Data-driven extraction, phenomenology and modeling of eccentric harmonics in binary black hole merger waveforms

Abstract

Newtonian and post-Newtonian (PN) calculations suggest that each spherical harmonic mode of the gravitational waveforms (radiation) emitted by eccentric binaries can be further decomposed into several eccentricity-induced modes (indexed by $j=1$ to $j=\infty$), referred to as eccentric harmonics. These harmonics exhibit monotonically time-varying amplitudes and instantaneous frequencies, unlike the full eccentric spherical harmonic modes. However, computing or extracting these harmonics are not straightforward in current numerical relativity (NR) simulations and eccentric waveform models. To address this, Patterson \textit{et al} have developed a framework to extract the eccentric harmonics directly from effective-one-body formalism waveforms. In this paper, we build on the ideas presented in Patterson \textit{et al} and propose a data-driven framework, utilizing singular-value decomposition (SVD), that incorporates additional features based on PN intuition to ensure monotonicity in the extracted harmonics. We further demonstrate that the phase (frequency) of these harmonics is simply $j{\varphi }_{\lambda }+{\varphi }_{\mathrm{ecc}}$ ($j{f}_{\lambda }+f_{\mathrm{ecc}}$) where ${\varphi }_{\lambda }$ ($f_{\lambda }$) is related to the secular orbital phase (frequency) and ${\varphi }_{\mathrm{ecc}}$ ($f_{\mathrm{ecc}}$) is an additional phase (frequency) that only depends on the eccentricity. We also provide simple analytical fits to obtain the harmonics as a function of the mean anomaly. These relations may prove useful in constructing faithful models that can be employed in cheap and efficient searches and parameter estimation of eccentric mergers. Our framework is modular and can be extended for any other eccentric waveform models or simulation frameworks. The framework is available through the \texttt{gwMiner} package.

References in corpus (66)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run
• Inspiral, merger and ring-down of equal-mass black-hole binaries
• Eccentric Black Hole Mergers Forming in Globular Clusters
• GW190521: orbital eccentricity and signatures of dynamical formation in a binary black hole merger signal
• Post-Newtonian Dynamics in Dense Star Clusters: Highly-Eccentric, Highly-Spinning, and Repeated Binary Black Hole Mergers
• Post-Newtonian Dynamics in Dense Star Clusters: Formation, Masses, and Merger Rates of Highly-Eccentric Black Hole Binaries
• Eccentric Black Hole Mergers in Dense Star Clusters: The Role of Binary-Binary Encounters
• Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits
• AGN as Potential Factories for Eccentric Black Hole Mergers
• Post-Circular Expansion of Eccentric Binary Inspirals: Fourier-Domain Waveforms in the Stationary Phase Approximation
• Phasing of gravitational waves from inspiralling eccentric binaries
• A waveform model for eccentric binary black hole based on effective-one-body-numerical-relativity (EOBNR) formalism
• A faithful analytical effective one body waveform model for spin-aligned, moderately eccentric, coalescing black hole binaries
• A Surrogate Model of Gravitational Waveforms from Numerical Relativity Simulations of Precessing Binary Black Hole Mergers
• Eccentric, nonspinning, inspiral, Gaussian-process merger approximant for the detection and characterization of eccentric binary black hole mergers
• 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
• GW190521 as a dynamical capture of two nonspinning black holes
• Effective-one-body multipolar waveforms for eccentric binary black holes with non-precessing spins
• Gravitational-wave phasing for low-eccentricity inspiralling compact binaries to 3PN order
• Third post-Newtonian angular momentum flux and the secular evolution of orbital elements for inspiralling compact binaries in quasi-elliptical orbits
• An eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory
• Complete waveform model for compact binaries on eccentric orbits
• Eccentric binary black hole surrogate models for the gravitational waveform and remnant properties: comparable mass, nonspinning case
• 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
• Foundations of an effective-one-body model for coalescing binaries on eccentric orbits
• Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral
• Phenomenology of amplitude-corrected post-Newtonian gravitational waveforms for compact binary inspiral. I. Signal-to-noise ratios
• Measuring orbital eccentricity and periastron advance in quasi-circular black hole simulations
• A first survey of spinning eccentric black hole mergers: Numerical relativity simulations, hybrid waveforms, and parameter estimation
• Defining eccentricity for gravitational wave astronomy
• Faithful effective-one-body waveform of small-mass-ratio coalescing black hole binaries: the eccentric, nonspinning, case
• Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory
• Ready-to-use Fourier domain templates for compact binaries inspiraling along moderately eccentric orbits
• Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform
• Higher harmonics increase LISA's mass reach for supermassive black holes
• New Avenue for Accurate Analytical Waveforms and Fluxes for Eccentric Compact Binaries
• Adding eccentricity to quasicircular binary-black-hole waveform models
• A Rosetta Stone for eccentric gravitational waveform models
• Spin effects in gravitational waveforms and fluxes for binaries on eccentric orbits to the third post-Newtonian order
• Numerically generated quasi-equilibrium orbits of black holes: Circular or eccentric?
• An efficient iterative method to reduce eccentricity in numerical-relativity simulations of compact binary inspiral
• Post-Newtonian Quasicircular Initial Orbits for Numerical Relativity
• Unveiling the merger structure of black hole binaries in generic planar orbits
• Effective-One-Body Numerical-Relativity waveform model for Eccentric spin-precessing binary black hole coalescence
• High accuracy post-Newtonian and numerical relativity comparisons involving higher modes for eccentric binary black holes and a dominant mode eccentric inspiral-merger-ringdown model
• Simple procedures to reduce eccentricity of binary black hole simulations
• Proposal for Determining the Total Masses of Eccentric Binaries Using Signature of Periastron Advance in Gravitational Waves
• ESIGMAHM: An Eccentric, Spinning inspiral-merger-ringdown waveform model with Higher Modes for the detection and characterization of binary black holes
• Spin effects in Spherical Harmonic Modes of Gravitational Waves from Eccentric Compact Binary Inspirals
• Tidally-Induced Apsidal Precession in Double White Dwarfs: a new mass measurement tool with LISA
• Gravitational-wave inference for eccentric binaries: the argument of periapsis
• Orbital eccentricity in general relativity from catastrophe theory
• Numerical relativity higher order gravitational waveforms of eccentric, spinning, non-precessing binary black hole mergers
• Impact of eccentricity and mean anomaly in numerical relativity mergers
• New search pipeline for gravitational waves with higher-order modes using mode-by-mode filtering
• Fast marginalization algorithm for optimizing gravitational wave detection, parameter estimation and sky localization
• Phenomenological relationship between eccentric and quasi-circular orbital binary black hole waveform
• Improved inspiral-merger-ringdown model for BBHs on elliptical orbits
• Mapping eccentricity evolutions between numerical relativity and effective-one-body gravitational waveforms
• Effective chirp mass captures the inspiral frequency evolution of the non-spinning eccentric compact binary
• Probing eccentric higher-order modes through an effective chirp mass model

Cited by in corpus (3)

• Testing the nature of GW200105 by probing the frequency evolution of eccentricity
• Biased parameter inference of eccentric, spin-precessing binary black holes
• Chase Orbits, not Time: A Scalable Paradigm for Long-Duration Eccentric Gravitational-Wave Surrogates