Formation of massive multiple-star systems: early migration and mergers

Abstract: Massive stars are often found in multiple systems, yet how binary-star systems with very close separations ($\lesssim$ au) assemble remains unresolved. We investigate the formation and inward migration of massive-star binaries in Solar-metallicity environments using the star-cluster formation simulation of Chon et al. (2024), which forms a $1200\,M_\odot$ stellar cluster and resolves binaries down to 1 au separation. Our results indicate that stars more massive than $2\,M_{\odot}$ predominantly assemble in binary or triple configurations, in agreement with observations, with member stars forming nearly coevally. In most of these systems, the inner binary hardens by one to three orders of magnitude and reaches a steady-state within the first $0.1\,$Myr. Notably, all binaries whose final separations are below 10 au are hardened with the aid of circumbinary discs, highlighting disc-driven migration as a key to produce tight massive binaries. We further find that binaries form with random inclinations relative to the initial rotation axis of the cloud, and that mutual inclinations in triple systems follow an isotropic distribution, implying that stochastic interactions driven by turbulence and few-body dynamics are crucial during assembly and migration. Finally, stars with $M>2\,M_{\odot}$ often undergo repeated merger events during cluster evolution, yielding extreme mass ratios ($q<0.1$). Some of these products may evolve into compact-object binaries containing a black hole or neutron star, including X-ray binaries and systems detectable by Gaia.

• The paper presents a high-resolution simulation of a 1200 M☉ cluster, detailing how disc-driven migration and mergers assemble tight massive binaries.
• It employs SPH with radiative feedback to analyze formation channels like filament, disc, core fragmentation, and dynamical capture across diverse mass regimes.
• The study finds that disc migration leads to sub-10 au binaries and high merger frequencies, significantly shaping the IMF and stellar multiplicity trends.

Formation Pathways and Early Evolution of Massive Multiple-Star Systems

Introduction

The assembly of massive stellar multiples—particularly close binaries—in star-forming clusters is a central issue in both star and cluster formation and in the astrophysics of compact-object populations. The article "Formation of massive multiple-star systems: early migration and mergers" (2601.06251) presents a comprehensive high-resolution radiation hydrodynamics simulation that follows the formation and evolution of a $1200\,M_\odot$ stellar cluster, probing binary and multiple formation from the protocluster scale ($>10^6$ au) down to separations of 1 au. The work advances understanding of the dominant processes that establish the tightest massive binaries and higher-order multiples, as well as the cluster-scale incidence of mergers.

Simulation Framework and Initial Conditions

The simulation exploits smooth-particle hydrodynamics (SPH) in a solar-metallicity, rotating and turbulent molecular cloud, starting from a Bonnor-Ebert sphere ($M \approx 6300\,M_\odot$; $n = 10^4\,\mathrm{cm}^{-3}$; $T=200\,\mathrm{K}$) seeded with a velocity field following a Larson-type power spectrum. Multi-phase cooling, UV radiation transfer, and radiative feedback from stars above $10\,M_\odot$ are incorporated. The effective spatial and mass resolution—post particle-splitting—reaches 1 au and 0.01 $M_\odot$, permitting the rare tracking of tight binaries and cluster dynamical evolution over $\sim2$ Myr.

Identification of binaries and higher-order systems is performed using an iterative gravitational binding analysis, and binary formation events are classified into four distinct modes: filament fragmentation, disc fragmentation, core (mini-cluster) fragmentation, and dynamical capture.

Multiplicity Formation Mechanisms

The global fragmentation cascade is captured in Figure 1, which demonstrates filamentary fragmentation on parsec scales, dense cores, and subsequently disc and stochastic mini-cluster fragmentation, together with late-time dynamical captures as additional binary pathways.

Figure 1: Snapshot of the base simulation showing the cloud-scale structure and zoom-ins on exemplary binary formation channels (filament, disc, core, and capture modes).

These channels contribute differently across primary mass and final separation:

• Filament Fragmentation: Dominant for low-mass primaries ($M_* \leq 2\,M_\odot$), produces binaries at $a\sim10^3$–$10^4$ au.
• Disc Fragmentation: Predominant in intermediate-mass progenitors ($2$–$8\,M_\odot$), forming binaries at $a\sim10^2$–$10^3$ au.
• Core Fragmentation: Key for massive primaries ($M_* \gtrsim 8\,M_\odot$), in highly turbulent cores.
• Dynamical Capture: Rare for massive stars and tight companions; mainly generates the widest systems ($a > 10^4$ au).

The mass ratio and eccentricity distributions at the end of the simulation strongly correlate with these channels. Filament and core fragmentation produce initial wide and eccentric binaries, while subsequent evolution alters these properties dramatically (cf. Figure 2).

Figure 2: Representative binary formation and evolution in key fragmentation pathways, showing time sequences of gas structure and stellar assembly.

Early Migration and Hardening Pathways

The assembly and orbital evolution of tight binaries are multi-phased. Following initial fragmentation/contraction (on $10^4$–$10^5$ yr timescales), binaries with $a\lesssim10^4$ au typically undergo rapid hardening via:

• Disc-Driven Migration: Interactions with circumstellar and circumbinary discs result in shrinkage by one to three orders of magnitude within 0.1–0.2 Myr, especially for primaries $M_*>2\,M_\odot$ (Figure 3).
• Dynamical Encounters: For massive primaries in crowded environments, multi-body interactions and subsequent mergers become common, often yielding very tight (potential "hidden") pairs.

  Figure 3: Evolution of binary separation, highlighting phases of disc-mediated migration and periods of tertiary-induced perturbations and mergers.

Both initially eccentric orbits and largely unequal mass ratios are dampened/corrected by gas dynamical torques during migration. All binaries attaining separations $<10$ au execute a final circumbinary disc phase; below this scale, further hardening is likely dominated by tidal processes and mass transfer (not resolved here).

The hardening is not monotonic but displays a bifurcated outcome: binaries either retain initial separations (if $a_\text{init}\gtrsim2\times10^4$ au) or shrink by more than a decade in $a$, with little population at intermediate $a_\text{final}/a_\text{init}$ (Figure 4).

Figure 4: Initial versus final separations ($a_\mathrm{final}$ vs. $a_\mathrm{initial}$) for simulated binaries, revealing bimodality in migration outcomes anchored at $\sim2\times10^4$ au.

Merger Statistics and Resultant Mass Function

Mergers are frequent for primaries $M_*\gtrsim2\,M_\odot$; over 15% of stars, and a majority of massive ones, experience at least one merger event. Cluster core interactions often yield extreme mass-ratio (sometimes $q<0.1$) binaries or merger remnants, as in Figure 5, and can create massive rejuvenated objects which will affect interpretations of cluster age and population studies.

Figure 5: Example multi-body evolution culminating in mergers, with resulting binary/triple configuration and ejected stars.

The resultant IMF, including a "merger-corrected" version where unresolved pairs are treated as binaries, remains consistent with the Salpeter slope at $M_*\gtrsim2\,M_\odot$ (Figure 6).

Figure 6: Mass spectrum comparing the raw and merger-corrected distributions, both consistent with the classical Salpeter IMF at high mass.

Multiplicity Fractions, Mass Dependence, and Orbital Architectures

There is an unequivocal increase in binary and tertiary fraction with primary mass (Figure 7). For $M_*\geq 8\,M_\odot$, nearly all systems are multiples; the tertiary fraction for massive stars is also high, reproducing observed trends. However, even after merger corrections, the simulation underestimates the low-mass binary fraction, likely due to the radiative feedback and dust heating suppressing disc fragmentation at low mass.

Figure 7: Binary and tertiary fractions as a function of primary mass; merger-corrected and original data, along with observational constraints.

Both the orientation of binary orbits with respect to the cloud's angular momentum and the mutual inclination of triple hierarchies are consistent with isotropy (Figure 8). This supports a scenario where turbulence and stochastic multi-body interactions erase memory of system-scale angular momentum, in contrast to scenarios predicting alignment via disc fragmentation.

Figure 8: Cumulative distribution functions of binary inclinations, consistent with uniform distributions in $\cos\theta$.

Implications for Stellar Evolution, Observations, and Future Work

The findings yield several impactful and at times bold claims:

• Disc-driven migration is the exclusive mechanism forming $a<10$ au binaries, contrary to any scenario where tidal or dynamical hardening alone could suffice.
• Merger frequency among high/intermediate-mass stars is high—implying observational consequences for rotational velocities, chemical anomalies, and the high incidence of blue stragglers/magnetic O-stars.
• Binaries and triples form nearly coevally, but mergers can occur up to 1 Myr after star formation, affecting age diagnostics for massive stars.
• The simulation robustly reproduces the observed dependence of wide companion fraction on primary mass (Figure 9), and generates extreme-mass-ratio systems.

  Figure 9: Wide binary fraction ($a = 10^2$–$10^4$ au) as a function of mass compared to observations from the field and the Orion Nebula Cluster.

Caveats include the lack of explicit magnetic field evolution, a merger prescription set by finite sink radii (likely underestimating tight binaries), and limitations imposed by radiative feedback models.

Future directions include systematic variation of metallicity, explicit MHD simulations (including non-ideal effects), and campaigns to extend resolution and physical fidelity (especially for sub-au binaries). Observational analogs exist for many empirical findings (e.g., wide binaries, spectroscopic binaries, extreme mass-ratio companions), suggesting upcoming synergy with surveys from Gaia, VLT Interferometry, and JWST in the study of massive star formation, binary black holes, and the IMF at the upper end.

Conclusion

This work provides decisive evidence that disc and circumbinary migration, in combination with cluster dynamics, are the principal means by which massive stars assemble into close binaries and higher-order multiples. The high incidence of mergers, random orientations, and the strong mass dependence of multiplicity rates yield a robust theoretical framework for interpreting cluster, massive star, and compact-object binary demographics. These simulations offer a benchmark for both future theoretical models—including those aiming to link star formation simulations to gravitational-wave source populations—and for observational studies in young clusters and the field.