Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform

Abstract

We derive fourth post-Newtonian (4PN) contributions to the Keplerian-type parametric solution associated with the conservative dynamics of eccentric, non-spinning 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 Pade 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 non-spinning, moderately eccentric black hole binaries, influenced by arXiv:1709.02007. Our updated waveform is expected to be valid over 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 ($e_t\lesssim 0.85$) 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.

38 pages, 4 figures

References in corpus (32)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog
• Gravitational waves from scattering of stellar-mass black holes in galactic nuclei
• GW190521: orbital eccentricity and signatures of dynamical formation in a binary black hole merger signal
• Distinguishing Spin-Aligned and Isotropic Black Hole Populations With Gravitational Waves
• Fourth post-Newtonian effective one-body dynamics
• A waveform model for eccentric binary black hole based on effective-one-body-numerical-relativity (EOBNR) formalism
• Eccentric, nonspinning, inspiral, Gaussian-process merger approximant for the detection and characterization of eccentric binary black hole mergers
• Searching for Eccentricity: Signatures of Dynamical Formation in the First Gravitational-Wave Transient Catalogue of LIGO and Virgo
• Accurate and efficient waveforms for compact binaries on eccentric orbits
• Effective one body multipolar waveform model for spin-aligned, quasi-circular, eccentric, hyperbolic black hole binaries
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order
• Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders
• Complete waveform model for compact binaries on eccentric orbits
• Sixth post-Newtonian nonlocal-in-time dynamics of binary systems
• Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order
• Foundations of an effective-one-body model for coalescing binaries on eccentric orbits
• Tail effects in the third post-Newtonian gravitational wave energy flux of compact binaries in quasi-elliptical orbits
• Fingerprints of binary black hole formation channels encoded in the mass and spin of merger remnants
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• High Eccentricities and High Masses Characterize Gravitational-wave Captures in Galactic Nuclei as Seen by Earth-based Detectors
• Solving post-Newtonian accurate Kepler Equation
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order
• Black Hole Binaries in Galactic Nuclei and Gravitational Wave Sources
• Ready-to-use Fourier domain templates for compact binaries inspiraling along moderately eccentric orbits
• Impact of eccentricity on the gravitational wave searches for binary black holes: High mass case
• Adding eccentricity to quasicircular binary-black-hole waveform models
• Pulsar timing array signals induced by black hole binaries in relativistic eccentric orbits

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• Gravitational Waves from Black-Hole Encounters: Prospects for Ground- and Galaxy-Based Observatories
• Orbital eccentricity in general relativity from catastrophe theory
• Adding higher-order spherical harmonics in non-spinning eccentric binary black hole merger waveform models
• Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications
• Mapping eccentricity evolutions between numerical relativity and effective-one-body gravitational waveforms
• Electromagnetic fields in compact binaries: post-Newtonian wave generation and application to double white dwarfs systems
• Universal phenomenological relations between spherical harmonic modes in non-precessing eccentric binary black hole merger waveforms
• Eccentricity estimation from initial data for Numerical Relativity Simulations
• Inferring Interference: Identifying a Perturbing Tertiary with Eccentric Gravitational Wave Burst Timing
• Importance of eccentricities in parameter estimation of compact binary inspirals with decihertz gravitational-wave detectors
• Action-angle variables of a binary black hole with arbitrary eccentricity, spins, and masses at 1.5 post-Newtonian order
• Tidal contributions to the full gravitational waveform to the second-and-a-half post-Newtonian order
• Data-driven extraction, phenomenology and modeling of eccentric harmonics in binary black hole merger waveforms
• Post-Newtonian theory-inspired framework for characterizing eccentricity in gravitational waveforms
• Gravitational waves from quasielliptic compact binaries in scalar-tensor theory to one-and-a-half post-Newtonian order
• A complete waveform comparison of post-Newtonian and numerical relativity in eccentric orbits
• Closed-form solutions of spinning, eccentric binary black holes at 1.5 post-Newtonian order
• Eccentric Catastrophes & What To Do With Them
• Testing modified gravity with the eccentric neutron star--black hole merger GW200105
• Efficient prescription to search for linear gravitational wave memory from hyperbolic black hole encounters and its application to the NANOGrav 12.5-year dataset
• Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order
• General Fourier expansion of post-Newtonian binary dynamics based on a quasi-Keplerian framework
• Hamiltonian normal forms for the post-Newtonian binary problem
• Exploiting Newton-factorized, 2PN-accurate, waveform multipoles in effective-one-body models for spin-aligned noncircularized binaries