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Register a new userFoundations of an effective-one-body model for coalescing binaries on eccentric orbits
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We develop the foundations of an effective-one-body (EOB) model for eccentric binary coalescences that includes the conservative dynamics, radiation reaction, and gravitational waveform modes from the inspiral and the merger-ringdown signals. We use the same approach as is commonly employed in black-hole perturbation theory by introducing a relativistic parameterization of the dynamics that is defined by the orbital geometry and consists of a set of phase variables and quantities that evolve only due to gravitational radiation reaction. Specializing to nonspinning binaries, we derive the EOB evolution equations and compute the binarys radiative multipole moments that determine the gravitational waves through a decomposition into the fundamental frequencies of the motion. The major differences between our treatment and the quasi-Keplerian approach often used in post-Newtonian (PN) calculations are that the orbital parameters describe strong-field dynamics, and that expressing the multipole moments in terms of the frequencies simplifies the calculations and also results in an unambiguous orbit-averaging operation. While our description of the conservative dynamics is fully relativistic, we limit explicit derivations in the radiative sector to 1.5PN order for simplicity. This already enables us to establish methods for computing both instantaneous and hereditary contributions to the gravitational radiation in EOB coordinates that have straightforward extensions to higher PN order. The weak-field, small eccentricity limit of our results for the orbit-averaged fluxes of energy and angular momentum agrees with known PN results when expressed in terms of gauge-invariant quantities. We further address considerations for the numerical implementation of the model and the completion of the waveforms to include the merger and ringdown signals, and provide illustrative results.
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We present a time domain waveform model that describes the inspiral-merger-ringdown (IMR) of compact binary systems whose components are non-spinning, and which evolve on orbits with low to moderate eccentricity. The inspiral evolution is described using third order post-Newtonian equations both for the equations of motion of the binary, and its far-zone radiation field. This latter component also includes instantaneous, tails and tails-of-tails contributions, and a contribution due to non-linear memory. This framework reduces to the post-Newtonian approximant TaylorT4 at third post-Newtonian order in the zero eccentricity limit. To improve phase accuracy, we incorporate higher-order post-Newtonian corrections for the energy flux of quasi-circular binaries and gravitational self-force corrections to the binding energy of compact binaries. This enhanced inspiral evolution prescription is combined with an analytical prescription for the merger-ringdown evolution using a catalog of numerical relativity simulations. This IMR waveform model reproduces effective-one-body waveforms for systems with mass-ratios between 1 to 15 in the zero eccentricity limit. Using a set of eccentric numerical relativity simulations, not used during calibration, we show that our eccentric model accurately reproduces the features of eccentric compact binary coalescence throughout the merger. Using this model we show that the gravitational wave transients GW150914 and GW151226 can be effectively recovered with template banks of quasi-circular, spin-aligned waveforms if the eccentricity $e_0$ of these systems when they enter the aLIGO band at a gravitational wave frequency of 14 Hz satisfies $e_0^{rm GW150914}leq0.15$ and $e_0^{rm GW151226}leq0.1$.
While most binary inspirals are expected to have circularized before they enter the LIGO/Virgo frequency band, a small fraction of those binaries could have non-negligible orbital eccentricity depending on their formation channel. Hence, it is important to accurately model eccentricity effects in waveform models used to detect those binaries, infer their properties, and shed light on their astrophysical environment. We develop a multipolar effective-one-body (EOB) eccentric waveform model for compact binaries whose components have spins aligned or anti-aligned with the orbital angular momentum. The waveform model contains eccentricity effects in the radiation-reaction force and gravitational modes through second post-Newtonian (PN) order, including tail effects, and spin-orbit and spin-spin couplings. We recast the PN-expanded, eccentric radiation-reaction force and modes in factorized form so that the newly derived terms can be directly included in the state-of-the-art, quasi-circular--orbit EOB model currently used in LIGO/Virgo analyses (i.e., the SEOBNRv4HM model).
We construct a new factorized waveform including $(l,|m|)=(2,2),(2,1),(3,3),(4,4)$ modes based on effective-one-body (EOB) formalism, which is valid for spinning binary black holes (BBH) in general equatorial orbit. When combined with the dynamics of $texttt{SEOBNRv4}$, the $(l,|m|)=(2,2)$ mode waveform generated by this new waveform can fit the original $texttt{SEOBNRv4}$ waveform very well in the case of a quasi-circular orbit. We have calibrated our new waveform model to the Simulating eXtreme Spacetimes (SXS) catalog. The comparison is done for BBH with total mass in $(20,200)M_odot$ using Advanced LIGO designed sensitivity. For the quasi-circular cases we have compared our $(2,2)$ mode waveforms to the 281 numerical relativity (NR) simulations of BBH along quasi-circular orbits. All of the matching factors are bigger than 98%. For the elliptical cases, 24 numerical relativity simulations of BBH along an elliptic orbit are used. For each elliptical BBH system, we compare our modeled gravitational polarizations against the NR results for different combinations of the inclination angle, the initial orbit phase and the source localization in the sky. We use the the minimal matching factor respect to the inclination angle, the initial orbit phase and the source localization to quantify the performance of the higher modes waveform. We found that after introducing the high modes, the minimum of the minimal matching factor among the 24 tested elliptical BBHs increases from 90% to 98%. Following our previous $texttt{SEOBNRE}$ waveform model, we call our new waveform model $texttt{SEOBNREHM}$. Our $texttt{SEOBNREHM}$ waveform model can match all tested 305 SXS waveforms better than 98% including highly spinning ($chi=0.99$) BBH, highly eccentric ($eapprox0.15$) BBH and large mass ratio ($q=10$) BBH.
We present TEOBResumS, a new effective-one-body (EOB) waveform model for nonprecessing (spin-aligned) and tidally interacting compact binaries.Spin-orbit and spin-spin effects are blended together by making use of the concept of centrifugal EOB radius. The point-mass sector through merger and ringdown is informed by numerical relativity (NR) simulations of binary black holes (BBH) computed with the SpEC and BAM codes. An improved, NR-based phenomenological description of the postmerger waveform is developed.The tidal sector of TEOBResumS describes the dynamics of neutron star binaries up to merger and incorporates a resummed attractive potential motivated by recent advances in the post-Newtonian and gravitational self-force description of relativistic tidal interactions. Equation-of-state dependent self-spin interactions (monopole-quadrupole effects) are incorporated in the model using leading-order post-Newtonian results in a new expression of the centrifugal radius. TEOBResumS is compared to 135 SpEC and 19 BAM BBH waveforms. The maximum unfaithfulness to SpEC data $bar{F}$ -- at design Advanced-LIGO sensitivity and evaluated with total mass $M$ varying between $10M_odot leq M leq 200 M_odot$ --is always below $2.5 times 10^{-3}$ except for a single outlier that grazes the $7.1 times 10^{-3}$ level. When compared to BAM data, $bar{F}$ is smaller than $0.01$ except for a single outlier in one of the corners of the NR-covered parameter space, that reaches the $0.052$ level.TEOBResumS is also compatible, up to merger, to high end NR waveforms from binary neutron stars with spin effects and reduced initial eccentricity computed with the BAM and THC codes. The model is designed to generate accurate templates for the analysis of LIGO-Virgo data through merger and ringdown. We demonstrate its use by analyzing the publicly available data for GW150914.
Compact objects inspiraling into supermassive black holes, known as extreme-mass-ratio inspirals, are an important source for future space-borne gravitational-wave detectors. When constructing waveform templates, usually the adiabatic approximation is employed to treat the compact object as a test particle for a short duration, and the radiation reaction is reflected in the changes of the constants of motion. However, the mass of the compact object should have contributions to the background. In the present paper, employing the effective-one-body formalism, we analytically calculate the trajectories of a compact object around a massive Kerr black hole with generally three-dimensional orbits and express the fundamental orbital frequencies in explicit forms. In addition, by constructing an approximate constant similar to the Carter constant, we transfer the dynamical quantities such as energy, angular momentum, and the Carter constant to the semilatus rectum, eccentricity, and orbital inclination with mass-ratio corrections. The linear mass-ratio terms in the formalism may not be sufficient for accurate waveforms, but our analytical method for solving the equations of motion could be useful in various approaches to building waveform models.
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