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Metal Enrichment by the First Stars Exploding at the Lower Energy Limit of Pair-Instability Supernovae

Using cosmological hydrodynamic simulations, this study demonstrates that even if low-energy pair-instability supernovae from the first stars were common, they would imprint distinct odd-even abundance patterns on second-generation stars, meaning their absence in observed extremely metal-poor stars strongly disfavours PISNe as the dominant mechanism for early metal enrichment.

Original authors: Aron Kordt, Simon C. O. Glover, Ralf S. Klessen

Published 2026-05-13

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CC BY 4.0

Original authors: Aron Kordt, Simon C. O. Glover, Ralf S. Klessen

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

The Big Picture: The Cosmic "Firsts"

Imagine the early Universe as a giant, pristine kitchen. When the Big Bang happened, the only ingredients available were hydrogen and helium (the "flour" and "sugar" of the cosmos). There were no other ingredients—no "metals" (in astronomy, this means anything heavier than helium, like iron or carbon).

The very first stars, called Population III stars, were made entirely of this pristine flour and sugar. Because they had no other ingredients to help them cool down, they grew incredibly massive—some were as heavy as 140 to 270 suns.

The Problem: The Missing "Odd-Even" Pattern

When these massive stars die, they explode as supernovae. There is a specific type of explosion called a Pair-Instability Supernova (PISN). Think of a PISN as a massive firework that doesn't just leave a little ash behind; it completely vaporizes the star and scatters a huge amount of new "ingredients" (metals) into the kitchen.

Scientists have a specific recipe for what a PISN explosion should look like in the chemical makeup of the next generation of stars. It's like a fingerprint: a distinct "odd-even" pattern where certain elements are much more common than their neighbors.

The Mystery: Astronomers have looked at the oldest, most metal-poor stars in our galaxy (the "EMP stars"). They are looking for that specific PISN fingerprint. But they can't find it. The stars they see don't have the right chemical pattern.

The Two Theories

Why can't we find these PISN stars? Scientists had two main guesses:

Theory A: Maybe these massive stars just didn't exist often enough.
Theory B: Maybe they did exist, but the stars that formed from their debris were so "rich" in metals that they didn't count as "metal-poor" anymore. If they were too rich, we wouldn't have looked for them in the "metal-poor" pile.

A previous study (Magg et al., 2022) tested Theory B using the most powerful PISN explosions imaginable (the biggest, most energetic fireworks). They found that even with these massive explosions, many of the new stars were still "metal-poor" enough to be found in our surveys. This suggested that if PISNe were common, we should have found them by now. Since we haven't, they probably weren't common.

This Paper's New Experiment: The "Small" Firework

The authors of this paper decided to test Theory B again, but with a twist. Instead of looking at the biggest, most energetic PISN (the "100-ton firework"), they looked at the smallest, weakest PISN allowed by physics (a "140-sun star" with a much smaller explosion energy).

The Analogy:
Imagine you drop a bucket of red paint into a swimming pool.

The High-Energy Case: You drop the paint in, and a massive wave (the explosion) spreads the paint out over the entire pool. The water turns a very light pink.
The Low-Energy Case (This Paper): You drop the paint in, but the wave is tiny. The paint stays mostly in a small puddle right where you dropped it. The water in that puddle is still very red, but the rest of the pool is clear.

What They Did

They ran a super-computer simulation of the early Universe. They created a scenario where a small, weak PISN exploded. They watched to see:

How far the "metal" (the paint) spread.
How much gas was blown away.
What the metal content was of the next stars that formed from that gas.

The Results: The Paint Didn't Spread Far

The simulation showed that because the explosion was weak:

The "Puddle" Effect: The metals didn't get swept out into the vastness of space. Instead, they stayed trapped in the immediate neighborhood of the explosion.
Fast Recollapse: The gas didn't get blown away; it just got pushed a little bit, then quickly fell back together (recollapsed) to form new stars.
Very Low Metal Content: Because the metals were concentrated in a small area and didn't get diluted by a huge amount of fresh gas, the new stars formed with extremely low metal content.

The Key Finding:
The new stars formed with a metal level of about [Fe/H] = -5.5.

This is much lower (about 3,000 times less metal) than the stars formed in the high-energy explosion study.
These stars are definitely "metal-poor." If they existed in real life, we would be looking for them right now in our surveys of ancient stars.

The Conclusion: The Fingerprint is Still Missing

The paper concludes that even if these weak, small PISN explosions happened, the stars they created would still be easy to find in our "metal-poor" surveys. And they would still carry that unique "odd-even" chemical fingerprint.

Since we still don't see these stars or their fingerprints in the real Universe, the authors conclude:
Pair-Instability Supernovae were likely very rare in the early Universe. The chemical makeup of the first stars was probably dominated by a different type of explosion (Core-Collapse Supernovae from smaller stars), not the massive PISN fireworks.

Summary in One Sentence

Even when the first stars exploded with the smallest possible energy allowed, the new stars they created were still so metal-poor that we should have found them by now; since we haven't, those massive explosions probably didn't happen very often.

Problem Statement
The first generation of stars (Population III or Pop III) is theorized to include massive stars (140–270 $M_\odot$ ) that end their lives as pair-instability supernovae (PISNe). These events are expected to release vast amounts of energy and synthesize substantial quantities of metals, imprinting a characteristic "odd-even" abundance pattern on the interstellar medium. However, no clear signature of PISN enrichment has been identified in the population of extremely metal-poor (EMP) stars ( $[Fe/H] \le -3$ ) observed in the local Universe. Two primary hypotheses attempt to explain this absence: either PISNe were rare events, or stars formed from PISN-enriched gas were too metal-rich to be classified as EMP stars. Previous work by Magg et al. (2022b) investigated the latter possibility by simulating the most energetic PISNe ( $270 M_\odot$ , $10^{53}$ erg), finding that while some second-generation stars exceeded the EMP threshold, the majority remained within the EMP regime. This paper addresses the opposite extreme of the theoretical PISN parameter space to determine if lower-energy events produce different enrichment outcomes.

Methodology
The authors performed a cosmological hydrodynamic simulation using the moving-mesh code AREPO to self-consistently track the formation of Pop III stars, their radiative and mechanical feedback, and the subsequent formation of second-generation stars. The simulation setup mirrors that of Magg et al. (2022b) to ensure a direct comparison, with the sole exception being the supernova properties.

Initial Conditions: The simulation began from a snapshot of the Magg et al. (2022b) run at redshift $z \approx 23.79$ , shortly before the first Pop III star formed.
Supernova Model: The study focuses on PISNe at the lower mass and energy limit: a progenitor mass of $140 M_\odot$ and an explosion energy of $5 \times 10^{51}$ erg. This is contrasted with the $10^{53}$ erg energy used in the high-energy case.
Feedback Implementation: Radiative feedback was modeled using the SPRAI code with specific energy bands for H $_2$ dissociation and ionization. Mechanical feedback involved injecting thermal energy and Monte Carlo tracer particles into the 1000 cells closest to the sink particle to track metal enrichment.
Resolution: The simulation employed adaptive mesh refinement, ensuring the Jeans length was resolved by at least 8 cells and the Strömgren sphere by at least 1000 cells. The maximum effective cell diameter was limited to 0.15 pc near stars to resolve the Sedov-Taylor radius.
Scope: The simulation ran for approximately 55 Myr, covering the period from the first star formation to the recollapse of gas and the formation of second-generation stars in 12 specific halos where radiative feedback was tracked self-consistently.

Key Contributions and Results

Internal Enrichment Dominance: The simulation reveals that all second-generation stars form exclusively via internal enrichment within the same halo that hosted the first Pop III star. No examples of external enrichment (where gas from one halo enriches a neighboring halo) were observed during the simulated timeframe.
Metallicity Outcomes: The median metallicity of the second-generation stars is $[Fe/H] \approx -5.5$ . This value is approximately 2.9 dex lower than the median found in the high-energy PISN simulation (Magg et al. 2022b), despite the theoretical iron yield of the low-energy PISN being 4 dex lower.
Dilution Mechanism: The discrepancy between the yield difference (4 dex) and the resulting metallicity difference (2.9 dex) is attributed to the lower explosion energy. The $5 \times 10^{51}$ erg blast wave is less capable of unbinding gas from the halo's potential well compared to the $10^{53}$ erg case. Consequently, the metal ejecta remain confined to a smaller volume near the explosion site, resulting in less dilution than in the high-energy scenario where gas is swept up and mixed more extensively.
Recollapse Times: The time delay between the supernova explosion and the formation of the second-generation star (recollapse time, $t_{rec}$ ) is generally shorter in the low-energy case (median $\sim 10$ Myr) compared to the high-energy case. In some halos, dense gas structures survived the shock, leading to very rapid recollapse ( $t_{rec} < 1$ Myr).
Abundance Patterns: The second-generation stars exhibit a high carbon-to-iron ratio ( $[C/Fe] \sim 3.6$ ) and the characteristic odd-even abundance pattern associated with PISN yields. These chemical signatures place them squarely within the observational parameter space of EMP stars found in the SAGA database.

Significance and Conclusions
The paper concludes that if Pop III PISNe were a common channel for early metal enrichment, the resulting second-generation stars would be readily detectable within the observed EMP population due to their low metallicities ( $[Fe/H] \sim -5.5$ ) and distinct chemical signatures. The fact that such stars are not observed, despite the simulations predicting they should exist and be observable, strongly disfavors the hypothesis that PISNe were the dominant source of early metal enrichment.

Instead, the authors propose that the bulk of enrichment in the observed EMP stars likely originates from lower-mass core-collapse supernovae (CCSNe) and/or hypernovae. The study suggests that if PISNe did occur, they were rare events. The results reinforce the need for alternative enrichment channels to explain the chemical composition of the earliest stellar generations, while highlighting that the absence of PISN signatures in EMP stars is a robust constraint on the frequency of these massive explosions in the early Universe.