Binary-single interactions with different mass ratios

Implications for gravitational waves from globular clusters

¹ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí Franquès 1, 08028 Barcelona, Spain
² Leiden Observatory, University of Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
³ ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
⁴ Gravity Exploration Institute, School of Physics and Astronomy, Cardiff University, CF24 3AA, UK

^★ Corresponding author: bruno.randof@gmail.com

Received: 28 May 2024
Accepted: 23 March 2025

Abstract

Context. Dynamical interactions in star clusters are an efficient mechanism to produce the coalescing binary black holes (BBHs) that have been detected with gravitational waves (GWs).

Aims. We want to understand how BBH coalescence can occur during – or after – binary-single interactions with different mass ratios.

Methods. We perform gravitational scattering experiments of binary-single interactions using different mass ratios of the binary components (q₂ ≡ m₂/m₁ ≤ 1) and the incoming single (q₃ ≡ m₃/m₁). We extract cross-sections and rates for (i) GW capture during resonant interactions; (ii) GW inspiral in between resonant interactions and apply the results to different globular cluster conditions.

Results. We find that GW capture during resonant interactions is most efficient if q₂ ≃ q₃ and that the mass-ratio distribution of BBH coalescence due to inspirals is ∝ m₁⁻¹q^2.9﹢α, where α is the exponent of the BH mass function. The total rate of GW captures and inspirals depends mostly on m₁ and is relatively insensitive to q₂ and q₃. We show that eccentricity increase in direct (that is, non-resonant) encounters approximately doubles the rate of BBH inspirals in between resonant encounters. For a given GC mass and radius, the BBH merger rate in metal-rich GCs is approximately double that of metal-poor GCs, because of their (on average) lower BH masses (m₁) and steeper BH mass function, yielding binaries with lower q.

Conclusions. Our results enable the mass-ratio distribution of dynamically formed BBH mergers to be translated to the underlying BH mass function. The additional mechanism that leads to a doubling of the inspirals provides an explanation for the reported high fraction of in-cluster inspirals in N-body models of clusters.