Hereditary Effects in Eccentric Compact Binary Inspirals to Third Post-Newtonian Order

Abstract

While there has been much success in understanding the orbital dynamics and gravitational wave emission of eccentric compact binaries in the post-Newtonian formalism, some problems still remain. The largest of these concerns hereditary effects: non-linear phenomena related to the scattering off of the background curved spacetime (tails) and to the generation of gravitational waves by gravitational waves (memory). Currently, these hereditary effects are only known numerically for arbitrary eccentricity through infinite sums of Bessel functions, with closed-form, analytic results only available in the small eccentricity limit. We here calculate, for the first time, closed-form, analytic expressions for all hereditary effects to third post-Newtonian order in binaries with arbitrary eccentricity. For the tails, we first asymptotically expand all Bessel functions in high eccentricity and find a superasymptotic series for each enhancement factor, accurate to better than $10^{-3}$ relative to post-Newtonian numerical calculations at all eccentricities. We further improve the small-eccentricity behavior of the superasymptotic series by generating hyperasymptotic expressions for each enhancement factor, typically accurate to better than $10^{-8}$ at all eccentricities. For the memory, we discuss its computation within the context of an osculating approximation of the binary's orbit and the difficulties that arise. Our closed-form analytic expressions for the hereditary fluxes allow us to numerically compute orbital phases that are identical to those found using an infinite sum of Bessel functions to double numerical precision.

51 pages, 5 figures. Updated to correct transcription errors in Eqs. (123), (169), & (170)

References in corpus (13)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Theoretical Physics Implications of the Binary Black-Hole Mergers GW150914 and GW151226
• Gravitational waves from scattering of stellar-mass black holes in galactic nuclei
• Detecting gravitational-wave memory with LIGO: implications of GW150914
• Accurate and efficient waveforms for compact binaries on eccentric orbits
• The third and a half post-Newtonian gravitational wave quadrupole mode for quasi-circular inspiralling compact binaries
• Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order
• Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux
• Tail effects in the third post-Newtonian gravitational wave energy flux of compact binaries in quasi-elliptical orbits
• Fast Frequency-domain Waveforms for Spin-Precessing Binary Inspirals
• Detecting gravitational waves from highly eccentric compact binaries
• A simple estimate of gravitational wave memory in binary black hole systems
• Full-analytic frequency-domain 1pN-accurate gravitational wave forms from eccentric compact binaries

Cited by in corpus (29)

• Eccentric, nonspinning, inspiral, Gaussian-process merger approximant for the detection and characterization of eccentric binary black hole mergers
• An eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory
• Foundations of an effective-one-body model for coalescing binaries on eccentric orbits
• The Gravitational-Wave Physics II: Progress
• The Science of the Einstein Telescope
• Validating the Effective-One-Body Numerical-Relativity Waveform Models for Spin-aligned Binary Black Holes along Eccentric Orbits
• Radiation-reaction force and multipolar waveforms for eccentric, spin-aligned binaries in the effective-one-body formalism
• Gravitational Waves Probes of Parity Violation in Compact Binary Coalescence
• Inferring eccentricity evolution from observations of coalescing binary black holes
• Spin effects in gravitational waveforms and fluxes for binaries on eccentric orbits to the third post-Newtonian order
• Fusing numerical relativity and deep learning to detect higher-order multipole waveforms from eccentric binary black hole mergers
• Effective-One-Body Numerical-Relativity waveform model for Eccentric spin-precessing binary black hole coalescence
• Upgraded waveform model of eccentric binary black hole based on effective-one-body-numerical-relativity for spin-aligned binary black holes
• Third post-Newtonian dynamics for eccentric orbits and aligned spins in the effective-one-body waveform model SEOBNRv5EHM
• Observation of eccentric binary black hole mergers with second and third generation gravitational wave detector networks
• Determination of new coefficients in the angular momentum and energy fluxes at infinity to 9PN for eccentric Schwarzschild extreme-mass-ratio inspirals using mode-by-mode fitting
• Characterization of numerical relativity waveforms of eccentric binary black hole mergers
• Eccentric-orbit extreme-mass-ratio-inspiral radiation II: 1PN correction to leading-logarithm and subleading-logarithm flux sequences and the entire perturbative 4PN flux
• Numerical relativity higher order gravitational waveforms of eccentric, spinning, non-precessing binary black hole mergers
• Eccentric-orbit EMRI radiation: Analytic forms of leading-logarithm and subleading-logarithm flux terms at high PN orders
• Mapping eccentricity evolutions between numerical relativity and effective-one-body gravitational waveforms
• Gravitational memory: new results from post-Newtonian and self-force theory
• Neutron Stars in the Effective Fly-By Framework: $f$-Mode Re-summation
• High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary
• Gravitational waves from quasielliptic compact binaries in scalar-tensor theory to one-and-a-half post-Newtonian order
• Repeated Bursts: Gravitational Waves from Highly Eccentric Binaries
• Approximate helical symmetry in compact binaries
• General Fourier expansion of post-Newtonian binary dynamics based on a quasi-Keplerian framework
• Probing modified gravitational-wave dispersion with bursts from eccentric black-hole binaries