Interactions among binary black holes in star clusters: Eccentric gravitational wave captures and triple formation

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Volume 698 (May 2025)

A&A, 698 (2025) A229

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Table A.1

Possible outcomes in a BBH-BBH interaction and the conditions used to classify them in our simulations.

Outcome name	Conditions
Binary-binary	The closest pair of BHs is bound (first binary)
	The other pair of BHs is bound (second binary)
	The two binaries are unbound from each other
	The two binaries are moving away from each other
	The absolute value of the relative tidal forces is at most 10⁻³ times the binding force of the binaries

Binary-single-single	The closest pair of BHs is bound (binary)
	The other pair of BHs is unbound (singles)
	Both singles are unbound from the binary
	Both singles are moving away from the binary
	The absolute value of the tidal force of each single is at most 10⁻³ times the binding force of the binary

Single-single-single-single	The closest pair of BHs is unbound
	All BHs are moving away from each other
	The total energy of the system is positive
	The total energy of all subsets of two BHs is positive
	The total energy of all subsets of three BHs is positive

Triple-single	The closest pair of BHs is bound (inner binary)
	One of the other two BHs is bound to the binary (outer BH), whereas the other one is unbound (single)
	The single is moving away from the binary
	The absolute value of the tidal force of the single is at most 10⁻³ times the binding force of the outer component of the triple
	The triple is Mardling & Aarseth (2001) stable

GW capture	The distance between two BHs is smaller than 10 times the sum of their Schwarzschild radii

Unresolved	None of the outcomes above is reached
Unresolved	The simulation time reaches $t = 10^{6} \sqrt{\frac{(1 A U)^{3}}{G (1 M_{⊙})}} = 0.16 M y r$ $t=10^{6} \sqrt{\frac{(1 \mathrm{AU})^{3}}{G\left(1 \mathrm{M}_{\odot}\right)}}=0.16 \mathrm{Myr}$

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