Relativistic encounters in dense stellar systems

TL;DR

This paper assesses the likelihood of three black holes interacting strongly in dense stellar systems, concluding such events are extremely rare, simplifying gravitational wave data analysis by focusing on two-body interactions.

Contribution

It quantifies the probability of triple black hole encounters in dense stellar environments, showing they are negligible for gravitational wave detection.

Findings

Triple black hole interactions are extremely rare in dense stellar systems.

Two-body waveform models are sufficient for gravitational wave analysis, reducing computational complexity.

Event rates for strong three-body encounters are negligible.

Abstract

Two coalescing black holes (BHs) represent a conspicuous source of gravitational waves (GWs). The merger involves 17 parameters in the general case of Kerr BHs, so that a successful identification and parameter extraction of the information encoded in the waves will provide us with a detailed description of the physics of BHs. A search based on matched-filtering for characterization and parameter extraction requires the development of some $10^{15}$ waveforms. If a third additional BH perturbed the system, the waveforms would not be applicable, and we would need to increase the number of templates required for a valid detection. In this letter, we calculate the probability that more than two BHs interact in the regime of strong relativity in a dense stellar cluster. We determine the physical properties necessary in a stellar system for three black holes to have a close encounter in this regime and also for an existing binary of two BHs to have a strong interaction with a third hole. In both cases the event rate is negligible. While dense stellar systems such as galactic nuclei, globular clusters and nuclear stellar clusters are the breeding grounds for the sources of gravitational waves that ground-based detectors like Advanced LIGO and Advanced VIRGO will be exploring, the analysis of the waveforms in full general relativity needs only to evaluate the two-body problem. This reduces the number of templates of waveforms to create by orders of magnitude.