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Star cluster formation from turbulent clumps. V. Stellar clustering around massive stars

This paper utilizes N-body simulations within the Turbulent Clump Core Accretion paradigm to demonstrate that massive stars rapidly acquire high-order multiplicity and local density enhancements through dynamical processes, with secondary multiplicity decreasing in more massive clusters due to higher velocity dispersions, while noting that these models produce shallower density profiles than competitive accretion scenarios and offer a better fit for the AFGL 5180 system.

Original authors: Aayush Gautam, Juan P. Farias, Jonathan C. Tan

Published 2026-05-01

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CC BY 4.0

Original authors: Aayush Gautam, Juan P. Farias, Jonathan C. Tan

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, chaotic construction site where stars are being built. For a long time, astronomers have debated how the "heavyweights" of this site—the massive stars (those at least eight times heavier than our Sun)—get their construction crews. Do they start building alone and then hire helpers later? Or do they start surrounded by a whole team of smaller workers from day one?

This paper, written by Aayush Gautam and colleagues, acts like a detective story, using computer simulations to solve this mystery. Here is the breakdown of their findings in everyday terms.

The Two Theories: The "Lone Wolf" vs. The "Crowded Room"

The scientists are testing two main ideas about how massive stars form:

The "Lone Wolf" Theory (Turbulent Core Accretion): Imagine a massive star being born in a relatively quiet, isolated room. It starts alone. Later, as the room fills up with other stars, it might accidentally bump into some smaller stars and grab them as "friends" (companions) through gravity.
The "Crowded Room" Theory (Competitive Accretion): Imagine a massive star being born in the middle of a mosh pit. It is surrounded by a swarm of smaller stars from the very beginning, all fighting for the same building materials (gas).

The key difference is when the massive star gets its companions. Does it start alone and gather them later (dynamically), or does it start with them already there (primordially)?

The Experiment: A Cosmic Dance Floor

To figure this out, the team ran thousands of computer simulations (like a high-tech video game) of star clusters forming. They created virtual "clouds" of gas and let gravity do its work.

The Setup: They started with clouds of different sizes and densities. They made sure that 50% of the stars started as pairs (binaries), but no one started as a trio or a group of four. If a massive star ended up with three or more friends, it had to have "picked them up" later through cosmic dance moves (dynamical interactions).
The Goal: They watched to see if massive stars in the center of the cluster could "catch" enough smaller stars to form complex families (triples, quadruples, etc.) just by being in a crowded, busy environment.

The Findings: Location, Location, Velocity

The simulations revealed some clear patterns about how these stellar families form:

1. The Center is King
Massive stars located in the center of the cluster are like popular kids at a busy party. They are surrounded by so many other stars that they easily grab onto companions. They quickly form groups of three or more.
In contrast, massive stars that get kicked out of the cluster (ejected stars) are like the kids who left the party early. They are mostly alone or just have one partner. They don't have the crowd necessary to gather more friends.

2. The Speed Matters
The "dance floor" speed (velocity dispersion) is crucial.

Slow Dance: In clusters where stars are moving slowly, gravity has an easier time grabbing passing stars. Massive stars here gather many companions.
Fast Dance: In clusters where stars are zooming around fast, it's harder to catch them. The massive stars end up with fewer friends.

3. The Density Factor
The denser the crowd, the more friends a massive star can gather. However, if the cluster is too massive and the stars are moving too fast, the "grabbing" becomes difficult.

The Showdown: Simulation vs. Reality

The team compared their "Lone Wolf" simulations against real observations of a star-forming region called AFGL 5180. They also compared their results to a different set of simulations that followed the "Crowded Room" theory.

The Shape of the Crowd: When they looked at how the density of stars changed as you moved away from the massive star, their "Lone Wolf" model (TCCA) produced a flatter, more gradual slope. The "Crowded Room" model (Competitive Accretion) produced a steep drop-off, meaning the stars were packed tightly right next to the massive star but thinned out very quickly.
The Match: The real observations of AFGL 5180 looked more like the flatter slope of the "Lone Wolf" model. This suggests that in this specific region, massive stars might have started relatively isolated and gathered their companions later as the cluster formed around them.
The Caveat: However, the "Crowded Room" model did a better job matching the very center (the innermost bin) of the observation. This suggests the truth might be a mix of both: maybe some companions form early, and others are gathered later.

The Missing Piece: The "Close Triple" Mystery

The team also looked at the specific types of families formed.

What they found: Their simulations were great at creating close pairs (binaries) and distant groups.
What they missed: They found very few close triple systems (three stars huddled very tightly together).
The Reality Check: Real observations of massive stars (from the SMASH+ survey) show that close triple systems do exist.
The Conclusion: Since the computer simulations (which only allowed stars to grab each other later) couldn't create these tight triples, the authors conclude that these tight triple systems must have been formed at the very beginning (primordially), likely when the gas cloud first broke apart. They couldn't be "picked up" later; they had to be born that way.

The Bottom Line

This paper tells us that massive stars are social creatures, but their social life depends heavily on where they are and how fast the crowd is moving.

If they are in the center of a slow-moving, dense cluster, they gather many friends.
If they are in a fast-moving or sparse environment, they stay mostly alone.
While they can gather many friends over time, the very tightest, most complex families (close triples) likely need to be born that way, not built later.

The authors suggest that to fully solve the mystery of massive star formation, we need more observations and even more sophisticated computer models that can handle both the gas and the stars perfectly together. But for now, the "Lone Wolf" theory with some later socializing seems to fit the AFGL 5180 data better than the "Crowded Room" theory.

1. Problem Statement

Massive stars ( $>8 M_\odot$ ) exhibit exceptionally high multiplicity rates, with approximately 60% existing in triple or higher-order multiple systems. A critical open question in astrophysics is the origin of this multiplicity:

Primary Multiplicity: Formed during the initial collapse and accretion phase (e.g., via core or disk fragmentation).
Secondary Multiplicity: Acquired later through dynamical interactions within dense star clusters.

Distinguishing between these mechanisms is essential for validating massive star formation theories, specifically Turbulent Core Accretion (TCA) versus Competitive Accretion. TCA suggests massive stars form in relative isolation and acquire companions dynamically, while Competitive Accretion predicts massive stars form surrounded by a dense swarm of low-mass companions from the outset. Furthermore, the role of the local cluster environment (density, velocity dispersion, formation timescale) in shaping these multiplicity levels remains poorly quantified.

2. Methodology

The authors utilized a suite of $N$ -body simulations to model the gradual formation of star clusters within turbulent clumps in Giant Molecular Clouds (GMCs).

Simulation Framework: The study employs the Turbulent Clump Core Accretion (TCCA) paradigm (based on Farias et al. 2019).
- Gas Treatment: The parent gas cloud is modeled using a semi-analytic potential representing a turbulent, magnetized clump. Gas is gradually dissipated as stars form.
- Star Formation: Massive stars are formed stochastically (randomly) within the cluster, approximating TCA where massive stars do not preferentially form in high-density regions.
- Initial Conditions: The simulations include a 50% primordial binary fraction but zero primordial triples or higher-order multiples. Any systems with $\ge3$ stars must form dynamically.
Parameter Space: The study varies three key environmental parameters:
1. Clump Mass ( $M_{cl}$ ): 300, 3,000, and 30,000 $M_\odot$ .
2. Cloud Surface Density ( $\Sigma_{cloud}$ ): Low (0.1 g cm $^{-2}$ ) and High (1.0 g cm $^{-2}$ ).
3. Star Formation Efficiency per Free-fall Time ( $\epsilon_{ff}$ ): Ranging from 0.01 to 1.0, controlling the formation timescale ( $t_*$ ).
Analysis Techniques:
- Bound System Identification: A recursive algorithm identifies bound companions by iteratively replacing stars with their center of mass and checking tidal stability against perturbers (using a tidal force criterion).
- Classification: Massive stars are categorized as Central (within 20% of the half-mass radius), Offset (20–100% of half-mass radius), or Ejected (unbound).
- Metrics:
  - $N_{bound}$ : Number of bound companions.
  - THF (Triple/Higher-order Fraction): Fraction of massive stars in systems with $\ge3$ members.
  - Projected Stellar Density ( $N_*$ ): Radial profiles of stellar surface density around massive stars.
- Comparisons: Results are compared against STARFORGE simulations (which model Competitive Accretion) and observational data from AFGL 5180 and G19.88-0.53.

3. Key Contributions

Quantification of Secondary Multiplicity: The paper provides benchmark statistics on how massive stars dynamically acquire companions in forming clusters, specifically tracking the evolution of Triple/Higher-order Fractions (THF) over time.
Environmental Dependence: It establishes a clear link between the local cluster environment (velocity dispersion and stellar density) and the efficiency of dynamical capture.
Model Discrimination: It offers a method to distinguish between TCA and Competitive Accretion models by analyzing the slope of stellar density profiles around massive stars.
Observational Benchmarking: The study bridges the gap between theoretical $N$ -body models and high-resolution observations of young massive stars, identifying specific regimes where TCCA models succeed or fail.

4. Key Results

A. Multiplicity and Environment

Location Matters: Massive stars in the central regions of clusters gather significantly more companions than those in the periphery or ejected stars. Ejected stars are predominantly single or binary.
Velocity Dispersion ( $\sigma_S$ ): There is an inverse relationship between velocity dispersion and multiplicity. Clusters with lower velocity dispersion (typically smaller $M_{cl}$ ) allow massive stars to capture more companions due to enhanced gravitational focusing.
Stellar Density ( $n_{S,b}$ ): Higher local stellar densities generally promote higher multiplicity, though the relationship is non-monotonic; intermediate densities often maximize $N_{bound}$ .
Formation Timescale: The number of companions evolves with time. $N_{bound}$ typically rises during the gas-embedded phase and declines or flattens after gas expulsion and cluster expansion.

B. Triple/Higher-order Fraction (THF)

THF increases rapidly in the first few Myrs in small, dense clusters (e.g., $M_{cl}=300 M_\odot$ ) but remains low in massive clusters ( $M_{cl}=30,000 M_\odot$ ) due to high velocity dispersions preventing stable capture.
In the TCCA models, triples form dynamically; no primordial triples were input.

**C. Stellar Density Profiles ( $N_*$ )**

TCCA vs. STARFORGE:
- TCCA (This work): Profiles are relatively flat out to $\sim0.25$ pc. The density builds up as the cluster forms and declines as the cluster expands.
- STARFORGE (Competitive Accretion): Profiles are steeper, dropping off quickly beyond $r > 0.1$ pc. This reflects the primordial presence of many low-mass companions close to the massive star.
Observational Comparison (AFGL 5180):
- The normalization (inner density) of AFGL 5180 matches STARFORGE models better.
- The radial slope (flatness) of AFGL 5180 matches the TCCA models better.
- This suggests a hybrid scenario: small-scale structure may be primordial (Competitive Accretion-like), while large-scale structure reflects dynamical mixing (TCCA-like).

D. Companion Properties

Separations: Simulated companions show a drop-off in equal-mass companions at large separations ( $>1000$ au), whereas observations (SMASH+ survey) show a drop-off at $\sim100$ au. This suggests dynamical stripping of wide companions in the simulations or that observed field stars have undergone more stripping.
Close Triples: The simulations lack close triple companions ( $<10$ au), which are observed in the SMASH+ survey. Since the TCCA models have no primordial triples, the authors conclude that close triples must form primordially (via core or disk fragmentation) rather than dynamically.

5. Significance

This paper provides a crucial step in understanding the "birth environment" of massive stars. By isolating the effects of dynamical processing in a controlled $N$ -body framework, the authors demonstrate that:

Dynamical capture is efficient in low-velocity, high-density environments, creating significant secondary multiplicity even without primordial triples.
Stellar density profiles serve as a powerful diagnostic tool to distinguish between formation theories, with TCCA predicting flatter profiles than Competitive Accretion.
Primordial vs. Dynamical: While dynamical processes explain many binaries and wide triples, the presence of close triple systems in observations implies that primordial formation channels (fragmentation) are necessary to explain the full population of massive star multiplicity.

The study highlights the need for future simulations that couple hydrodynamics with $N$ -body dynamics and include primordial triples to fully reproduce the observed multiplicity statistics of massive stars.