Inspiraling compact binaries with non-negligible orbital eccentricities are plausible gravitational wave (GW) sources for the upcoming network of GW observatories. In this paper, we present two prescriptions to compute post-Newtonian (PN) accurate inspiral templates for such binaries. First, we adapt and extend the post-circular scheme of Yunes et al. [Phys. Rev. D 80, 084001 (2009)] to obtain a Fourier-domain inspiral approximant that incorporates the effects of PN-accurate orbital eccentricity evolution. This results in a fully analytic frequency-domain inspiral waveform with Newtonian amplitude and 2PN order Fourier phase while incorporating eccentricity effects up to sixth order at each PN order. The importance of incorporating eccentricity evolution contributions to the Fourier phase in a PN consistent manner is also demonstrated. Second, we present an accurate and efficient prescription to incorporate orbital eccentricity into the quasi-circular timedomain TaylorT4 approximant at 2PN order. New features include the use of rational functions in orbital eccentricity to implement the 1.5PN order tail contributions to the far-zone fluxes. This leads to closed form PN-accurate differential equations for evolving eccentric orbits and the resulting time-domain approximant is accurate and efficient to handle initial orbital eccentricities ≤ 0.9. Preliminary GW data analysis implications are probed using match estimates.

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Accurate and efficient modeling of the dynamics of binary black holes (BBHs) is crucial to their detection through gravitational waves (GWs), with LIGO/Virgo/KAGRA, and LISA in the future. Solving the dynamics of a BBH system with arbitrary parameters without simplifications (like orbit-or precession-averaging) in closed-form is one of the most challenging problems for the GW community. One potential approach is using canonical perturbation theory which constructs perturbed action-angle variables from the unperturbed ones of an integrable Hamiltonian system. Having action-angle variables of the integrable 1.5 post-Newtonian (PN) BBH system is therefore imperative. In this paper, we continue the work initiated by two of us in [Tanay et al., Phys. Rev. D 103, 064066 (2021)], where we presented four out of five actions of a BBH system with arbitrary eccentricity, masses, and spins, at 1.5PN order. Here we compute the remaining fifth action using a novel method of extending the phase space by introducing unmeasurable phase space coordinates. We detail how to compute all the frequencies, and sketch how to explicitly transform to angle variables, which analytically solves the dynamics at 1.5PN. This lays the groundwork to analytically solve the conservative dynamics of the BBH system with arbitrary masses, spins, and eccentricity, at higher PN order, by using canonical perturbation theory.

The space-based detector LISA may observe gravitational waves from the early inspiral of stellarmass black hole binaries, some of which could have significant eccentricity. Current gravitational waveform templates are only valid for small orbital velocities (i.e., in a post-Newtonian expansion) and small initial eccentricity e0 ("post-circular" expansion). We conventionally define e0 as the eccentricity corresponding to an orbital frequency of 5 mHz, and we study the convergence properties of frequency-domain inspiral templates that are accurate up to 2PN and order e 6 0 in eccentricity [1]. We compute the so-called "unfaithfulness" between the full template and "reduced" templates obtained by dropping some terms in the phasing series; we investigate the conditions under which systematic errors are negligible with respect to statistical errors, and we study the convergence properties of statistical errors. In general, eccentric waveforms lead to larger statistical errors than circular waveforms due to correlations between the parameters, but the error estimates do not change significantly as long as we include terms of order e 2 0 or higher in the phasing.arXiv:1905.08811v2 [gr-qc]

We derive fourth post-Newtonian (4PN) contributions to the Keplerian type parametric solution associated with the conservative dynamics of eccentric, nonspinning compact binaries. The solution has been computed while ignoring certain zero-average, oscillatory terms arising due to 4PN tail effects. We provide explicit expressions for the parametric solution and various orbital elements in terms of the conserved energy, angular momentum and symmetric mass ratio. Canonical perturbation theory (along with the technique of Padé approximant) is used to incorporate the 4PN nonlocal-in-time tail effects within the action-angles framework. We then employ the resulting solution to obtain an updated inspiral-merger-ringdown (IMR) waveform that models the coalescence of nonspinning, moderately eccentric black hole binaries, influenced by Hinder et al.[Phys. Rev. D 98, 044015 ( 2018)]. Our updated waveform is expected to be valid over a similar parameter range as the above reference. We also present a related waveform which makes use of only the post-Newtonian equations and thus is valid only for the inspiral stage. This waveform is expected to work for a much larger range of eccentricity (e t ≲ 0.85) than our full IMR waveform (which assumes circularization of the binaries close to merger). We finally pursue preliminary data analysis studies to probe the importance of including the 4PN contributions to the binary dynamics while constructing gravitational waveform templates for eccentric mergers.