Scattering and dynamical capture of two black holes: synergies between numerical and analytical methods

Abstract: We study initially unbound systems of two black holes using numerical relativity (NR) simulations performed with GR-Athena++. We focus on regions of the parameter space close to the transition from scatterings to dynamical captures, considering equal mass and spin-aligned configurations, as well as unequal mass and nonspinning ones. The numerical results are then used to validate the effective-one-body (EOB) model TEOBResumS-Dal\'i for dynamical captures and scatterings. We find good agreement for the waveform phenomenologies, scattering angles, mismatches, and energetics in the low energy regime ($E_0\lesssim 1.02\,M$). In particular, mismatches weighted with the zero-detuned, high-power noise spectral density of Advanced LIGO are typically below or around the $1\%$ level, with only a few cases, corresponding to spinning binaries, slightly above the $3\%$ threshold, thus suggesting the usability of TEOBResumS-Dal\'i for current data analysis of low-energy scatterings and dynamical captures. We also discuss dynamical captures in the test-mass limit by solving numerically the Zerilli equation with the time domain code RWZHyp. The latter analysis provides valuable insights into both the analytical noncircular corrections of the EOB waveform and the integration of NR Weyl scalars.