Observational limits on the rate of radiation-driven binary black hole capture events

Dense astrophysical environments like globular clusters and galactic nuclei can host hyperbolic encounters of black holes which can lead to gravitational-wave driven capture. There are several astrophysical models which predict a fraction of binary black hole mergers to come from these radiation-driven capture scenarios. In this paper we present the sensitivity of a search towards gravitational-wave driven capture events for O3, the third observing run of LIGO and Virgo. We use capture waveforms produced by numerical relativity simulations covering four different mass ratios and at least two different values of initial angular momentum per mass ratio. We employed the most generic search for short-duration transients in O3 to evaluate the search sensitivity in this parameter space for a wide range in total mass in terms of visible spacetime volume. From the visible spacetime volume we determine for the first time the merger rate upper limit of such systems. The most stringent estimate of rate upper limits at 90\% confidence is $0.2~\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$ for an equal mass $200~M_\odot$ binary. Furthermore, in recent studies the event GW190521 has been suggested to be a capture event. With this interpretation of GW190521, we find the merger rate of similar events to be $0.47~\mathrm{Gpc}^{-3}\,\mathrm{yr}^{-1}$.