Binary-single Interactions with Different Mass Ratios

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). We want to understand how BBH coalescence can occur during - or after - binary-single interactions with different mass ratios. We perform gravitational scattering experiments of binary-single interactions using different mass ratios of the binary components (q_2≡ m_2/m_1≤1) and the incoming single (q_3≡ m_3/m_1). 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. We find that GW capture during resonant interactions is most efficient if q_2≃ q_3 and that the mass-ratio distribution of BBH coalescence due to inspirals is ∝ m_1^-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 m_1 and is relatively insensitive to q_2 and q_3. We show that eccentricity increase by non-resonant encounters approximately doubles the rate of BBH inspiral 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 (m_1) and steeper BH mass function, yielding binaries with lower q. Our results enable the translating from the mass-ratio distribution of dynamically formed BBH mergers 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.