Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order

Abstract

[abridged] Although gravitational radiation causes inspiralling compact binaries to circularize, a variety of astrophysical scenarios suggest that binaries might have small but nonnegligible orbital eccentricities when they enter the low-frequency bands of ground and space-based gravitational-wave detectors. If not accounted for, even a small orbital eccentricity can cause a potentially significant systematic error in the mass parameters of an inspiralling binary. Gravitational-wave search templates typically rely on the quasi-circular approximation, which provides relatively simple expressions for the gravitational-wave phase to 3.5 post-Newtonian (PN) order. The quasi-Keplerian formalism provides an elegant but complex description of the post-Newtonian corrections to the orbits and waveforms of inspiralling binaries with any eccentricity. Here we specialize the quasi-Keplerian formalism to binaries with low eccentricity. In this limit the non-periodic contribution to the gravitational-wave phasing can be expressed explicitly as simple functions of frequency or time, with little additional complexity beyond the well-known formulas for circular binaries. These eccentric phase corrections are computed to 3PN order and to leading order in the eccentricity for the standard PN approximants. For a variety of systems these eccentricity corrections cause significant corrections to the number of gravitational wave cycles that sweep through a detector's frequency band. This is evaluated using several measures, including a modification of the useful cycles. We also evaluate the role of periodic terms that enter the phasing and discuss how they can be incorporated into some of the PN approximants. While the eccentric extension of the PN approximants is our main objective, this work collects a variety of results that may be of interest to others modeling eccentric relativistic binaries.

49 pages, 4 figures. Submitted to Phys. Rev. D. Supplementary materials available at http://link.aps.org/supplemental/10.1103/PhysRevD.93.124061. V2: minor updates to match published version

References in corpus (40)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors
• Gravitational waves from scattering of stellar-mass black holes in galactic nuclei
• Model Waveform Accuracy Standards for Gravitational Wave Data Analysis
• Phenomenological template family for black-hole coalescence waveforms
• Reducing orbital eccentricity in binary black hole simulations
• High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants
• Accurate and efficient waveforms for compact binaries on eccentric orbits
• 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
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Circularization and Final Spin in Eccentric Binary Black Hole Inspirals
• Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order
• Eccentric binary black-hole mergers: The transition from inspiral to plunge in general relativity
• Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral
• Tail effects in the third post-Newtonian gravitational wave energy flux of compact binaries in quasi-elliptical orbits
• Observing complete gravitational wave signals from dynamical capture binaries
• Projected Constraints on Scalarization with Gravitational Waves from Neutron Star Binaries
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• Computing inspirals in Kerr in the adiabatic regime. I. The scalar case
• Research Update on Extreme-Mass-Ratio Inspirals
• Measuring orbital eccentricity and periastron advance in quasi-circular black hole simulations
• Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms
• Conservative self-force correction to the innermost stable circular orbit: comparison with multiple post-Newtonian-based methods
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Black Hole Binaries in Galactic Nuclei and Gravitational Wave Sources
• Comparison between numerical relativity and a new class of post-Newtonian gravitational-wave phase evolutions: the non-spinning equal-mass case
• An efficient iterative method to reduce eccentricity in numerical-relativity simulations of compact binary inspiral
• Detecting gravitational waves from highly eccentric compact binaries
• Eccentric mergers of black holes with spinning neutron stars
• The detectability of eccentric compact binary coalescences with advanced gravitational-wave detectors
• Initial data for binary neutron stars with adjustable eccentricity
• Inspiral of Generic Black Hole Binaries: Spin, Precession, and Eccentricity
• Full-analytic frequency-domain 1pN-accurate gravitational wave forms from eccentric compact binaries
• Accurate and efficient gravitational waveforms for certain galactic compact binaries
• Gravitational waves from spinning eccentric binaries
• Gravitational waves from binaries on unbound orbits
• Searching for gravitational-wave signals emitted by eccentric compact binaries using a non-eccentric template bank: implications for ground-based detectors
• Gravitational waves from compact binaries inspiralling along post-Newtonian accurate eccentric orbits: Data analysis implications

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• Complete waveform model for compact binaries on eccentric orbits
• Foundations of an effective-one-body model for coalescing binaries on eccentric orbits
• Ready-to-use Fourier domain templates for compact binaries inspiraling along moderately eccentric orbits
• $N-$body dynamics of Intermediate mass-ratio inspirals in globular clusters
• Modeling Mergers of Known Galactic Systems of Binary Neutron Stars