sodium and oxygen {is} a defining feature of globular clusters, but, to date, the astrophysical site responsible for this unique chemical signature remains unknown. Sodium enrichment within these clusters depends sensitively on reaction rate of the sodium destroying reactions $^{23}$Na$(p, \gamma)$ and $^{23}$Na$(p, \alpha)$. In this paper, we report the results of a $^{23}$Na$(^3\text{He}, d)^{24}$Mg transfer reaction carried out at Triangle Universities Nuclear Laboratory using a $21$ MeV $^3$He beam. Astrophysically relevant states {in $^{24}$Mg} between $11 < E_x < 12$ MeV were studied using high resolution magnetic spectroscopy, thereby allowing the extraction of excitation energies and spectroscopic factors. Bayesian methods are combined with the distorted wave Born approximation to assign statistically meaningful uncertainties to the extracted spectroscopic factors. For the first time, these uncertainties are propagated through to the estimation of proton partial widths. Our experimental data are used to calculate the reaction rate. The impact of the new rates are investigated using asymptotic giant branch star models. It is found that while the astrophysical conditions still dominate the total uncertainty, intra-model variations on sodium production from the $^{23}$Na$(p, \gamma)$ and $^{23}$Na$(p, \alpha)$ reaction channels are a lingering source of uncertainty.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The star to star anticorrelation of sodium and oxygen {is} a defining feature of globular clusters, but, to date, the astrophysical site responsible for this unique chemical signature remains unknown. | gap 0.64 | 0.04 | 0.03 | asserted 1.00 |
| s1 | Sodium enrichment within these clusters depends sensitively on reaction rate of the sodium destroying reactions $^{23}$Na$(p, \gamma)$ and $^{23}$Na$(p, \alpha)$. | background 0.99 | 0.06 | 0.03 | asserted 1.00 |
| s2 | In this paper, we report the results of a $^{23}$Na$(^3\text{He}, d)^{24}$Mg transfer reaction carried out at Triangle Universities Nuclear Laboratory using a $21$ MeV $^3$He beam. | method 0.56 | 0.97 | 0.03 | asserted 0.99 |
| s3 | Astrophysically relevant states {in $^{24}$Mg} between $11 < E_x < 12$ MeV were studied using high resolution magnetic spectroscopy, thereby allowing the extraction of excitation energies and spectroscopic factors. | method 0.87 | 0.95 | 0.03 | asserted 1.00 |
| s4 | Bayesian methods are combined with the distorted wave Born approximation to assign statistically meaningful uncertainties to the extracted spectroscopic factors. | method 0.98 | 0.92 | 0.02 | asserted 1.00 |
| s5 | For the first time, these uncertainties are propagated through to the estimation of proton partial widths. | contribution 0.83 | 0.92 | 0.05 | asserted 1.00 |
| s6 | Our experimental data are used to calculate the reaction rate. | method 0.57 | 0.93 | 0.07 | asserted 1.00 |
| s7 | The impact of the new rates are investigated using asymptotic giant branch star models. | method 0.71 | 0.86 | 0.06 | asserted 0.81 |
| s8 | It is found that while the astrophysical conditions still dominate the total uncertainty, intra-model variations on sodium production from the $^{23}$Na$(p, \gamma)$ and $^{23}$Na$(p, \alpha)$ reaction channels are a lingering source of uncertainty. | result 0.66 | 0.93 | 0.68 | asserted 0.99 |
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Original abstract
The star to star anticorrelation of sodium and oxygen {is} a defining feature of globular clusters, but, to date, the astrophysical site responsible for this unique chemical signature remains unknown. Sodium enrichment within these clusters depends sensitively on reaction rate of the sodium destroying reactions $^{23}$Na$(p, \gamma)$ and $^{23}$Na$(p, \alpha)$. In this paper, we report the results of a $^{23}$Na$(^3\text{He}, d)^{24}$Mg transfer reaction carried out at Triangle Universities Nuclear Laboratory using a $21$ MeV $^3$He beam. Astrophysically relevant states {in $^{24}$Mg} between $11 < E_x < 12$ MeV were studied using high resolution magnetic spectroscopy, thereby allowing the extraction of excitation energies and spectroscopic factors. Bayesian methods are combined with the distorted wave Born approximation to assign statistically meaningful uncertainties to the extracted spectroscopic factors. For the first time, these uncertainties are propagated through to the estimation of proton partial widths. Our experimental data are used to calculate the reaction rate. The impact of the new rates are investigated using asymptotic giant branch star models. It is found that while the astrophysical conditions still dominate the total uncertainty, intra-model variations on sodium production from the $^{23}$Na$(p, \gamma)$ and $^{23}$Na$(p, \alpha)$ reaction channels are a lingering source of uncertainty.
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What this paper does with the arXiv papers it cites
What it cites · 5 sentences without a confident label
Builds on 1 paper
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To do this we construct two updated versions of the rates in Ref. [ref] , which are themselves updates of STARLIB Version v6.5 [ref] .
STARLIB: A Next-Generation Reaction-Rate Library for Nuclear Astrophysics · The $^23$Na$(p, γ)$ and $^23$Na$(p, α)$ Reaction Rates · 0.84
Uses the method or tool of 4 papers
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Folding different $ℓ$ probabilities estimated directly from transfer reactions is only possible due to the Bayesian methods developed in Ref. [ref] and the Monte-Carlo reaction rate developed in Ref. [ref] .
Thermonuclear reaction rate of $^{18}$Ne($\alpha$,$p$)$^{21}$Na from Monte-Carlo calculations · Partial Widths Update · 1.00
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For each state, affine invariant MCMC [ref] , as implemented in the package [ref] was run with $400$ walkers taking $8000$ steps, giving a total of $3.2 ×10^6$ samples.
emcee: The MCMC Hammer · Results · 1.00
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The evolutionary sequences were run with the Monash stellar evolution code ( [ref] ; described most recently in Ref. [ref] and Ref. [ref] ) and post processing nucleosynthesis code (see Refs. [ref] ).
Bridging the Gap between Intermediate and Massive Stars I: Validation of MESA against the State-of-the-Art Monash Stellar Evolution Program for a 2$M_{\odot}$ AGB Star · AGB Models · 1.00
Cites as background 1 paper
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Comprised of tens to hundreds of thousands of stars that are gravitationally bound, they offer a unique probe of galactic and stellar evolution [ref] .
Multiple populations in globular clusters. Lessons learned from the Milky Way globular clusters · Introduction · 1.00
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