51 pages, 2 figures. Invited chapter for "Handbook of Gravitational Wave Astronomy" (Eds. C. Bambi, S. Katsanevas and K. Kokkotas; Springer Singapore, 2021. V2: corrects typos and updates references
To enable detection and maximise the physics output of gravitational wave observations from compact binary systems, it is crucial the availability of accurate waveform models. The present work aims at giving an overview for non-experts of the (inspiral) waveforms used in the gravitational wave data analysis for compact binary coalescence. We first provide the essential elements of gravitational radiation physics within a simple Newtonian orbital dynamics and the linearized gravity theory, describing the adiabatic approximation applied to binary systems: the key element to construct the theoretical gravitational waveforms in practice. We next lay out the gravitational waveforms in the post-Newtonian approximation to General Relativity, and highlight the basic input for the inspiral waveform of the slowly evolving, spinning, nonprecessing, quasicircular binary black holes, namely, post-Newtonian energy, fluxes and the (absorption-corrected) balance equation. The post-Newtonian inspiral templates are then presented both in the time and frequency domain. Finally, including the merger and subsequent ringdown phase, we briefly survey the two families of the full waveform models of compact binary mergers currently implemented in LSC Algorithm Library Simulation: the effective-one-body approach and the phenomenological frequency domain model.
Emission of anisotropic gravitational radiation from compact binary system leads to a flux of linear momentum. This results in the recoil of the system. We investigate the rate of loss of Linear momentum flux in the far zone of the source using various mass type and current type multipole moments for inspiralling compact binary mergers in quasi-elliptical orbits at 2.5 Post Newtonian order. We compute the linear momentum flux accurate up to $\mathcal{O}(e_t)$ in harmonic coordinate. A 2.5 Post Newtonian Quasi-Keplarian representation of the parametric solution to the Post Newtonian equation of…
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 …
The post-Newtonian approximation is useful to discuss gravitational waveforms for binary inspirals. In this note, for retrograde circular orbits in the equatorial plane, we discuss the region of validity of the post-Newtonian approximation by using the gravitational energy flux derived numerically and analytically in the black hole perturbation approach. It is found that the edge of the allowable region behaves quite intricately, including prograde orbits even if we treat higher post-Newtonian orders.
Searches for gravitational waves (GWs) from binary black holes using interferometric GW detectors require the construction of template banks for performing matched filtering while analyzing the data. Placement of templates over the parameter space of binaries, as well as coincidence tests of GW triggers from multiple detectors make use of the definition of a metric over the space of gravitational waveforms. Although recent searches have employed waveform templates coherently describing the inspiral, merger and ringdown (IMR) of the coalescence, the metric used in the template banks and coincid…
On the ability of various circular inspiral templates to capture inspiral gravitational waves from compact binaries having tiny orbital eccentricities
我们探讨了各种类型的后牛顿（PN）精确的圆形模板捕捉inspiral引力波（GW）信号的能力，从紧凑的双星具有微小的轨道偏心率。GW信号通过适应T. Damour，A. Gopakumar和B. R. Iyer，[Phys.Rev.D70，064028（2004）]，采用轨道能量和时间偏心率来描述轨道演化。使用与初始LIGO相关的拟合因子估计，我们表明基于绝热TaylorT1，完全绝热TaylorT1和TaylorT4近似的圆形模板无法从具有微小剩余轨道偏心率的紧凑双星中捕获我们的GW信号。然而，基于最近引入的泰勒近似式的2PN阶圆形内旋模板被发现在从具有中等偏心率的内旋致密双星中捕获GW方面既有效又忠实，并且我们为我们的观察提供了物理解释。
Observations of transient gravitational wave (GW) events with non-negligible orbital eccentricity can be highly rewarding from astrophysical considerations. Ready-to-use fully analytic frequency domain inspiral GW templates are crucial ingredients to construct eccentric inspiral-merger-ringdown waveform families, required for the detection of such GW events. It turns out that a fully analytic, post-Newtonian (PN) accurate frequency domain inspiral template family, which uses certain post-circular approximation, may only be suitable to model events with initial eccentricities $e_0 \leq 0.2$.We …
Spherical harmonic modes of gravitational waveforms for inspiraling compact binaries in eccentric orbits from post-Newtonian (PN) theory accurate to third post-Newtonian order, and those extracted from numerical relativity (NR) simulations for binary black holes (BBHs) are compared. We combine results from the two approaches (PN and NR) to construct time-domain hybrid waveforms that describe the complete evolution of BBH mergers through inspiral-merger-ringdown (IMR) stages. These hybrids are then used in constructing a fully analytical dominant mode ($\ell$=2, $|m|$=2) eccentric IMR model. A …
An extreme mass ratio inspiral takes place when a compact stellar object is inspiraling into a supermassive black hole due to gravitational radiation reaction. Gravitational waves (GWs) from this system can be calculated using the Teukolsky equation (TE). In our case, we compute the asymptotic GW fluxes of a spinning body orbiting a Kerr black hole by solving numerically the TE both in time and frequency domain. Our ultimate goal is to produce GW templates for space-based detectors such as LISA.
We derive analytic expressions that provide Fourier domain gravitational wave (GW) response function for compact binaries inspiraling along moderately eccentric orbits. These expressions include amplitude corrections to the two GW polarization states that are accurate to the first post-Newtonian (PN) order. Additionally, our fully 3PN accurate GW phase evolution incorporates eccentricity effects up to sixth order at each PN order. Further, we develop a prescription to incorporate analytically the effects of 3PN accurate periastron advance in the GW phase evolution. This is how we provide a rea…
Accuracy of the post-Newtonian approximation. II. Optimal asymptotic expansion of the energy flux for quasicircular, extreme mass-ratio inspirals into a Kerr black hole
The early inspiral phase of a compact binary coalescence is well modelled by the post-Newtonian (PN) approximation to the orbital energy and gravitational wave flux. The transition from the inspiral phase to the plunge can be defined by the minimum energy circular orbit (MECO). In the extreme mass-ratio limit, up to the highest PN order known, the PN energy equals the energy of the exact Kerr solution. However, for comparable-mass systems the MECO of the PN energy does not exist when bodies have large spins. By including the exact Kerr limit and recently published post-Newtonian terms we extra…
We study the validity of inspiral templates in gravitational wave data analysis with Advanced LIGO sensitivity for low mass binary black holes with total masses of $M \leq 30 Msun$. We mainly focus on the nonspinning system. As our complete inspiral-merger-ringdown waveform model ($IMR$), we assume the phenomenological model, "PhenomA", and define our inspiral template model ($Imerg$) by taking the inspiral part into account from $IMR$ up to the merger frequency (fmerg). We first calculate the {\it true} statistical uncertainties using $IMR$ signals and $IMR$ templates. Next, using $IMR$ signa…
We revisit the accuracy of the post-Newtonian (PN) approximation and its region of validity for quasi-circular orbits of a point particle in the Kerr spacetime, by using an analytically known highest post-Newtonian order gravitational energy flux and accurate numerical results in the black hole perturbation approach. It is found that regions of validity become larger for higher PN order results although there are several local maximums in regions of validity for relatively low-PN order results. This might imply that higher PN order calculations are also encouraged for comparable-mass binaries.
Gravitational waves from compact binaries inspiralling along post-Newtonian accurate eccentric orbits: Data analysis implications
沿偏心轨道旋转的致密双星是地基激光干涉仪的引力波源。我们探索的损失，在事件发生率时，从紧凑的二进制文件，沿着后牛顿精确偏心轨道与某些明显的非最佳搜索模板的灵感搜索GW。对于本分析，具有2.5后牛顿精确轨道演化的GW信号按照[T. Damour，A. Gopakumar和B. R. Iyer，Phys. Rev. \textbf{70}，064028（2004）]。我们证明了搜索模板，模型在规范不变的方式GWs从紧凑的二进制inspirling qudrupolar辐射反应下沿2 PN精确的圆形轨道是非常有效的捕捉我们有点现实的GW信号。然而，基于绝热、完全绝热和规范依赖的完全非绝热近似的三种类型的搜索模板在[P. Ajith，B. R.伊耶角A. K. Robinson和B. S. Sathyaprakash，%``A new class of post-Newtonian approximants to the dynamics of inspiralling compact binaries：Test-mass in the Schwarzschild spacetime，'' Phys. Rev. D { \bf 71}，044029（2005）]，与四极辐射反应下的圆形内旋相关，发现在捕获上述偏心信号方面效率低下。我们的结论是，将需要进一步的调查，以探测各种类型的PN准确的…
We present a prescription to compute the time-domain gravitational wave (GW) polarization states associated with spinning compact binaries inspiraling along quasi-circular orbits. We invoke the orbital angular momentum ${\bf L}$ rather than its Newtonian counterpart ${\bf L_{\rm N}}$ to describe the orbits and the two spin vectors are freely specified in the source frame associated with the initial direction of the total angular momentum. We discuss the various implications of our approach.
In this work we complete the spin-dependent conservative dynamics of inspiralling compact binaries at the fourth post-Newtonian order, and in particular the derivation of the next-to-next-to-leading order spin-squared interaction potential. We derive the physical equations of motion of the position and the spin from a direct variation of the action. Further, we derive the quadratic-in-spin Hamiltonians, as well as their expressions in the center-of-mass frame. We construct the conserved integrals of motion, which form the Poincaré algebra. This construction provided a consistency check for the…
This paper is motivated by the need to improve the post-Newtonian (PN) amplitude accuracy of waveforms for gravitational waves generated by inspiralling compact binaries, both for use in data analysis and in the comparison between post-Newtonian approximations and numerical relativity computations. It presents: (i) the non-linear couplings between multipole moments of general post-Newtonian matter sources up to order 3.5PN, including all contributions from tails, tails-of-tails and the non-linear memory effect; and (ii) the source mass-type octupole moment of (non-spinning) compact binaries up…
Gravitational waves from inspiralling compact binaries: Angular momentum flux, evolution of the orbital elements and the wave form to the second post-Newtonian order
The tidal deformations of neutron stars within an inspiraling compact binary alter the orbital dynamics, imprinting a signature on the gravitational wave signal. Modeling this signal could be done with numerical-relativity simulations, but these are too computationally expensive for many applications. Analytic post-Newtonian treatments are limited by unknown higher-order nontidal terms. This paper further builds upon the "tidal splicing" model in which post-Newtonian tidal terms are "spliced" onto numerical relativity simulations of black-hole binaries. We improve on previous treatments of tid…
We use equations of motion containing gravitational radiation-reaction terms through 4.5 post-Newtonian order to calculate the late-time eccentricities of inspiraling binary systems of non-spinning compact bodies as they cross the detection threshold of ground-based gravitational-wave interferometers. The initial eccentricities can be as large as 0.999. We find that the final eccentricities are systematically smaller than those predicted by the leading quadrupole approximation, by as much as 30 percent for a 300 solar mass binary crossing the LIGO/Virgo detection threshold at 10 Hz, or eight p…
