Jacob Lange, Danilo Chiaramello, Peter Lott, Chad Henshaw, Alessandro Nagar, Richard O'Shaughnessy, Laura Cadonati

Close hyperbolic encounters between black holes produce distinctive bursts of gravitational radiation with a time-frequency morphology that is qualitatively different from that of quasi-circular inspirals. Expected to arise in dense stellar environments through dynamical interactions, these encounters probe formation channels and mass ranges inaccessible to isolated binary evolution, making them a compelling target for current and next-generation detectors. In this work, we reanalyze \totalevents high-mass events from the LIGO-Virgo-KAGRA catalogs using the hyperbolic configuration of the~\dali~waveform model. We compare these with analyses using the quasi-circular, precessing configuration of the same model, computing Bayes factors to evaluate which description is favored by the data. We find that most events strongly to mildly favor the quasi-circular, precessing scenario, except for GW190521. For this event, we find that the signal is best fit by a dynamical capture waveform, with Bayes factor $\ln \mathcal{B}^{\rm hyp}_{\rm prec}=3.71^{+0.11}_{-0.11}$. We confirm this preference via further analyses with~\dali~in different configurations (quasi-circular, non-precessing; eccentric, non-precessing; and eccentric, precessing), as well as one using the quasi-circular, precessing numerical relativity surrogate model \nrsur. We also highlight the results we obtain for GW231123, another high-mass signal linked to evidence of strong precession, for which we find strong preference for the quasi-circular, precessing scenario, with $\ln \mathcal{B}^{\rm hyp}_{\rm prec}=-15.80^{+0.24}_{-0.24}$. The analysis of mock signals generated with the best fitting waveforms for GW190521 and GW231123 suggest that the former might belong to a region of parameter space where high-mass, bound, precessing signals can be hard to distinguish from dynamical captures in parameter estimation.