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

TL;DR

This paper combines numerical relativity simulations and analytical models to study unbound black hole encounters, validating the effective-one-body model for low-energy scatterings and captures, with implications for gravitational wave data analysis.

Contribution

It provides a comprehensive validation of the TEOBResumS-Dalí model against NR simulations for unbound black hole interactions, including new insights into waveform accuracy and capture dynamics.

Findings

Good agreement between NR and EOB waveforms for low-energy encounters.

Mismatches generally below 1%, slightly above 3% for spinning cases.

TEOBResumS-Dalí is suitable for current gravitational wave data analysis in relevant regimes.

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.