Convergence of Fourier-domain templates for inspiraling eccentric compact binaries

Abstract

The space-based detector LISA may observe gravitational waves from the early inspiral of stellar-mass 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 $e_0$ ("post-circular" expansion). We conventionally define $e_0$ as the eccentricity corresponding to an orbital frequency of $5\text{ mHz}$, and we study the convergence properties of frequency-domain inspiral templates that are accurate up to 2PN and order $e_0^6$ in eccentricity. 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 $e_0^2$ or higher in the phasing.

arXiv comment13 pages, 4 figures

References in corpus (45)

• The Confrontation between General Relativity and Experiment
• Testing General Relativity with Present and Future Astrophysical Observations
• Physics, Astrophysics and Cosmology with Gravitational Waves
• Black holes, gravitational waves and fundamental physics: a roadmap
• The construction and use of LISA sensitivity curves
• Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
• Gravitational Wave Tests of General Relativity with Ground-Based Detectors and Pulsar Timing Arrays
• The promise of multi-band gravitational wave astronomy
• Estimating spinning binary parameters and testing alternative theories of gravity with LISA
• Eccentric Black Hole Mergers Forming in Globular Clusters
• Are merging black holes born from stellar collapse or previous mergers?
• Post-Newtonian Dynamics in Dense Star Clusters: Formation, Masses, and Merger Rates of Highly-Eccentric Black Hole Binaries
• Post-Newtonian Dynamics in Dense Star Clusters: Highly-Eccentric, Highly-Spinning, and Repeated Binary Black Hole Mergers
• Eccentric Black Hole Mergers in Dense Star Clusters: The Role of Binary-Binary Encounters
• Measuring the binary black hole mass spectrum with an astrophysically motivated parameterization
• Spin orientations of merging black holes formed from the evolution of stellar binaries
• Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits
• Where are LIGO's Big Black Holes?
• Post-Circular Expansion of Eccentric Binary Inspirals: Fourier-Domain Waveforms in the Stationary Phase Approximation
• Constructing Gravitational Waves from Generic Spin-Precessing Compact Binary Inspirals
• Phasing of gravitational waves from inspiralling eccentric binaries
• Black Hole Mergers From Globular Clusters Observable by LISA I: Eccentric Sources Originating From Relativistic $N$-body Dynamics
• Constraining Formation Models of Binary Black Holes with Gravitational-Wave Observations
• Distinguishing Between Formation Channels for Binary Black Holes with LISA
• eLISA eccentricity measurements as tracers of binary black hole formation
• Resonant-plane locking and spin alignment in stellar-mass black-hole binaries: a diagnostic of compact-binary formation
• Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order
• Constraining stellar binary black hole formation scenarios with eLISA eccentricity measurements
• Accuracy of inference on the physics of binary evolution from gravitational-wave observations
• Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order
• Frequency and time domain inspiral templates for comparable mass compact binaries in eccentric orbits
• The Black Hole Mass Function from Gravitational Wave Measurements
• Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order
• Distinguishing compact binary population synthesis models using gravitational-wave observations of coalescing binary black holes
• Multiband gravitational-wave event rates and stellar physics
• Black Hole Mergers From Globular Clusters Observable by LISA II: Resolved Eccentric Sources and the Gravitational Wave Background
• The binary black-hole dynamics at the third-and-a-half post-Newtonian order in the ADM-formalism
• Constraining alternative theories of gravity by gravitational waves from precessing eccentric compact binaries with LISA
• A Fourier Domain Waveform for Non-Spinning Binaries with Arbitrary Eccentricity
• Gravitational waves from eccentric compact binaries: Reduction in signal-to-noise ratio due to nonoptimal signal processing
• Parameter estimation for inspiraling eccentric compact binaries including pericenter precession
• Ready-to-use Fourier domain templates for compact binaries inspiraling along moderately eccentric orbits
• Expanding the LISA Horizon from the Ground
• How Post-Newtonian Dynamics Shape the Distribution of Stationary Binary Black Hole LISA Sources in nearby Globular Clusters
• Eccentric first post-Newtonian waveforms for compact binaries in frequency domain with Hansen coefficients

Cited by in corpus (20)

• Effective-one-body multipolar waveforms for eccentric binary black holes with non-precessing spins
• Eccentric binary black hole surrogate models for the gravitational waveform and remnant properties: comparable mass, nonspinning case
• Probing Fundamental Physics with Gravitational Waves: The Next Generation
• The Gravitational-Wave Physics II: Progress
• Validating the Effective-One-Body Numerical-Relativity Waveform Models for Spin-aligned Binary Black Holes along Eccentric Orbits
• Are stellar-mass black-hole binaries too quiet for LISA?
• A higher-multipole gravitational waveform model for an eccentric binary black holes based on the effective-one-body-numerical-relativity formalism
• Accurate waveforms for eccentric, aligned-spin binary black holes: The multipolar effective-one-body model SEOBNRv5EHM
• Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform
• Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory
• ESIGMAHM: An Eccentric, Spinning inspiral-merger-ringdown waveform model with Higher Modes for the detection and characterization of binary black holes
• Residual eccentricity of inspiralling orbits at the gravitational-wave detection threshold: Accurate estimates using post-Newtonian theory
• 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
• The minimum measurable eccentricity from gravitational waves of LISA massive black hole binaries
• Time-domain phenomenological multipolar waveforms for aligned-spin binary black holes in elliptical orbits
• Data Analysis Implications of Moderately Eccentric Gravitational Waves
• Importance of eccentricities in parameter estimation of compact binary inspirals with decihertz gravitational-wave detectors
• Spin effects in the phasing formula of eccentric compact binary inspirals up to the third post-Newtonian order
• Biased parameter inference of eccentric, spin-precessing binary black holes