Mapping between black-hole perturbation theory and numerical relativity II: gravitational-wave momentum

Abstract

We report an approximate, non-trivial mapping of angular (linear) momentum in gravitational waves obtained from numerical relativity (NR) and adiabatic point-particle black hole perturbation theory (BHPT) in the comparable mass regime for quasi-circular, non-spinning binary black holes. This mapping involves two time-independent scaling parameters, $\alpha_{J}$ ($\alpha_{P}$) and $\beta_{J}$ ($\beta_{P}$), that adjust the BHPT angular (linear) momentum and the BHPT time respectively such a way that it aligns with NR angular (linear) momentum. Our findings indicate that this scaling mechanism works really well until close to the merger. In addition to the comparison of $\alpha_{J}$ ($\alpha_{P}$) with relevant values obtained from the waveform and flux scalings, we explore the mass ratio dependence of the scaling parameter $\alpha_{J}$ ($\alpha_{P}$). Finally, we investigate their possible connection to the missing finite size correction for the secondary black hole within the BHPT framework and the implication of these scalings on the remnant properties of the binary.