Interplay between numerical-relativity and black hole perturbation theory in the intermediate-mass-ratio regime

We investigate the interplay between numerical relativity (NR) and point-particle black hole perturbation theory (ppBHPT) for quasi-circular non-spinning binary black holes in the intermediate mass ratio regime: 7<=q<=128 (where $q:=m_1/m_2$ is the mass ratio of the binary with m_1 and m_2 being the mass of the primary and secondary black hole respectively). Initially, we conduct a comprehensive comparison between the dominant (l,m) = (2,2) mode of the gravitational radiation obtained from state-of-the-art NR simulations and ppBHPT waveforms along with waveforms generated from recently developed NR-informed ppBHPT surrogate model, BHPTNRSur1dq1e4. This surrogate model employs a simple but non-trivial rescaling technique known as the $\alpha$-$\beta$ scaling to effectively match ppBHPT waveforms to NR in the comparable mass ratio regime. Subsequently, we analyze the amplitude and frequency differences between NR and ppBHPT waveforms to investigate the non-linearities, beyond adiabatic evolution, that are present during the merger stage of the binary evolution and propose fitting functions to describe these differences in terms of both the mass ratio and the symmetric mass ratio. Finally, we assess the performance of the $\alpha$-$\beta$ scaling technique in the intermediate mass ratio regime.