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Mass and Spin Growth of Very Massive Stars in Star Clusters Potentially Associated with Little Red Dots

Using gravitational N-body simulations, this study demonstrates that very massive stars in dense star clusters can grow to masses of $10^3$ -- $10^4\,M_\odot$ and acquire extreme spins, potentially collapsing into rapidly rotating intermediate-mass black holes with massive accretion disks that could explain the gravitational wave events GW190521 and GW231123.

Original authors: Ataru Tanikawa, Masaru Shibata, Kunihito Ioka

Published 2026-06-02

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CC BY 4.0

Original authors: Ataru Tanikawa, Masaru Shibata, Kunihito Ioka

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 a cosmic dance floor so crowded that stars are bumping into each other constantly. This is the setting of a new study by Ataru Tanikawa and colleagues, who used supercomputer simulations to see what happens when stars in these ultra-dense clusters crash into one another.

Here is the story of their findings, broken down into simple concepts:

The "Little Red Dots" Mystery

Astronomers recently spotted strange, tiny, red objects in the early universe called "Little Red Dots." No one is quite sure what they are. Some think they are massive black holes wrapped in gas; others think they are just incredibly crowded groups of stars. This paper asks: Could these be the result of stars smashing together to form a "super-star"?

The Cosmic Pinball Machine

The researchers simulated four different types of crowded star clusters. They watched what happened over a million years.

The Setup: In these clusters, the biggest stars naturally sink to the center, like heavy bowling balls rolling to the bottom of a bowl.
The Crash: Because the crowd is so tight, these heavy stars start crashing into each other. Instead of bouncing off, they stick together (like two blobs of wet clay merging).
The Result: This creates a runaway effect. One star gets bigger, then bigger, then massively bigger. The simulations showed these "Very Massive Stars" (VMS) could grow to be 1,000 to 10,000 times heavier than our Sun.

The "Puffy" Secret Sauce

The most exciting part of the paper is a new twist they added to the simulation: The Bloated State.

Usually, when stars crash, they might shrink or stay normal. But the researchers realized that after a crash, a star might get "puffy" and expand, like a balloon being blown up.

The Analogy: Imagine a normal star is a solid marble. A "bloated" star is like that same marble wrapped in a giant, fluffy pillow.
Why it matters: A fluffy pillow is much easier to hit than a marble. Because the star is so big and puffy, it catches other stars much more easily.
The Outcome: When the researchers let the stars stay "puffy" (specifically if they are eating other stars fast enough), the final super-star ended up three times heavier than it would have been if it stayed compact.

The Cosmic Top (Spin)

There is another surprising result: These super-stars spin incredibly fast.

The Analogy: Think of a figure skater. When they pull their arms in, they spin faster. Now, imagine a skater who keeps getting hit by other skaters running into them from the side. Every time someone bumps into them, they spin faster and faster.
The Finding: Because these stars are formed by crashing into each other, they inherit all that spinning energy. The study found these stars spin so fast that if they collapsed into black holes, they would be the most extreme, high-speed spinners imaginable.

What Happens Next?

The paper suggests that when these massive, super-spinning stars finally die, they don't just fade away quietly.

They likely collapse into a Black Hole surrounded by a massive, swirling disk of material.
This system could trigger a giant explosion and send out a burst of gravitational waves (ripples in space-time).
The authors suggest this might explain some of the weirdest signals we've seen recently, like the mysterious gravitational wave events named GW190521 and GW231123.

The Caveat (The "Maybe")

The authors are careful to say this is a "best-case scenario." They didn't include every possible way a star could lose mass or spin during a crash. In reality, the stars might not get quite as big or spin quite as fast as the simulation shows. However, even with these limits, the study proves that dense star clusters can create massive, fast-spinning stars that could be the engines behind the "Little Red Dots" we see in the sky.

In short: The universe might be full of cosmic pinball machines where stars smash together, get puffy, spin like crazy tops, and eventually explode into the black holes and ripples we are trying to understand.

Technical Summary: Mass and Spin Growth of Very Massive Stars in Star Clusters Potentially Associated with Little Red Dots

Problem Statement
This study investigates the formation and evolution of Very Massive Stars (VMSs) with initial masses of $\sim 10^2\text{--}10^4 \, M_\odot$ within dense star clusters. These clusters are proposed as progenitors for "Little Red Dots" (LRDs), a population of red, massive, compact objects recently identified by the James Webb Space Telescope (JWST). While LRDs are characterized by broad emission lines, they often lack detectable X-ray or radio emission. Two primary models exist for LRDs: a "BH envelope model" (massive black holes embedded in dense gas) and a "star-only model" (extremely dense stellar systems). In both scenarios, runaway stellar collisions are a likely mechanism for forming VMSs, which may subsequently collapse into Intermediate-Mass Black Holes (IMBHs).

A critical gap in previous numerical simulations is the treatment of the post-collision state of VMSs. Stellar collisions are expected to produce bloated objects that remain on the Hayashi track with expanded radii and low effective temperatures ( $\sim 5000$ K) over the Kelvin-Helmholtz (KH) timescale. This bloated state significantly increases the collision cross-section, potentially facilitating further runaway growth. However, previous studies often assumed higher temperatures or did not fully account for this persistent bloating. Additionally, the spin angular momentum of such VMSs—crucial for determining the nature of their collapse and potential gravitational wave (GW) signatures—has not been comprehensively tracked in the context of these specific cluster conditions.

Methodology
The authors performed gravitational $N$ -body simulations using the PETAR code to model the evolution of four distinct dense star cluster models. The simulations incorporated the following physical and numerical assumptions:

Initial Conditions: Clusters followed a King model ( $W_0=12$ ) with no initial mass segregation or fractal configurations. They were treated as isolated systems with a metallicity of $Z = 2 \times 10^{-3}$ ( $0.1 \, Z_\odot$ ).
Stellar Populations: Two Initial Mass Functions (IMFs) were tested: a standard Kroupa IMF and a "top-heavy" IMF ( $dN/dm \propto m^{-1}$ for $10 \le m/M_\odot \le 150$ ).
Stellar Evolution: The simulations utilized a custom single-star evolution model ("L model") based on 1D HOSHI code results for masses up to $1280 \, M_\odot$ . Stellar winds were modeled using the BSE package prescriptions for hot massive stars and Luminous Blue Variables (LBVs).
Collision Physics: Collisions were treated as perfectly sticky with no mass loss. Upon merging, collision products underwent "rejuvenation," with the degree of rejuvenation dependent on the mass ratio of the progenitors.
Bloated State Implementation: A key methodological innovation was the explicit modeling of the bloated state for collision products ( $M > 150 \, M_\odot$ ). The stellar radius was fixed to maintain an effective temperature of $T_{\text{eff}} = 5000$ K, while luminosity was preserved from the unbloated state. This was applied to two sets of simulations for each cluster model: one including the bloated state ("Y" suffix) and one excluding it ("N" suffix).
Post-Processing Validation: The authors evaluated the self-consistency of the bloated state assumption by checking if the VMS accretion rate exceeded a critical threshold ( $\dot{M}_{\text{crit}} = 3 \times 10^{-2} \, M_\odot \, \text{yr}^{-1}$ ) and if the time between collisions remained shorter than the KH timescale (calculated for both bloated and unbloated radii).

Key Results
The simulations demonstrated that runaway collisions occur in all models, leading to the formation of VMSs with masses exceeding $1000 \, M_\odot$ .

Mass Growth: The inclusion of the bloated state significantly enhanced VMS growth. In the most extreme case (Model M6D7H-Y), the VMS mass reached $\sim 9.5 \times 10^4 \, M_\odot$ (approximately $10\%$ of the total cluster mass) within 1 Myr. This is roughly three times the mass achieved in the unbloated scenario (Model M6D7H-N, $\sim 2.4 \times 10^4 \, M_\odot$ ). Even in models where the accretion rate dropped below the critical threshold after 0.5 Myr, the early bloated phase allowed the VMS to reach masses significantly higher than in non-bloated cases.
Spin Evolution: The dimensionless spin parameter ( $J c / G M^2$ ) of the resulting VMSs was found to be extremely high, exceeding 10 in all cases. This rapid rotation is attributed to the conversion of the orbital angular momentum of colliding stars into the spin angular momentum of the VMS. The authors derived an analytical estimate (Eq. 15) consistent with simulation results, showing that spin scales with the square root of the impact parameter and the number of collisions.
Cluster Dependence: VMS mass ratios were anti-correlated with the initial half-mass relaxation time. Higher initial mass densities, top-heavy IMFs, and lower total star counts (in specific configurations) favored more efficient runaway growth.

Significance and Claims
The paper claims that VMSs formed in dense star clusters resembling LRD progenitors are naturally highly spinning and can reach masses in the range of $10^3\text{--}10^4 \, M_\odot$ (or higher in specific bloated scenarios). The authors posit that such rapidly spinning VMSs, upon collapse, are expected to form a black hole surrounded by a massive accretion disk. This BH-disk system is a plausible engine for:

Electromagnetic Transients: Powering explosions via viscous angular momentum transport and potentially launching relativistic jets (ultra-long gamma-ray bursts).
Gravitational Waves: Emitting burst GWs due to non-axisymmetric instabilities in the massive accretion disk, potentially explaining events like GW190521 and GW231123 which involve remnant masses in the pair-instability mass gap.

The authors explicitly note that their results represent upper limits. The simulations omitted mass and angular momentum loss during collisions, post-main-sequence evolution, and specific VMS wind mass-loss mechanisms. Furthermore, the assumption of rigid rotation may be an overestimate if angular momentum transport (e.g., via magnetic fields) is inefficient. Despite these caveats, the study concludes that accounting for the bloated state is essential for accurately modeling VMS growth in LRD-like environments and that the resulting objects are strong candidates for multi-messenger transients.