🔭 astrophysics

Impact of initial mass function on the chemical evolution of high-redshift galaxies

Using the semi-analytical code \textsc{a-sloth}, this study demonstrates that an initial mass function with an upper mass limit of at least 200 solar masses is required to reproduce observed high-redshift galaxy properties, highlighting the critical role of pair-instability supernovae from very massive stars in the chemical evolution and star formation history of galaxies at $z \gtrsim 4$ .

Original authors: Boyuan Liu, Michela Mapelli, Volker Bromm, Ralf S. Klessen, Lumen Boco, Tilman Hartwig, Simon C. O. Glover, Veronika Lipatova, Guglielmo Costa, Marco Dall'Amico, Giuliano Iorio, Kendall Shepherd, Ales

Published 2026-04-08

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CC BY 4.0

Original authors: Boyuan Liu, Michela Mapelli, Volker Bromm, Ralf S. Klessen, Lumen Boco, Tilman Hartwig, Simon C. O. Glover, Veronika Lipatova, Guglielmo Costa, Marco Dall'Amico, Giuliano Iorio, Kendall Shepherd, Alessandro Bressan

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 early universe as a giant, chaotic construction site. Billions of years ago, right after the Big Bang, the first galaxies were being built from clouds of gas and dust. For a long time, astronomers thought they knew the rules of this construction: stars form, they live, they die in explosions, and they scatter heavy elements (like gold, oxygen, and iron) into space to build the next generation of stars and planets.

But recently, the James Webb Space Telescope (JWST) has started taking pictures of these ancient construction sites, and the blueprints don't quite match what we expected. The galaxies look "too heavy" in terms of their chemical makeup, and they seem to be forming stars in ways that defy our old rules.

This paper is like a team of cosmic architects running a massive simulation to figure out what's missing from the blueprint. Here is the story of what they found, explained simply.

The Mystery: The "Heavy" Galaxies

The astronomers noticed a strange pattern in the early universe. There is a relationship between three things:

How big a galaxy is (its Mass).
How fast it is building new stars (Star Formation Rate).
How "polluted" it is with heavy elements (Metallicity).

In the nearby universe (where we live), these three things dance together in a predictable rhythm. But in the early universe (around 13 billion years ago), the dance changed. The galaxies were surprisingly rich in heavy elements, even though they were young. It's like walking into a brand-new house and finding it already filled with antique furniture and gold-plated fixtures. Where did all that "furniture" (heavy elements) come from so quickly?

The Suspect: The "Initial Mass Function" (IMF)

To solve this, the team looked at the Initial Mass Function (IMF). Think of the IMF as the "recipe" for how stars are born. It tells us how many small stars (like our Sun) versus how many giant stars are created in a single batch.

For decades, we assumed the recipe was universal: you get a few giants and a lot of small stars, no matter where or when you are in the universe. But the JWST data suggested this recipe might be wrong for the early universe. Maybe the early universe was baking a lot more "giant cakes" (massive stars) than we thought.

The Experiment: A Cosmic Kitchen Simulation

The authors used a super-computer program called a-sloth (yes, named after the slow-moving animal, but it's actually a fast and powerful tool for galaxy modeling). They ran 165 different simulations, tweaking the "recipe" to see what would happen.

They asked: What if the early universe allowed for stars that are incredibly massive—up to 600 times the mass of our Sun?

In our current universe, stars usually top out around 100-150 solar masses. But in the early, hot, and dense universe, maybe stars could grow much bigger.

The Big Discovery: The "Pair-Instability" Supernova

The simulation revealed a smoking gun. To match the JWST observations, the early universe needed a specific type of star: Super-Massive Stars (over 200 times the mass of the Sun).

Here is why these giants are special:

Normal Stars: When a normal massive star dies, it explodes as a supernova, scattering some heavy elements.
Super-Massive Stars: When a star over 200 solar masses dies, it doesn't just explode; it undergoes a Pair-Instability Supernova (PISN). Imagine a star so heavy that its own gravity creates a pressure cooker effect. It becomes so unstable that it blows itself apart completely, with zero remnants left behind.

This explosion is a "chemical fireworks display." It spews out a massive amount of heavy elements into the galaxy—far more than a normal star could ever produce.

The Analogy:
Imagine you are trying to fill a swimming pool with water.

Old Theory: You use a garden hose (normal stars). It takes a long time to fill the pool.
New Discovery: The early universe had a fire hose (super-massive stars) that blasted water into the pool instantly. This explains why the "pool" (the galaxy) was so full of "water" (heavy elements) so quickly.

The Result: A New Cosmic Recipe

The team found that if they assumed the early universe had a "top-heavy" recipe (lots of stars over 200 solar masses), their simulations perfectly matched the JWST data.

The Sweet Spot: The best fit was a universe where the largest stars were about 200 to 250 times the mass of the Sun.
The Consequence: These giants died young and exploded violently, enriching the universe with metals much faster than we previously thought possible.

Why Does This Matter?

This isn't just about filling in a gap in a textbook. This discovery changes our understanding of the early universe in three big ways:

Reionization: Those faint, tiny galaxies that we can't see yet might be the ones actually lighting up the early universe, thanks to these massive stars.
Gravitational Waves: When these massive stars die, they leave behind black holes. If they were in pairs, they would crash into each other, creating gravitational waves (ripples in space-time). This paper suggests there should be many more of these collisions happening in the early universe than we thought.
The "Excess" of Bright Galaxies: It helps explain why JWST is seeing so many bright, blue galaxies that shouldn't exist according to our old models. They are bright because they are full of these massive, energetic stars.

The Bottom Line

The early universe wasn't just a quiet place where small stars formed slowly. It was a chaotic, high-energy factory churning out giant, short-lived stars that exploded like cosmic firecrackers, seeding the universe with the ingredients for life much faster than we ever imagined.

The "recipe" for the universe changed over time. In the beginning, it was heavy on the giants; today, it's mostly small stars. This paper proves that to understand our cosmic origins, we have to rewrite the recipe for the very first stars.

1. Problem Statement

Recent observations by the James Webb Space Telescope (JWST) have revealed a specific scaling relation between stellar mass ( $M_*$ ), gas-phase metallicity ( $Z$ ), and star formation rate (SFR) in galaxies up to redshift $z \sim 8$ . However, this relation appears to break down at higher redshifts ( $z > 8$ ), where galaxies are systematically more metal-poor.

The Core Question: What physical mechanisms drive the chemical enrichment and star formation histories of high-redshift galaxies? Specifically, does the Initial Mass Function (IMF) play a critical role, particularly regarding the presence of very massive stars ( $>100 M_\odot$ ) and Pair-Instability Supernovae (PISNe)?
The Challenge: Standard cosmological models often assume a universal IMF (e.g., Kroupa or Chabrier) with an upper mass limit of $\sim 100 M_\odot$ . It is unclear if this assumption holds for the extreme environments of the early Universe ( $z \gtrsim 4$ ) and whether it can reproduce the observed metallicity-SFR relations and the Cosmic Star Formation History (CSFH).

2. Methodology

The authors utilized the semi-analytical galaxy evolution code a-sloth coupled with high-resolution cosmological merger trees to simulate galaxy evolution.

Simulation Setup:
- Cosmology: Based on a high-resolution $\Lambda$ CDM simulation (Ishiyama et al. 2016) with a box size of $\sim 1750$ cMpc $^3$ and a dark matter resolution of $5000 h^{-1} M_\odot$ .
- Redshift Range: $z \sim 4.5 - 30$ , focusing on $z \sim 4 - 10$ .
- Parameter Space: 165 simulations were run varying three key parameters:
  1. $m_{max}$ : The upper mass limit of the Pop II IMF (ranging from $100$ to $600 M_\odot$ ).
  2. $\alpha_{out}$ : The slope of the galactic outflow efficiency vs. halo mass relation.
  3. $M_{out0}$ : The normalization mass scale for outflows.
- IMF Assumption: A Kroupa-like IMF with a fixed low-mass slope and a varying high-mass end slope ( $\alpha_{II} = 2.3$ ) and upper limit ( $m_{max}$ ). Pop III stars were modeled with a fixed top-heavy IMF.
Key Model Updates (vs. previous versions):
- Star Formation: Updated the characteristic radius ( $R_*$ ) for star formation to better match observed galaxy sizes ( $R_{50}$ ) rather than halo virial radii, reducing $R_*$ by a factor of $\sim 4$ .
- Stellar Feedback & Yields: Implemented a comprehensive grid of PARSEC stellar evolution tracks covering metallicities $Z \sim 10^{-11} - 0.03$ $Z \sim 1 0^{- 11} - 0.03$ and masses $2 - 600 M_\odot$ $2 - 600 M_{⊙}$ .
  - Includes metal yields from stellar winds, core-collapse SNe, pulsational pair-instability SNe (PPISNe), pair-instability SNe (PISNe), and Type Ia SNe.
  - Explicitly models the metallicity dependence of yields and SN energies.
- Outflows: Modeled galactic outflows driven by SN energy, with efficiency dependent on halo binding energy.
Observational Constraints:
The models were constrained by a likelihood analysis against three main observational datasets:
1. Cosmic Star Formation History (CSFH): SFR density and stellar mass density from $z \sim 5 - 16$ (JWST, HST, ALMA).
2. Mass-Metallicity-SFR Relation (MZSFR): The invariant relation at $z \sim 4-8$ and its breakdown at $z > 8$ (JWST spectroscopy).
3. Stellar-Halo Mass Relation (SHMR): Derived from semi-empirical abundance matching.

3. Key Contributions

Updated Stellar Physics: The paper introduces a significantly more detailed treatment of stellar feedback, incorporating metal yields from stellar winds and a full spectrum of SN types (including PISNe) across a wide metallicity range, which was previously simplified in semi-analytical models.
Systematic Parameter Scan: It performs a rigorous grid search over IMF upper mass limits and outflow parameters to jointly constrain the chemical evolution and star formation history of high- $z$ galaxies.
Resolution of the "Excess" UV Problem: It provides a physical explanation for the high UV luminosity and specific chemical signatures of early galaxies by linking them to a top-heavy IMF and enhanced PISN yields.

4. Key Results

A. The Necessity of Very Massive Stars ( $m_{max} \gtrsim 200 M_\odot$ )

Metallicity Constraint: Models with a standard upper mass limit ( $m_{max} = 100 M_\odot$ ) fail to reproduce the observed MZSFR relation, predicting metallicities that are too low (or requiring unrealistically weak outflows).
Best-Fit Model: The only models that simultaneously reproduce the CSFH and the MZSFR relation at $z \gtrsim 4$ require an IMF upper mass limit of $m_{max} \gtrsim 200 M_\odot$ .
Mechanism: The enhanced metal yields required to match observations come primarily from Pair-Instability Supernovae (PISNe). Stars in the mass range $140 - 260 M_\odot$ (and up to $600 M_\odot$ in the models) produce significantly higher metal yields per unit stellar mass compared to standard core-collapse SNe.
Best-Fit Parameters: The global best-fit model has:
- $m_{max} = 250 M_\odot$
- $\alpha_{out} = 0$ (outflow efficiency independent of halo mass)
- $M_{out0} = 3 \times 10^9 M_\odot$

B. Chemical Evolution and Scaling Relations

Invariant MZSFR: The model successfully reproduces the invariant MZSFR relation at $z \sim 4-8$ .
Breakdown at High- $z$ : The model naturally reproduces the observed "breakdown" of the relation at $z > 8$ , where galaxies become more metal-poor due to strong pristine gas inflows diluting the metal content, a feature driven by the specific balance of metal production (PISNe) and dilution.
FMR Slope: The Fundamental Metallicity Relation (FMR) slope in the simulation matches observations, confirming that the anti-correlation between SFR and metallicity holds up to $z \sim 8$ .

C. Implications for the Faint Galaxy Population

Faint Galaxies Dominate SFRD: While JWST observes bright galaxies ( $M_{UV} \lesssim -17$ $M_{U V} ≲ - 17$ ), the simulation predicts that faint, low-mass galaxies ( $M_{UV} \gtrsim -17$ $M_{U V} ≳ - 17$ ) dominate the total Cosmic Star Formation Rate Density (SFRD).
- At $z \gtrsim 12$ , faint galaxies contribute $>90\%$ of the total SFRD.
- At $z \sim 5-7$ , they still contribute $30-50\%$ .
Reionization: These faint, metal-poor galaxies are likely the primary drivers of cosmic reionization.

D. Transient Rates and Gravitational Waves

PISN Rates: The high $m_{max}$ implies a high rate of PISNe. The predicted all-sky rate peaks at $z \sim 5$ with $\sim 10$ events yr $^{-1}$ deg $^{-2}$ , dominated by Pop II stars. In contrast, models with $m_{max}=100 M_\odot$ predict a much lower rate dominated by Pop III stars at $z \sim 10-15$ .
Binary Black Holes (BBH): The model predicts a significant population of metal-poor ( $Z \lesssim 0.1 Z_\odot$ ) stars in faint galaxies. Since low metallicity enhances BBH formation efficiency, these faint galaxies are the dominant source of high-redshift BBH mergers, potentially detectable by 3rd-generation gravitational wave detectors.

5. Significance and Conclusion

IMF Evolution: The study provides strong evidence that the IMF in the early Universe ( $z \gtrsim 4$ ) was likely top-heavy, extending to masses of $\sim 250 M_\odot$ or higher, rather than being universal.
Role of PISNe: Pair-Instability Supernovae are identified as a crucial mechanism for early chemical enrichment, resolving the tension between observed metallicities and standard stellar population models.
Future Observations: The results predict a large, unseen population of faint, metal-poor galaxies that are critical for reionization and gravitational wave sources. Future surveys (e.g., Roman Space Telescope, Rubin Observatory, and 3rd-gen GW detectors) are expected to test these predictions.
Caveats: The authors note that results depend on the specific stellar evolution tracks and the assumption of a uniform metal mixing model. However, the requirement for high metal yields ( $M_Z \sim 0.025$ ) is robust across different model variations, strongly pointing toward the existence of very massive stars.

In summary, this paper establishes that very massive stars ( $m_{max} \gtrsim 200 M_\odot$ ) and the resulting PISNe are essential to explain the chemical evolution and star formation history of high-redshift galaxies observed by JWST.