Weak r-Process Pattern in Metal-Poor Stars

• The weak r-process pattern is defined by an excess of first-peak and some second-peak elements, distinguishing it from the main r-process signature in metal-poor stars.
• Parametric modeling using a two-component linear mixing approach quantifies weak and main r-process contributions with fits typically within 0.2–0.3 dex.
• Observations associate weak r-process yields with core-collapse supernovae, providing critical constraints on stellar nucleosynthesis and early Galactic chemical evolution.

The weak r-process pattern describes the abundance distribution and nucleosynthetic origin of lighter neutron-capture elements (notably Sr, Y, Zr, Pd, Ag, Mo, Ru) in r-process-enriched, metal-poor stars, as distinct from the "main" or "full" r-process responsible for heavier nuclei (Ba, La, Eu, third-peak elements, actinides). Weak r-process yields are characterized by an excess of first-peak and some second-peak elements but a pronounced deficiency in heavier r-process species, and are typically attributed to relatively neutron-deficient, high-entropy or moderately neutron-rich ejecta in core-collapse supernovae and related astrophysical environments. This pattern is crucial for parsing the star formation history, chemical enrichment, and nucleosynthetic sites in the early Galaxy.

1. Parametric Modeling of r-Process Contributions

Holistic abundance analyses in r-rich metal-poor stars adopt a two-component linear mixing model for each element's observed abundance $N_i$: $$N_i = C_w' N_{i,(\text{rw})} + C_m' N_{i,(\text{rm})}$$ where $N_{i,(\text{rw})}$ and $N_{i,(\text{rm})}$ are the weak and main r-process yields for element $i$, and $C_w'$, $C_m'$ are the relative scaling coefficients. Abundance residuals are assessed via reduced $\chi^2$ fitting across the compositional array of O–Zn (light/Fe-peak) through heavy n-capture elements (Ba–Pb) (Zhang et al., 2010).

This approach allows robust disentanglement of the two r-process contributions and demonstrates that the weak r-process pattern in the $38 \leq Z \leq 47$ regime (Sr–Ag) is distinct from the main r-process signature for $Z \geq 56$ (Ba and heavier), with lighter n-capture abundances generally requiring a mix of both processes. Comprehensive application to 14 well-studied r-rich stars achieves fits typically good to 0.2–0.3 dex, revealing that weak r-process contributions track with light and Fe-group elements, while main r-process contributions are nearly decoupled from them.

2. Astrophysical Sites and Environment Dependence

The empirical dichotomy between weak and main r-process regimes is mirrored by theoretical arguments for distinct astrophysical origins:

• Weak r-process production is preferentially associated with core collapse supernovae of intermediate mass progenitors (Fe core-collapse, $12–25 \ M_\odot$). These events efficiently eject light and Fe-peak elements together with lighter n-capture material, and imprint a stable weak r-process abundance signature in their enrichment products.
• Main r-process events (possibly O–Ne–Mg core-collapse SNe or other rare phenomena) produce heavy r-process nuclei, but do not co-synthesize light/Fe-peak and lighter n-capture elements at the same level.

Thus, a star forming in a molecular cloud polluted by both weak and main r-process ejecta inherits a hybrid abundance pattern: light/Fe-group and lighter n-capture elements derived mostly from the weak r-process, heavy r-process elements from the main component (Zhang et al., 2010).

3. Universality and Diversity of the Weak r-Process Pattern

Weak r-process abundance patterns, specifically in the range $38 \leq Z \leq 47$, are found to be remarkably uniform across extensively studied sample stars, suggesting a process with a robust yield template. Abundance comparisons of stars such as HD 221170 and canonical weak r-process stars like HD 122563 indicate that their lighter n-capture distributions are nearly invariant, while heavy elements mirror the universal main r-process pattern traced by solar r-process residuals.

However, recent work suggests that subtle diversity may exist, especially in the production efficiency of elements beyond Mo (e.g., Ru, Pd), tied to modest variations in physical parameters (e.g., $Y_e$, entropy, proto-NS mass) in supernova ejecta. Nonetheless, the data collectively support a consistent, patterned weak r-process outcome under a defined range of astrophysical conditions (Zhang et al., 2010).

4. Observational Signatures and Model Comparison

The weak r-process is diagnosed observationally by:

• Excesses in light n-capture elements (Sr, Y, Zr, Mo, Pd, Ag) relative to the expected scaled main r-process pattern.
• Low heavy r-process element abundances (Ba, Eu, and above) compared to expectations for main r-process events.
• Close matches between observed and calculated abundance patterns within 0.2–0.3 dex for O–Zn plus Ba–Pb, when fit with the two-component model.
• Component coefficients ($C_w', C_m'$) in these fits often indicate neither process exclusively dominates; e.g., HD 221170 with $C_w' = 3.755$, $C_m' = 0.612$ shows inferred dominance of the weak process for lighter elements, main for heavier.

This two-component modeling provides quantitative predictions in agreement with observed trends from light through heavy elements in stars with [Fe/H] $< -2.1$.

5. Implications for Early Galactic Chemical Evolution

Evidence from abundance patterns in the Galactic halo and dwarf galaxy stars implies the integrated ISM at low metallicity is often enriched by both weak and main r-process nucleosynthetic events. Quantifying the weak r-process's yield and its abundances in metal-poor stars constrains the fraction of supernovae acting as its sites, places limits on progenitor mass distributions, and guides the supernova models needed to match Galactic chemical evolution.

The strong association between weak r-process yields and Fe-group (as well as light elements) supports models in which the weak r-process acts as a "primary" process, contributing its signature consistently across Galactic epochs. This is distinct from the stochastic, often inhomogeneous main r-process contributions.

A summary table capturing the relationship between weak and main r-process yields for key elements:

Element	Weak r-Process (High $C_w'$)	Main r-Process (High $C_m'$)
Sr, Y, Zr	High	Low
Ba, Eu, Pb	Low	High
O–Zn (Fe-group)	High	Low

6. Theoretical and Observational Directions

Outstanding directions to further refine understanding of the weak r-process pattern include:

• Expanded, higher-precision spectroscopic surveys to disentangle weak and main r-process contributions, particularly at very low metallicities and in environments with moderate [Eu/Fe].
• Detailed nucleosynthesis modeling, incorporating supernova parameter variations and multi-dimensional effects, to constrain weak r-process yields and clarify their dependence on $Y_e$, entropy, and progenitor mass.
• Improved measurements of lighter n-capture element abundances (especially for $38 \leq Z \leq 47$), enabling tighter tests of universality and robustness.
• Integration with Galactic chemical evolution models to estimate the relative frequencies and contributions of weak versus main r-process events as a function of metallicity.

These further studies are essential for establishing the weak r-process as a distinct and quantifiable channel in the synthesis of heavy elements and for determining its impact in the broader context of stellar and Galactic evolution (Zhang et al., 2010).