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Constraining r-process nucleosynthesis with multi-objective Galactic chemical evolution models

This study employs multi-objective optimization on a grid of Galactic chemical evolution models to demonstrate that a single r-process event class with solar-scaled yields cannot simultaneously explain the observed abundances of both light and heavy neutron-capture elements, necessitating at least two distinct enrichment components.

Original authors: M. Molero, A. Arcones, F. Montes, C. J. Hansen

Published 2026-05-27

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CC BY 4.0

Original authors: M. Molero, A. Arcones, F. Montes, C. J. Hansen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Milky Way as a giant, bustling kitchen where stars are the chefs and heavy elements (like gold, uranium, and even the Europium used in your phone's screen) are the ingredients. For decades, astronomers have been trying to figure out exactly who is cooking these heavy ingredients and when they are adding them to the galactic soup.

This paper is like a massive, computerized taste-test. The authors built a simulation of the galaxy's history and ran it about 150,000 times, tweaking the recipe each time to see which version tastes most like the real universe we observe today.

Here is the breakdown of their experiment, using simple analogies:

1. The Mystery of the "Heavy Ingredients"

There are two main ways stars make heavy elements:

The Slow Cook (s-process): Like a slow-simmering stew, this happens in aging stars. It's predictable and steady.
The Fast Burn (r-process): This is the mystery. It happens in violent, explosive events (like crashing neutron stars or special supernovae). It creates the heaviest, rarest elements.

The big question is: Who is the chef? Is it the neutron star crashes? The special supernovas? Or both? And how often do they happen?

2. The "Taste-Test" Simulation

Instead of guessing which specific type of explosion is the chef, the authors took a flexible approach. They treated the "r-process" as a generic ingredient dispenser with four adjustable knobs:

How much "Eu" (Europium) is dumped per event? (The yield)
How often do the events happen? (The rate)
How long do we wait after a star is born before it explodes? (The delay)
How big are the stars that explode? (The mass range)

They ran 150,000 simulations, changing these knobs in every possible combination, to see which settings produced a galaxy that looked like our own.

3. The Results: Finding the "Sweet Spot"

When they looked at the best-fitting models (the ones that matched the real data best), they found a very specific recipe:

The Chefs are Young and Fast: The events happen very quickly after stars are born (within 30 million years). This is crucial because we see heavy elements in very old, "metal-poor" stars. If the events took too long (like waiting for neutron stars to crash, which can take billions of years), those old stars would have been born without any heavy ingredients.
The Chefs are Medium-Sized: The best models suggest the explosions come from stars about 20 to 25 times the mass of our Sun.
The "Too Big" Problem: They tried using massive stars (over 80 times the Sun's mass), but the simulation showed there just aren't enough of them. They are too rare to be the only source of heavy elements.

4. The "Scaling" Problem: The Recipe Doesn't Work for Everyone

Here is where the paper gets interesting. The authors assumed that if they got the amount of Europium right, the other heavy elements (like Strontium, Yttrium, Zirconium, Barium, etc.) would automatically fall into place, just like a recipe that says "add 1 cup of flour, and the rest of the ingredients will follow a standard ratio."

The simulation showed this assumption is broken.

The Heavyweights (Barium, Lanthanum, Cerium): The "standard recipe" worked pretty well. The models could reproduce the abundance of these heavy elements quite accurately.
The Lightweights (Strontium, Yttrium, Zirconium): The recipe failed miserably. The models consistently produced too little of these lighter elements compared to what we actually see in stars.

Think of it like baking a cake: You can perfectly match the amount of chocolate (Europium) and the heavy nuts (Barium), but the model keeps underestimating the amount of sugar (Strontium) needed. No matter how you tweak the oven temperature or the mixing speed, you can't get the sugar and the chocolate to be perfect at the same time using a single recipe.

5. The Conclusion: We Need Two Different Chefs

Because the "single recipe" (scaling everything off Europium) failed for the lighter elements, the authors conclude that one single type of cosmic event cannot explain all the heavy elements.

They propose that the galaxy needs two different types of "chefs":

The "Main" Chef: This one makes the heavy, third-peak elements (like Barium and Uranium) and follows the "solar pattern" (similar to what we see in the Sun and "r-rich" stars).
The "Weak" Chef: This one is specialized in making the lighter elements (Strontium, Yttrium, Zirconium) in higher amounts relative to the heavy ones. This matches what we see in "r-poor" stars (stars that are poor in heavy elements but rich in these lighter ones).

Summary

The paper argues that the universe doesn't use a single, universal "heavy element factory." Instead, it likely uses a combination of two different processes: one that makes the heavy stuff (like gold and uranium) and another, distinct process that is better at making the lighter heavy stuff (like strontium). Trying to force them into one single model is like trying to bake a perfect cake and a perfect loaf of bread using the exact same instructions—it just doesn't work.

Technical Summary: Constraining r-process nucleosynthesis with multi-objective Galactic chemical evolution models

Problem Statement
The astrophysical origin of the rapid neutron-capture process (r-process) remains uncertain, with competing scenarios including neutron star mergers (NSMs) and magneto-rotational supernovae (MR-SNe). While multi-messenger observations have confirmed NSMs as viable sites, their delayed occurrence and low rates challenge their ability to explain r-process enrichment in the earliest, low-metallicity stars. Conversely, prompt sources like MR-SNe are theoretically plausible but lack direct observational constraints on their frequency and yields. A critical issue in Galactic chemical evolution (GCE) modeling is the assumption of "r-process universality"—the hypothesis that the relative abundance pattern of r-process elements scales uniformly from Europium (Eu) to other elements, based on the solar r-process distribution. Observations of low-metallicity stars suggest this universality may hold for heavy elements ( $Z \ge 56$ ) but fails for lighter neutron-capture elements ( $38 < Z < 50$ ), which often show enhanced ratios relative to Eu in r-process-poor stars. Current models often rely on single-objective optimization (fitting Eu only), potentially masking trade-offs required to simultaneously reproduce the chemical evolution of multiple elements.

Methodology
The authors employ a systematic, data-driven approach using a grid of $\sim 1.5 \times 10^5$ one-infall, homogeneous Galactic chemical evolution models. Rather than fixing the r-process to a specific astrophysical site (e.g., NSMs or MR-SNe), they adopt a flexible, parametric framework varying four key parameters:

Eu yield per event ( $Y_{Eu,r}$ ): Logarithmically sampled in $[10^{-7}, 10^{-5}] M_\odot$ .
Event rate fraction ( $\alpha$ ): The fraction of progenitor stars producing r-process material, linearly sampled in $[0, 1]$ .
Delay time ( $\tau$ ): The time between stellar death and enrichment, sampled quasi-logarithmically in $[0, 14]$ Gyr.
Progenitor mass range ( $[M_l, M_u]$ ): Varied in steps of $5 M_\odot$ from $[8, 10)$ to $[95, 100] M_\odot$ .

The yields of other neutron-capture elements are derived by scaling the Eu yield according to the solar r-process pattern (Simmerer et al. 2004). The models are compared against observational datasets spanning a wide metallicity range ( $-2.7 \le [\text{Fe/H}] \le \text{solar}$ ), constructed by combining data from the Gaia-ESO Survey, MINCE, and the SAGA database.

To evaluate model performance, the authors utilize a multi-objective optimization strategy based on Pareto front analysis. Instead of seeking a single "best-fit" model, they identify the set of Pareto-optimal solutions—models where improving the fit for one element necessarily worsens the fit for another. This allows for the mapping of trade-offs between different elemental constraints (e.g., Eu vs. Zr, or the light group Sr-Y-Zr vs. the heavy group Ba-La-Ce).

Key Contributions and Results

Parameter Constraints: The best-performing models consistently favor short delay times ( $\tau \le 30$ Myr), low-mass progenitors (centered around $20-25 M_\odot$ ), and an effective Eu injection rate of $\sim 2 \times 10^{-7} M_\odot$ per event. Progenitors more massive than $\sim 80 M_\odot$ are found to be too rare to account for the observed r-process enrichment alone, even with high yields.
Failure of Solar Scaling for Light Elements: When the best-Eu models are scaled to the solar r-process pattern, they systematically underestimate the abundances of lighter elements (Sr, Zr) at intermediate to low metallicities, while reproducing heavier elements (Ba, La, Ce) more successfully.
Pareto Trade-offs:
- Eu vs. Zr: In the two-dimensional optimization, no single model simultaneously reproduces both Eu and Zr trends. Models that fit Zr well systematically overestimate Eu, and vice versa.
- Light vs. Heavy Groups: The three-dimensional optimization for the light group (Sr, Y, Zr) reveals significant conflicts, with the Pareto front showing large distances from the ideal solution. In contrast, the heavy group (Ba, La, Ce) can be reproduced simultaneously with Eu with much lower trade-offs and smaller distances to the ideal point.
- Global Comparison: When combining Eu with the light group (Sr-Y-Zr), the distance to the ideal point in objective space is significantly larger ( $D \approx 200$ ) compared to combining Eu with the heavy group ( $D \approx 50$ ), confirming that the solar-scaled relation becomes progressively less valid toward lighter neutron-capture elements.

Significance and Conclusions
The paper concludes that no single class of r-process events, operating under a solar-scaled yield assumption, can simultaneously account for the chemical evolution of both light and heavy neutron-capture elements in the Milky Way. The observed tension suggests that the r-process universality does not extend across the entire mass range.

Instead, the results imply the necessity of at least two distinct scaling components:

A main r-process component (H-component), similar to the solar pattern and observed in r-process-rich stars, which dominates the production of heavy elements ( $Z \ge 56$ ).
A weak r-process component (L-component), characterized by enhanced production of lighter elements (Sr, Y, Zr) relative to the lanthanides, similar to patterns observed in r-process-poor stars.

The authors posit that these components likely arise from different astrophysical conditions or events, though they do not identify the specific physical sites. The study highlights the limitations of assuming a universal r-process pattern in chemical evolution models and demonstrates the utility of multi-objective optimization in disentangling complex nucleosynthetic contributions. Future work is suggested to constrain the weak component directly within GCE models or via simulated abundance patterns.