New Avenue for Accurate Analytical Waveforms and Fluxes for Eccentric Compact Binaries

Abstract

We introduce a new paradigm for constructing accurate analytic waveforms (and fluxes) for eccentric compact binaries. Our recipe builds on the standard Post-Newtonian (PN) approach but (i) retains implicit time-derivatives of the phase space variables in the instantaneous part of the noncircular waveform, and then (ii) suitably factorizes and resums this partly PN-implicit waveform using effective-one-body (EOB) procedures. We test our prescription against the exact results obtained by solving the Teukolsky equation with a test-mass source orbiting a Kerr black hole, and compare the use of the exact vs PN equations of motion for the time derivatives computation. Focusing only on the quadrupole contribution, we find that the use of the exact equations of motion yields an analytical/numerical agreement of the (averaged) angular momentum fluxes that is improved by $40\%$ with respect to previous work, with $4.5\%$ fractional difference for eccentricity $e=0.9$ and black hole dimensionless spin $-0.9\le \hat{a}\le +0.9$. We also find a remarkable convergence trend between Newtonian, 1PN and 2PN results. Our approach carries over to the comparable mass case using the resummed EOB equations of motion and paves the way to faithful EOB-based waveform model for long-inspiral eccentric binaries for current and future gravitational wave detectors.

7 pages, 6 figures, supplementary material fixed

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• Improved post-Newtonian waveform model for inspiralling precessing-eccentric compact binaries
• Unveiling the merger structure of black hole binaries in generic planar orbits
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• Third post-Newtonian dynamics for eccentric orbits and aligned spins in the effective-one-body waveform model SEOBNRv5EHM
• Scattering and dynamical capture of two black holes: synergies between numerical and analytical methods
• Effective one body Hamiltonian in scalar-tensor gravity at third post-Newtonian order
• Adding higher-order spherical harmonics in non-spinning eccentric binary black hole merger waveform models
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• Improved inspiral-merger-ringdown model for BBHs on elliptical orbits
• Universal phenomenological relations between spherical harmonic modes in non-precessing eccentric binary black hole merger waveforms
• Testing eccentric corrections to the radiation-reaction force in the test-mass limit of effective-one-body models
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• Data-driven extraction, phenomenology and modeling of eccentric harmonics in binary black hole merger waveforms
• Modeling matter(s) in SEOBNRv5THM: Generating fast and accurate effective-one-body waveforms for spin-aligned binary neutron stars
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