Eccentric Black Hole Mergers in Dense Star Clusters: The Role of Binary–Binary Encounters

Abstract

We present the first systematic study of strong binary-single and binary-binary black hole (BH) interactions with the inclusion of general relativity. By including general relativistic effects in the equations of motion during strong encounters, the dissipation of orbital energy from the emission of gravitational waves (GWs) can lead to captures and subsequent inspirals with appreciable eccentricities when entering the sensitive frequency ranges of the LIGO and Virgo GW detectors. It has been shown that binary-single interactions significantly contribute to the rate of eccentric mergers, but no studies have looked exclusively into the contribution from binary-binary interactions. To this end, we perform binary-binary and binary-single scattering experiments with general relativistic dynamics up through the 2.5 post-Newtonian order included, both in a controlled setting to gauge the importance of non-dissipative post-Newtonian terms and derive scaling relations for the cross section of GW captures, as well as experiments tuned to the strong interactions from state-of-the art globular cluster (GC) models to assess the relative importance of the binary-binary channel in facilitating GW captures and the resultant eccentricity distributions of inspiral from channel. Although binary-binary interactions are 10-100 times less frequent in GCs than binary-single interactions, their longer lifetime and more complex dynamics leads to a higher probability for GW captures to occur during the encounter. We find that binarybinary interactions contribute 25-45% of the eccentric mergers that occur during strong BH encounters in GCs, regardless of the properties of the cluster environment. The inclusion of higher multiplicity encounters in dense star clusters therefore have major implications on the predicted rates of highly eccentric binaries potentially detectable by the LIGO/Virgo network. Becse gravitational waveforms of eccentric inspirals are distinct from those generated by merging binaries that have circularized, measurements of eccentricity in such systems would highly constrain their formation scenario.

Searching for eccentricity: signatures of dynamical formation in the first gravitational-wave transient catalogue of LIGO and Virgo

“…Compact objects that remain in the dense cluster core may form triples and quadruples, which can experience chaotic resonant interactions (Wen 2003;Antonini et al 2016;Rodriguez et al 2018a,b;. Binaries that harden during such interactions can merge before their next strong encounter, and have an eccentricity distribution that peaks at e ∼ 10 −4 at 10 Hz (Rodriguez et al 2018a,b;Zevin et al 2019b). During a close dynamical encounter between two compact objects in a globular cluster, the strong loss of gravitational energy at periapsis can lead to a gravitational-wave capture merger.…”

Gravitational-wave emission from binary black holes formed in open clusters

“…The core of globular clusters (10 5 -10 6 M ⊙ ) has long been investigated as a formation site of BBHs in many previous works (e.g. Portegies Zwart & McMillan 2000;O'Leary et al 2006;Sadowski et al 2008;Downing et al 2010Downing et al , 2011Banerjee et al 2010;Tanikawa 2013;Bae et al 2014;Rodriguez et al 2015Rodriguez et al , 2016Fujii et al 2017;Park et al 2017;Askar et al 2017;Hong et al 2018;Zevin et al 2019).…”

Analytic waveforms for eccentric gravitational wave bursts

“…This may be fixed by matching to the known value of the exact solution at pericenter, which can be found by taking u = 0 in Eq. (8). Finally, the definition of ψ, and the action of holding it fixed when expanding in 1, helps to ensure that the resulting expressions remain phase accurate compared to an exact answer.…”

“…where 2 F 1 is the hypergeometric function, the functions A l1,l2,s (f ) are listed in Appendix C, (l 1 , l 2 ) are integers that belong to the set L = {(2, 4), (4,8), (1,5), (5, 7), (7, 11), (10, 8)}, and s ∈ {−1/2, 1/2}. Note that we have not expanded this expression about = 1 − e 2 0 1.…”