[Paper Review] Chemical clocks and their time zones: understanding the [s/Mg]--age relation with birth radii

Bridget Ratcliffe, Ivan Minchev+6 more|arXiv (Cornell University)|Jul 20, 2023

Stellar, planetary, and galactic studiesPhysics and Astronomy3 citations

TL;DR

This study reveals that the [s/Mg]–age relation in the Milky Way is not universal but strongly dependent on stellar birth radius (R_birth), with inner-disk stars showing the weakest correlation due to evolving radial gradients in s-process and α-element abundances. By using R_birth to disentangle radial migration effects, the authors demonstrate that the tight [s/Mg]–age relation in solar-like stars arises from their similar birth radii, and they constrain metallicity-dependent AGB yields and mild radial migration in a Galactic chemical evolution model to reproduce observed trends.

ABSTRACT

The relative enrichment of s-process to $α$-elements ([s/$α$]) has been linked with age, providing a potentially useful avenue in exploring the Milky Way's chemical evolution. However, the age--[s/$α$] relationship is non-universal, with dependencies on metallicity and current location in the Galaxy. In this work, we examine these chemical clock tracers across birth radii ($ m ext{R}_ ext{birth}$), recovering the inherent trends between the variables. We derive $ m ext{R}_ ext{birth}$ and explore the [s/$α$]--age--$ m ext{R}_ ext{birth}$ relationship for 36,652 APOGEE DR17 red giant and 24,467 GALAH DR3 main sequence turnoff and subgiant branch disk stars using [Ce/Mg], [Ba/Mg], and [Y/Mg]. We discover that the age--[s/Mg] relation is strongly dependent on birth location in the Milky Way, with stars born in the inner disk having the weakest correlation. This is congruent with the Galaxy's initially weak, negative [s/Mg] radial gradient, which becomes positive and steep with time. We show that the non-universal relations of chemical clocks is caused by their fundamental trends with $ m ext{R}_ ext{birth}$ over time, and suggest that the tight age--[s/Mg] relation obtained with solar-like stars is due to similar $ m ext{R}_ ext{birth}$ for a given age. Our results are put into context with a Galactic chemical evolution model, where we demonstrate the need for data-driven nucleosynthetic yields.

Motivation & Objective

• To understand why the [s/Mg]–age relation varies across the Galactic disk, challenging the assumption of universality in chemical clocks.
• To disentangle the effects of radial migration on the observed [s/Mg]–age relation by reconstructing stellar birth radii (R_birth).
• To investigate how the radial gradient in [s/Mg] evolves over time and influences age–abundance correlations.
• To constrain the metallicity dependence of AGB nucleosynthetic yields and radial migration strength using data-driven models.
• To demonstrate that the tight [s/Mg]–age relation in solar-like stars is a consequence of their similar R_birth, not a universal physical law.

Proposed method

• Derived R_birth for 36,652 APOGEE DR17 red giants and 24,467 GALAH DR3 main-sequence turnoff/subgiant stars using kinematic and abundance data.
• Analyzed the [s/Mg]–age–R_birth relationship using [Ce/Mg], [Ba/Mg], and [Y/Mg] as tracers of s-process enrichment.
• Constructed time-evolving radial abundance gradients by binning stars by R_birth and look-back time, revealing the evolution of the [s/Mg] gradient.
• Used a Galactic chemical evolution (GCE) model with standard nucleosynthetic yields to simulate [s/Mg] evolution, then modified yields and added radial migration to match observations.
• Applied smoothing and running mean techniques to extract trends in [s/Mg] across R_birth and look-back time, isolating the influence of birth location.
• Validated model results against observed [s/Mg] trends in APOGEE and GALAH data, adjusting yield metallicity dependence and migration fraction to improve fit.

Experimental results

Research questions

• RQ1 How does the [s/Mg]–age relation vary across different birth radii in the Milky Way disk?
• RQ2 Why is the [s/Mg]–age correlation weaker in the inner disk compared to the outer disk?
• RQ3 To what extent does radial migration obscure the intrinsic age–abundance relation in stellar populations?
• RQ4 What modifications to nucleosynthetic yields and migration strength are needed to reproduce observed [s/Mg] trends with R_birth and time?
• RQ5 Why is the [s/Mg]–age relation tight in solar-like stars, while it appears scattered in broader samples?

Key findings

• The [s/Mg] radial gradient starts weakly negative at early times, flattens during the high-to-low α transition, and becomes increasingly positive toward the present day.
• Stars born in the inner disk exhibit the weakest correlation between [s/Mg] and age due to the initial negative radial gradient and strong radial migration.
• The scatter in the [s/Mg]–age relation across the disk is primarily due to variations in R_birth for a given age, not intrinsic age-dating uncertainty.
• When R_birth dispersion is small—such as in solar-like stars—the [s/Mg]–age relation becomes tight and predictable.
• A simple GCE model with metallicity-dependent AGB yields and mild radial migration (≈10% of AGB products) successfully reproduces the observed [s/Mg] trends across R_birth and time.
• The study demonstrates that birth radius is a critical parameter for interpreting chemical clocks, and that radial migration fundamentally shapes the observed [s/Mg]–age relation.