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The measurement of orbital eccentricity in gravitational-wave (GW) signals will provide unique insights into the astrophysical origin of binary systems, while ignoring eccentricity in waveform models could introduce significant biases in parameter estimation and tests of general relativity. Upcoming LIGO-Virgo-KAGRA observing runs are expected to detect a subpopulation of eccentric signals, making it vital to develop accurate waveform models for eccentric orbits. Here, employing recent analytical results through the third post-Newtonian order, we develop v5: a new time-domain, effective-one-body, multipolar waveform model for eccentric binary black holes with spins aligned (or antialigned) with the orbital angular momentum. Besides the dominant (2, 2) mode, the model includes the (2, 1), (3, 3), (3, 2), (4, 4), and (4, 3) modes. We validate the model’s accuracy by computing its unfaithfulness against 99 (28 public and 71 private) eccentric numerical-relativity (NR) simulations, produced by the Simulating eXtreme Spacetimes Collaboration. Importantly, for NR waveforms with initial GW eccentricities below 0.5, the maximum (2, 2)-mode unfaithfulness across the total mass range $20–200M_{\odot }$is consistently below or close to 1%, with a median value of $\sim 0.02\%$, reflecting an accuracy improvement of approximately an order of magnitude compared to the previous-generation v4 and the state-of-the-art esumalí eccentric model. In the quasi-circular-orbit limit, v5 is in excellent agreement with the highly accurate v5 model. The accuracy, robustness, and speed of v5 make it suitable for data analysis and astrophysical studies. We demonstrate this by performing a set of recovery studies of synthetic NR-signal injections, and parameter-estimation analyses of the events GW150914 and GW190521, which we find to have no eccentricity signatures. 

In this work, we test an effective-one-body radiation-reaction force for eccentric planar orbits of a test mass in a Kerr background, which contains third-order post-Newtonian (PN) nonspinning and second-order PN spin contributions. We compare the analytical fluxes connected to two different resummations of this force, truncated at different PN orders in the eccentric sector, with the numerical fluxes computed through the use of frequency- and time-domain Teukolsky-equation codes. We find that the different PN truncations of the radiation-reaction force show the expected scaling in the weak gravitational-field regime, and we observe a fractional difference with the numerical fluxes that is $<5\%$, for orbits characterized by eccentricity $0\le e\le 0.7$, central black-hole spin $-0.99M\le a\le 0.99M$and fixed orbital-averaged quantity $x=⟨M\mathrm{\Omega }{⟩}^{2/3}=0.06$, corresponding to the mildly strong-field regime with semilatera recta $9M<p<17M$. Our analysis provides useful information for the development of spin-aligned eccentric models in the comparable-mass case. Published by the American Physical Society2025 

Abstract Accurate modelling of black hole binaries is critical to achieve the science goals of gravitational-wave detectors. Modelling such configurations relies strongly on calibration to numerical-relativity (NR) simulations. Binaries on quasi-circular orbits have been widely explored in NR, however, coverage of the broader 9-dimensional parameter space, including orbital eccentricity, remains sparse. This article develops a new procedure to control orbital eccentricity of binary black hole simulations that enables choosing initial data parameters with precise control over eccentricity and mean anomaly of the subsequent evolution, as well as the coalescence time. We then calculate several sequences of NR simulations that nearly uniformly cover the 2-dimensional eccentricity--mean anomaly space for equal mass, non-spinning binary black holes. We demonstrate that, for fixed eccentricity, many quantities related to the merger dynamics of binary black holes show an oscillatory dependence on mean anomaly. The amplitude of these oscillations scales nearly linearly with the eccentricity of the system. We find that for the eccentricities explored in this work, the magnitude of deviations in various quantities such as the merger amplitude and peak luminosity can approach $$\sim5\%$$ of their quasi-circular value. We use our findings to explain eccentric phenomena reported in other studies. We also show that methods for estimating the remnant mass employed in the effective-one-body approach exhibit similar deviations, roughly matching the amplitude of the oscillations we find in NR simulations. This work is an important step towards a complete description of eccentric binary black hole mergers, and demonstrates the importance of considering the entire 2-dimensional parameter subspace related to eccentricity.