Binary-Related Formation Mechanisms

Updated 25 September 2025

Binary-related formation mechanisms are the diverse physical processes that create gravitationally bound two-body systems across astronomical and condensed matter settings.
They encompass dynamic interactions such as tidal capture, three-body encounters, and rotational fission, which drive binary formation in planetary, stellar, and small-body systems.
In condensed matter, phase separation and stoichiometric tuning guide binary assembly in colloidal and superlattice structures, linking kinetic pathways to material properties.

Binary-related formation mechanisms encompass the diverse physical processes by which bound systems of two distinguishable or identical constituents—ranging from planetary, stellar, or substellar objects to colloids and crystalline phases—arise, evolve, and attain their observed statistical and structural properties. Their paper is fundamental for understanding planetary system architectures, stellar populations, material properties, and phase behavior in condensed matter systems. The mechanisms vary by context (e.g., planet–planet, star–star, colloid–colloid), physical environment (e.g., dense vs. sparse), and the relevant dynamical, thermodynamical, or kinetic drivers.

1. Dynamical Formation and Capture in Planetary and Planetesimal Systems

In dynamically active planetary or planetesimal systems, direct physical mechanisms such as close encounters, resonant interactions, and three-body processes dominate binary formation.

Planet–Planet Tidal Capture: When two massive planets (or brown dwarfs) in a system undergo a close encounter—typically within a few radii—the excitation of strong tides induces damping of orbital kinetic energy and facilitates gravitational binding rather than either collision or escape. The process is modeled by treating each planet as an $n=3/2$ polytrope and quantifying the tidal energy loss during passage (originating from the conversion of orbital energy to internal heat). The stability of the resultant binary against disruption by the host star’s tides is constrained by the condition

$a_{\text{in}} (1 + e_{\text{in}}) < \frac{2}{3} a_{\text{out}} (1 - e_{\text{out}}) \left( \frac{m_1 + m_2}{3M_\star} \right)^{1/3}$

followed by gradual circularization:

$a_{\text{circ}} = a_{\text{in}} (1 - e_{\text{in}}^2)$

Such binary planets are most efficiently formed among thermally bloated young bodies, with enhanced cross-sections for tidal dissipation. The process can occur via direct capture in a single close passage or through a sequence of weaker encounters culminating in binding (Podsiadlowski et al., 2010).

Three-body Processes in Planetesimal Disks: In the trans-Neptunian region, binary formation is dominated by dynamical three-body encounters. Two planetesimals may become temporarily bound if they traverse mutual Hill spheres, and a third planetesimal subsequently interacts, draining sufficient energy to stabilize the binary. The effective cross-section for such three-body capture events greatly exceeds that for simple two-body gravitational focusing:

$\sigma_{\text{com,2}} \approx 0.4 \left( \frac{G m}{v_{\text{rel}}^2 a_b} \right)^{0.6} R_p^2$

with the orbital distance scaling leading to a collision rate enhancement by a factor of a few over two-body processes in the outer solar system. The higher $R_H/R_p$ ratio in the trans-Neptunian region is critical for binary survival and subsequent collisional outcomes (Daisaka et al., 2011).

2. Binary Formation via Rotational Fission, Tides, and Radiative Effects in Small Body Populations

Asteroid and minor body binaries showcase complex formation and evolutionary sequences involving rotational, tidal, and radiative torques.

Rotational Fission and Tidal Evolution: Small asteroids subjected to YORP (Yarkovsky–O'Keefe–Radzievskii–Paddack) spin-up reach critical rotation, fragment, and produce satellites. Subsequent evolution involves rapid tidal locking of the secondary, expansion of the mutual orbit via both continued tidal torques and the Binary YORP (BYORP) effect, and—crucially for wide asynchronous binaries—the growth of librational amplitude until the secondary desynchronizes. The adiabatic invariance of libration induces a "stall" in orbital expansion once the secondary enters circulation, at which point YORP acting on the satellite precludes re-synchronization (Jacobson et al., 2013). The evolution is governed by coupled equations such as

$\dot{a} = \frac{k_p}{Q}(A_T + a^7 A_B) a^{-11/2}$

where $A_T$ (tides) and $A_B$ (BYORP) depend on system parameters.

Collisional and Rotational Channels in Asteroids: For larger bodies ( $D > 20$ km), catastrophic collisions and gravitational reaccumulation favor satellite formation, while for smaller bodies rotational fission dominates. Long-term monitoring and mutual gravitational/radiative (BYORP) torques dictate whether systems end as close binaries, unbound pairs, or evolve into complex hierarchical architectures (Walsh et al., 2015).

3. Statistical, Fragmentation, and Capture Constraints in Stellar Binaries

Stellar binary formation is tightly constrained by observed multiplicity distributions and theoretical considerations of fragmentation, random pairing, and dynamical processing.

Fragmentation-Dominated Outcomes: Observed companion mass ratio distributions (CMRDs) for primary masses spanning M, G, and intermediate types in various environments reveal a statistically significant excess of near-equal-mass binaries, inconsistent with independent random pairing from the initial mass function (IMF). Instead, CMRDs across environments (e.g., field, Pleiades, α Persei, Taurus) are best represented by a power-law:

$\frac{dN}{dq} \propto q^\beta, \quad \beta = -0.50 \pm 0.29$

supporting fragmentation—the coeval formation and co-accretion of binary components from the same reservoir—as the primary mechanism (Reggiani et al., 2011).

Wide Binary Formation from Adjacent Cores: Very wide binaries ( $a \gtrsim 10^4$ AU) arise from the binding of adjacent prestellar cores with sub-parabolic relative velocities, not from the fragmentation of a single collapsing core. The statistical condition for bound formation is

$s < a_0 = 1.9 \times 10^4\, M^{1/2}\ \mathrm{AU}$

and the observed high fraction of wide pairs in low-density regions (Taurus, β Pic Moving Group) indicates this channel is dominant only in sparse environments. Cluster dissolution and triple unfolding mechanisms can only explain a small fraction of wide systems and are strongly constrained by observed orbital properties (Tokovinin, 2017).

4. Binary Formation and Evolution under Environmental and Dynamical Influences

Dense stellar systems, clusters, and their associated dynamics alter the formation and destruction rates of binaries, imparting unique signatures on the resulting populations.

Dynamical Encounters and Binary Hardness: In dense clusters, binaries form and are modified via physical collisions (e.g., red giant–compact object encounters), binary–binary and single–binary encounters, and the dynamical formation of triples capable of driving Kozai–Lidov cycles. The "hardness" parameter

$\eta = \frac{\text{binding energy}}{kT}$

dictates survival, with soft binaries ( $\eta \lesssim 1$ ) easily destroyed. These processes serve as an energy sink, potentially driving core contraction and binary-burning phases. In such regimes, the observable binary fraction can be much lower than the true fraction due to blending, dim companions, and ongoing dynamical alterations (Ivanova, 2011).

Enhanced X-ray Populations via Compact Object Binaries: Dynamical binaries with compact members (neutron stars, white dwarfs) formed through exchange and collision processes serve as progenitors for X-ray binaries, especially in core-collapsed clusters. Binaries developed in this manner can subsequently be hardened or disrupted, feeding back into the dynamical evolution of the core.

5. Binary Formation Mechanisms in Condensed Matter and Colloidal Systems

In binary mixtures and colloidal suspensions, formation mechanisms depend fundamentally on the interplay between thermodynamics, energy landscapes, and kinetic pathways.

Phase Separation by Nucleation and Spinodal Decomposition: Binary mixtures exhibit phase separation via nucleation (high local energy, high entropy) or spinodal decomposition (intermediate energy, bicontinuous structures). Inherent structure analysis shows that even at high temperatures (homogeneous parent phase), the underlying minima (inherent structures) reveal an intrinsic phase-separated tendency. The characteristic wavelength of instability is given by

$\lambda^* = \left( \frac{2\pi K}{f''} \right)^{1/2}$

with $K$ the surface tension and $f''$ the curvature at the instability (Sarkar et al., 2010).

Kinetically Driven Crystallization in Binary Colloids: Binary colloidal crystals (e.g., NaCl type) can nucleate metastably even if another phase (e.g., CsCl) is thermodynamically preferred. Crystallization proceeds via a two-step mechanism—first, the system forms a dense, disordered aggregate with nascent short-range order, measured by order parameters $P_1$ (coordination) and $P_2$ (second-neighbor arrangement). The type of crystalline phase that emerges is then dictated by this initial local order, not global thermodynamic minima. Hydrodynamics has negligible impact on the kinetic selection pathway (Bochicchio et al., 2013).
Stoichiometry as a Mechanistic Lever in Superlattice Formation: The propensity of binary colloidal superlattices to self-assemble depends on the mixture ratio. An excess of smaller species acts as a "plasticizer", increases supersaturation, and suppresses formation of competing phases, thereby promoting the target binary structure both by enhancing dynamics and favoring the correct free energy landscape:

$\Delta \mu_{C,F} = \mu_{C} - (1 - x_C) \mu_{F}^L - x_C \mu_{F}^S$

Generality across particle shapes demonstrates this as a robust route for binary assembly (LaCour et al., 2021).

Binary formation among compact objects (black holes, neutron stars) is highly sensitive to stellar evolution, metallicity, and natal kicks.

Metallicity Dependence in Double Compact Object Formation: Binary black hole (BHBH) formation efficiency is orders of magnitude higher at low metallicity due to reduced stellar winds ( $\dot{M} \propto Z^\alpha$ ), smaller core radii, and lower mass-loss-induced kicks, allowing survival of tight binaries. In contrast, binary neutron star (NSNS) formation efficiency is largely flat with metallicity, as NS precursors experience less dramatic wind loss and kicks are modeled as mass-independent. The formation efficiency can be expressed as

$\eta = \frac{f_{\mathrm{primary}} \times f_{\mathrm{secondary}} \times f_{\mathrm{init\,sep}} \times f_{\mathrm{survive\,SN1}} \times f_{\mathrm{survive\,SN2}}}{\langle M_{\rm SF} \rangle}$

where the $f$ factors reflect mass, separation, and supernova survival probabilities. Formation channels (e.g., chemically homogeneous evolution, common envelope) are differentially sensitive to metallicity (Son et al., 4 Nov 2024).

Formation Pathways in Binary Black Hole Mergers: Isolated binary evolution involves core-collapse, possible common envelope ejection (with uncertain efficiency $\alpha_{\rm CE}$ ), and GW-driven in-spiral. Dynamical channels (in clusters) rely on exchange, three-body interactions, and hardening by repeated encounters, with hierarchical mergers possible. Key signatures distinguishing the channels are in mass, spin orientation (aligned in isolated, isotropic in dynamical), and residual eccentricity (Mapelli, 2021).

Gradual destabilization in binary mixtures (slow quenches towards phase separation) reveals universal critical dynamics distinct from mean-field predictions.

The emergent morphology length scale $R_*$ $R_{*}$ exhibits a scaling with the quench rate ( $\Gamma$ $Γ$ ) that is much more sensitive than mean-field models predict:
- Mean-field: $R_* \propto \Gamma^{-1/6}$
- Critical dynamics (2D): $R_* \propto \Gamma^{-4/15}$
- The result arises from pretransitional critical fluctuations dynamically "ageing" the system before macroscopic phase separation sets in. This is relevant for understanding pattern formation in slow-processing regimes and the ultimate control over nanostructure in biological and materials systems (Schaefer et al., 2019).

In summary, binary-related formation mechanisms are multifaceted and context-dependent, encompassing close-encounter tidal capture and three-body processes (planetary and small-body systems), fragmentation and accretion flow (stellar binaries), dynamical formation and destruction in dense environments, and kinetic-trapping and compositional tuning in condensed matter. Each context yields unique diagnostic signatures and parameter dependencies, such as the role of energy dissipation, environment-dependent cross-sections, initial mass ratios, and metallicity-sensitive stellar winds. The paper of these mechanisms is pivotal for interpreting observed multiplicity distributions, constraining dynamical and thermal histories of astrophysical systems, and designing targeted synthetic strategies in soft materials and nanotechnology.