Predictions from $s$-process AGB models of the isotopic variations of zirconium and neodymium for comparison to bulk meteorites

Technical Deep Dive: Predictions from $s$-process AGB Models of Zr and Nd Isotopic Variations in Meteorites

Overview

This paper presents a detailed comparison between the isotopic variations of the first ($s$-process peak element Zr) and second ($s$-process peak element Nd) observed in bulk meteorites, and predictions from models of low-mass asymptotic giant branch (AGB) stars of metallicity from solar to twice solar. The key findings are:

• The roughly 10-fold difference in the magnitude of $s$-process variations between Zr and Nd can be matched by models of AGB stars with metallicity higher than solar.
• Higher convective overshoot and/or a smaller mass of the $^{13}$C-rich region that produces the neutrons favor this match.
• The high-metallicity AGB stars that could have contributed this signature may have belonged to the old, metal-rich stellar population observed in the solar neighborhood today.

Methodology

• The Monash stellar evolution code was used to compute 79 models of low-mass AGB stars with initial masses 2-3.5 $M_\odot$ and metallicities $Z=0.014$, 0.02, 0.03, 0.04, and 0.05.
• The nucleosynthesis was calculated using a detailed nuclear reaction network and a parametrized partial mixing zone to produce the $^{13}$C neutron source.
• The AGB surface abundances were diluted by a factor of $10^4$ and used to calculate the $\epsilon$ values for $^{96}$Zr/$^{90}$Zr and $^{148}$Nd/$^{144}$Nd, which were then compared to meteoritic data.

Results

• Higher metallicity AGB models ($Z > 0.014$) with higher convective overshoot ($N\mathrm{ov} \gtrsim 2$) and/or smaller $^{13}$C pocket masses ($M\mathrm{mixed} \lesssim 10^{-3} M_\odot$) can match the observed $\sim$10-fold difference in $\epsilon$ values between Zr and Nd.
• This is because higher metallicity makes it harder for the $s$-process to reach the second peak (Nd), resulting in relatively larger variations in the first peak (Zr).
• Ingestion of the $^{13}$C pocket into the convective thermal pulse region can also enhance the Zr variations relative to Nd, especially for models with high convective overshoot.
• The maximum $\epsilon$96Zr/$\epsilon$148Nd ratio of 13 is reached for the 3 $M\odot$, $Z=0.03$ model with $N\mathrm{ov}=4$ and $M\mathrm{mixed} = 5 \times 10^{-4} M\odot$.

Interpretation

• The high-metallicity AGB stars that produced the observed Zr and Nd variations could have belonged to the old, metal-rich stellar population currently seen in the solar neighborhood.
• This population may have contributed stardust to the molecular cloud from which the Solar System formed, around 4.6 Gyr ago.
• The model predictions are also consistent with the $s$-process compositions observed in large presolar SiC grains and in Ba stars, providing independent constraints.

Limitations & Uncertainties

• The slope of the observed $\epsilon$96Zr vs $\epsilon$148Nd correlation is not yet well-defined, requiring more meteoritic data.
• The full inventory of AGB stardust carriers in the early Solar System is still uncertain, affecting the mass balance.
• The impact of updated neutron-capture cross sections and reaction rates needs to be explored.
• Consistency with other nucleosynthetic signatures in meteorites (e.g., short-lived radioactivities) should be checked.

Future Work

• Explore models with the latest solar abundance updates and compositions representative of the high-metallicity stellar population.
• Perform a detailed comparison between model predictions and presolar grain data.
• Measure Zr and Nd variations in the same meteoritic samples to better define the observational constraints.
• Investigate the potential relevance of other neutron-capture processes and grain types.