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FORGE'd in the Early Universe: The Effect of Protostellar Outflows on Pop III Accretion

Using a high-resolution RMHD simulation, this study demonstrates that protostellar jets launched from a magnetized, rotating disk regulate accretion and limit the final mass of a Population III star to approximately 27 solar masses, thereby shaping the initial mass function and feedback processes in the early Universe.

Original authors: Yasmine J. Meziani, Philip F. Hopkins, Michael Y. Grudić, Shivan Khullar, Claude-André Faucher-Giguère, Pratik J. Gandhi

Published 2026-02-04

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CC BY 4.0

Original authors: Yasmine J. Meziani, Philip F. Hopkins, Michael Y. Grudić, Shivan Khullar, Claude-André Faucher-Giguère, Pratik J. Gandhi

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 universe as a giant, dark construction site just after the Big Bang. There are no bricks (metals) yet, just pure, raw gas. In this paper, scientists used a super-powerful computer simulation to watch how the very first stars (called "Population III" stars) were born in this metal-free environment.

Here is the story of what they found, explained simply:

1. The Cosmic Zoom-In

Think of the simulation like a camera that starts with a wide shot of a whole galaxy and then zooms in, zooms in, and zooms in even more—past the galaxy, past the cloud of gas, right down to the size of our solar system. They focused on one specific spot in the early universe (about 14 billion years ago) to watch a single baby star form.

2. The Star and Its "Swirl"

As the gas collapsed to make the star, it didn't just fall straight in. Because the gas was spinning, it formed a giant, flat, swirling disk around the baby star, like water going down a drain but made of gas.

The Result: The baby star grew quickly, reaching a size about 27 times heavier than our Sun.
The Stability: Usually, when a disk gets too heavy, it breaks apart into chunks (like a cookie crumbling). But in this simulation, the disk stayed smooth and stable. Why? Because the gas was hot and moving chaotically (turbulent), acting like a cushion that kept the disk from breaking apart.

3. The "Firehose" Effect (The Jets)

This is the most exciting part. The scientists found that this baby star didn't just sit there; it started shooting out powerful beams of gas, like a high-pressure firehose, from its poles. These are called protostellar jets.

Why did they happen? The gas had a tiny bit of magnetic field (like a faint magnet). As the gas spun and squished, this magnetic field got stronger and stronger. Once it got strong enough, it acted like a nozzle, squeezing the gas and shooting it out in tight beams.
The Analogy: Imagine trying to fill a bucket (the star) with a garden hose (falling gas). But, the bucket has a powerful sprinkler attached to it that shoots water back out. The sprinkler doesn't stop the water from hitting the bucket entirely, but it pushes back hard enough to slow down how fast the bucket fills up.

4. The Great Balancing Act

The paper argues that these "firehose" jets are the reason the star stopped growing at 27 solar masses instead of becoming a giant monster star (which some older theories predicted).

The Mechanism: The jets carry a lot of momentum. When they hit the incoming gas cloud, they create a "traffic jam" or a shockwave that slows down the gas trying to fall in.
The Result: The star essentially regulates its own appetite. The jets push back against the food supply, ensuring the star doesn't eat too much too fast.

5. The Final Picture

By the end of the simulation (which covered about 31,000 years of star life), the star had:

Grown to about 27 times the mass of our Sun.
Developed a stable, spinning disk of gas around it.
Been "fed" and "regulated" by the magnetic jets shooting out from its poles.

In a nutshell: The first stars weren't just passive balls of gas growing until they ran out of fuel. They were active participants in their own birth, using magnetic "firehoses" to push back against the universe, controlling their own size and keeping their surrounding disks from breaking apart. This helps explain why the first stars might not have been as massive as we once thought.

Technical Summary: FORGE'd in FIRE Simulation of a Pop. III (Proto)star

Problem Statement
The formation and evolution of the first generation of stars (Population III) remain poorly constrained due to the lack of direct observations and the immense dynamic range required to connect cosmological structure formation to detailed protostellar physics. Previous theoretical models often relied on idealized initial conditions, omitted critical physics (such as magnetic fields, radiation, and jets), or failed to produce realistic Initial Mass Functions (IMF) and stellar multiplicities observed in metal-rich environments. A specific debate exists regarding whether Pop. III stars can launch protostellar jets, a process dependent on the amplification of trace magnetic fields and the presence of a rotating, magnetized circumstellar disk.

Methodology
This study presents a cosmological "zoom-in" radiation magneto-hydrodynamic (RMHD) simulation using the FORGE'd in FIRE framework. The simulation tracks the formation and evolution of a single, metal-free Pop. III (proto)star at redshift $z \sim 14$ within a fully cosmological context.

Simulation Framework: The code GIZMO is used, employing the meshless finite-mass (MFM) method to solve coupled equations of gravity, magneto-hydrodynamics (MHD), and radiation transport.
Physics Included: The simulation incorporates the FIRE-3 physics model, including:
- Radiation: Multi-frequency transport (photo-ionizing, Lyman-Werner, etc.) coupled self-consistently with gas and dust.
- Thermo-chemistry: Extended to temperatures of $1\text{--}10^{10}$ K and densities of $10^{-8}\text{--}10^{24}$ cm $^{-3}$ , tracking H, He, HD, and dust abundances.
- Magnetic Fields: Initialized with trace cosmological seed fields ( $\sim 10^{-15}$ G) that amplify self-consistently. Non-ideal MHD effects (Ohmic resistivity, Hall effect, ambipolar diffusion) are neglected, justified by post-processing timescale comparisons showing they are negligible compared to dynamical timescales in metal-free gas.
- Protostellar Evolution: Sink particles represent (proto)stars, evolving through accretion, main-sequence tracks, and feedback mechanisms.
Jet and Wind Modeling: Protostellar jets are modeled following Cunningham et al., diverting a fraction ( $f_W = 0.3$ ) of accreted mass into collimated bipolar outflows launched at a fraction ( $f_K = 0.3$ ) of the Keplerian velocity. Stellar winds are neglected for metal-free stars as they scale with metallicity.
Resolution: The simulation utilizes "hyper-refinement," resolving gas cells down to $\sim 10^{-3} M_\odot$ and spatial scales of $\sim 10^{-4}$ pc ( $< 100$ au) near the (proto)star, while maintaining cosmological context from $z \sim 100$ .

Key Results

Stellar Growth and Mass:
- The (proto)star grows from an initial accretion rate of $\sim 5 \times 10^{-3} M_\odot \text{yr}^{-1}$ to a final mass of $\sim 27 M_\odot$ over 31,000 years.
- The growth rate stabilizes as the star enters the "Shell D burning" phase. The final mass is regulated by feedback (jets and radiation) rather than the depletion of the surrounding reservoir.
- At the end of the simulation, the star has a radius of $\sim 10 R_\odot$ , an effective temperature of $\sim 3.5 \times 10^4$ K, and a luminosity of $\sim 1.3 \times 10^5 L_\odot$ . The Kelvin-Helmholtz timescale ( $t_{KH}$ ) becomes shorter than the accretion timescale ( $t_{acc}$ ), indicating the star will reach the main sequence before accreting significantly more mass.
Circumstellar Disk:
- A rotationally supported disk forms, extending to $\sim 0.01$ pc ( $\sim 2000$ au).
- The disk remains gravitationally stable throughout the simulation, with a Toomre $Q$ parameter consistently $>> 1$ .
- Stability is maintained by a combination of thermal support (in the inner regions, $T \sim 10^4$ K) and turbulent support (in outer regions, $R > 1000$ au).
- The surface density profile transitions from $\Sigma \propto R^{-1}$ in the outer disk to an $\alpha$ -disk profile in the inner regions, with a sharp rise in density at $\sim 20$ au.
Protostellar Jets and Outflows:
- Jet Launching: Jets form because the magnetic mass-to-flux ratio ( $\mu$ ) falls within the regime ( $\mu \sim 10^{-1} \text{--} 10^1$ ) that permits jet launching, as defined by Machida and Doi. This occurs despite the use of trace seed magnetic fields.
- Dynamics: Jets propagate out to $\sim 1$ pc, colliding with infalling gas to form termination shocks.
- Regulation: The jets drive substantial momentum, sweeping up gas and reducing the net inward accretion rate by roughly an order of magnitude at large radii. This momentum-driven feedback regulates the final stellar mass.
- The outflow rate peaks at $\sim 10^{-3} M_\odot \text{yr}^{-1}$ within the first 1,000 years before declining, while the inflow rate stabilizes around $3\text{--}5 \times 10^{-4} M_\odot \text{yr}^{-1}$ .
Chemical and Thermal Structure:
- In the inner disk, high temperatures ( $T \sim 10^4$ K) suppress molecular hydrogen ( $H_2$ ) in favor of ionized hydrogen, shifting cooling mechanisms from $H_2$ to Lyman cooling.
- The disk remains optically thin to its dominant cooling radiation, allowing IR photons to escape efficiently.

Significance and Claims
The paper claims to present the first application of the FORGE'd in FIRE framework to an individually resolved Pop. III (proto)star within a fully cosmological zoom-in setup. The primary significance lies in demonstrating that:

Jets are viable in Pop. III formation: Even with trace cosmological magnetic fields, the conditions for strong jet launching are met, challenging previous assumptions that jets might be absent in metal-free environments.
Feedback regulates mass: Protostellar jets play a critical role in shaping the final mass of Pop. III stars by regulating accretion through momentum-driven outflows, rather than the star simply consuming its entire reservoir.
Disk Stability: The formation of a stable, non-fragmenting circumstellar disk is possible in this regime, maintained by thermal and turbulent support.

These results provide a more physically complete picture of the earliest star-forming regions, offering insights into the Pop. III Initial Mass Function (IMF) and feedback processes. The authors note that future work will expand this to a group of Pop. III stars to fully characterize the predicted IMF and stellar multiplicity.

1. The Cosmic Zoom-In

2. The Star and Its "Swirl"

3. The "Firehose" Effect (The Jets)

4. The Great Balancing Act

5. The Final Picture

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