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

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.Comment: 13 pages, 13 figure

Study of eccentric binary black hole mergers using numerical relativity and an inspiral-merger-ringdown model

We study the phenomenology of non-spinning eccentric binary black hole (BBH) mergers using numerical relativity (NR) waveforms and \texttt{EccentricIMR} waveform model, as presented in Ref. \cite{Hinder:2017sxy} (Hinder, Kidder, and Pfeiffer, arXiv:1709.02007). This model is formulated by combining an eccentric inspiral, derived from a post-Newtonian (PN) approximation including 3PN conservative and 2PN reactive contributions to the BBH dynamics, with a circular merger model. A distinctive feature of \texttt{EccentricIMR} is its two-parameter treatment, utilizing eccentricity and mean anomaly, to characterize eccentric waveforms. We implement the \texttt{EccentricIMR} model in \texttt{Python} to facilitate routine use. We then validate the model against 35 eccentric NR waveforms obtained from both the SXS and RIT NR catalogs. We find that \texttt{EccentricIMR} model reasonably match NR data for eccentricities up to $0.16$, specified at a dimensionless reference frequency of $x=0.07$, and mass ratios up to $q=4$. Additionally, we use this model as a tool for cross-comparing eccentric NR data obtained from the SXS and RIT catalogs. Furthermore, we explore the validity of a circular merger model often used in eccentric BBH merger modelling using both the NR data and \texttt{EccentricIMR} model. Finally, we use this model to explore the effect of mean anomaly in eccentric BBH mergers.Comment: 22 figure

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.Comment: 11 pages, 10 figure

On the approximate relation between black-hole perturbation theory and numerical relativity

We investigate the interplay between numerical relativity (NR) and point-particle black hole perturbation theory (ppBHPT) in the comparable mass regime. Specifically, we reassess the $\alpha$-$\beta$ scaling technique, previously introduced by Islam et al, as a means to effectively match ppBHPT waveforms to NR waveforms within this regime. Utilizing publicly available long NR data for a mass ratio of $q=3$ (where $q:=m_1/m_2$ represents the mass ratio of the binary, with m_1 and m_2 denoting the masses of the primary and secondary black holes, respectively), encompassing the final $\sim 65$ orbital cycles of the binary evolution, we examine the range of applicability of such scalings. We observe that the scaling technique remains effective even during the earlier stages of the inspiral. Additionally, we provide commentary on the temporal evolution of the $\alpha$ and $\beta$ parameters and discuss whether they can be approximated as constant values. Consequently, we derive the $\alpha$-$\beta$ scaling as a function of orbital frequencies and demonstrate that it is equivalent to a frequency-dependent correction. We further provide a brief comparison between Post-Newtonian waveform and the rescaled ppBHPT waveform at $q=3$ and comment on their regime of validity. Finally, we explore the possibility of using PN to obtain the $\alpha$-$\beta$ calibration parameters and still provide a rescaled ppBHPT waveform that matches NR.Comment: 14 pages, 11 figure

Interplay between numerical relativity and perturbation theory : finite size effects

We investigate the interplay between numerical relativity (NR) and point-particle black hole perturbation theory (ppBHPT) in the comparable mass ratio regime. In the ppBHPT framework, the secondary black hole is treated as a point particle, neglecting its finite size. Our study focuses on addressing the missing finite size effect in the ppBHPT framework and proposing a method for incorporating the size of the secondary into the perturbation theory framework. We demonstrate that by considering the secondary as a finite size object, the BHPT waveforms closely match NR waveforms. Additionally, we revisit the $\alpha$-$\beta$ scaling technique, which was previously introduced by Islam et al, as a means to effectively match ppBHPT waveforms to NR waveforms. We further analyze the scaling procedure and decompose it into different components, attributing them to various effects, including the corrections arising from the finite size of the secondary black hole.Comment: 12 pages, 10 figure

Comparing numerical relativity and perturbation theory waveforms for a non-spinning equal-mass binary

Past studies have empirically demonstrated a surprising agreement between gravitational waveforms computed using adiabatic-driven-inspiral point-particle black hole perturbation theory (ppBHPT) and numerical relativity (NR) following a straightforward calibration step, sometimes referred to as $\alpha$-$\beta$ scaling. Specifically focusing on the quadrupole mode, this calibration technique necessitates only two time-independent parameters to scale the overall amplitude and time coordinate. In this article, part of a special issue, we investigate this scaling for non-spinning binaries at the equal mass limit. Even without calibration, NR and ppBHPT waveforms exhibit an unexpected degree of similarity after accounting for different mass scale definitions. Post-calibration, good agreement between ppBHPT and NR waveforms extends nearly up to the point of the merger. We also assess the breakdown of the time-independent assumption of the scaling parameters, shedding light on current limitations and suggesting potential generalizations for the $\alpha$-$\beta$ scaling technique.Comment: Published in a themed issue in honor of Prof. Jorge Pullin on his 60th anniversary; Universe 2024, 10(1), 2