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。
英文摘要：
We probe the ability of various types of post-Newtonian(PN)-accurate circular templates to capture inspiral gravitational-wave (GW) signals from compact binaries having tiny orbital eccentricities. The GW signals are constructed by adapting the phasing formalism, available in T. Damour, A. Gopakumar, and B. R. Iyer, [Phys. Rev. D 70, 064028 (2004)], employing the orbital energy and the time-eccentricity to describe the orbital evolution. Using the fitting factor estimates, relevant for the initial LIGO, we show that circular templates, based on the adiabatic TaylorT1, complete adiabatic TaylorT1 and TaylorT4 approximants are unable to capture our GW signals from compact binaries having tiny residual orbital eccentricities. However, the 2PN-order circular inspiral templates based on the recently introduced TaylorEt approximant are found to be both effectual and faithful in capturing GWs from inspiralling compact binaries having moderate eccentricities and we provide physical explanations for our observations.
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…
Neutron star (NS) binaries formed dynamically may have significant eccentricities while emitting gravitational waves (GWs) in the LIGO/VIRGO band. We study tidal effects in such eccentric inspiralling NS binaries using a set of hybrid equations. The NS is modelled as a compressible ellipsoid, which can deform nonlinearly due to tidal forces, while the orbit evolution is treated with the post-Newtonian (PN) theory up to 2.5-PN order. We find that in general, the tidal interaction can accelerate the inspiral, and cause orbital frequency and phase shifts. For circular inspirals, our calculations …
Inspiraling compact binaries with non-negligible orbital eccentricities are plausible gravitational wave (GW) sources for the upcoming network of GW observatories. In this paper, we present two prescriptions to compute post-Newtonian (PN) accurate inspiral templates for such binaries. First, we adapt and extend the post-circular scheme of Yunes {\it et al.} [Phys. Rev. D 80, 084001 (2009)] to obtain a Fourier-domain inspiral approximant that incorporates the effects of PN-accurate orbital eccentricity evolution. This results in a fully analytic frequency-domain inspiral waveform with Newtonian…
I present an analytical fit to the duration of the inspiral of two point masses driven by gravitational-wave emission. The fit is accurate to within 3% over the entire range of initial eccentricities from 0 to 0.99999.
We provide a systematic analysis of the multipolar gravitational waveform, energy and angular momentum fluxes emitted by a nonspinning test particle orbiting a Kerr black hole along equatorial, eccentric orbits. These quantities are computed by numerically solving the Teukolsky equation in the time domain and are then used to test and improve the radiation reaction (and waveform) of an effective-one-body (EOB) model. Eccentricity is incorporated into EOB by replacing the quasi-circular Newtonian (or leading-order) prefactors in the EOB-factorized multipolar waveform (and fluxes) with their gen…
We model the inspiral of a compact stellar-mass object into a massive nonrotating black hole including all dissipative and conservative first-order-in-the-mass-ratio effects on the orbital motion. The techniques we develop allow inspirals with initial eccentricities as high as $e\sim0.8$ and initial separations as large as $p\sim 50$ to be evolved through many thousands of orbits up to the onset of the plunge into the black hole. The inspiral is computed using an osculating elements scheme driven by a hybridized self-force model, which combines Lorenz-gauge self-force results with highly accur…
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 …
We study the effect of tidal interaction between two compact bodies in an eccentric orbit. We assume the tidal fields to be static. Therefore, we ignore the dynamic tides and resonant excitations. Using the results, we find the analytical expression for the phase shift of the emitted gravitational wave. In the process, we find that in the leading order, the initial eccentricity $e_0$ and the dimensionless tidal deformability $Λ$ couple as $\sim e_0^nΛ$, where $n$ is a positive number. We only focus on the dominant contribution, i.e., $e_0^2Λ$. We also compute the accumulated dephasing for bina…
A waveform model for the eccentric binary black holes named SEOBNRE has been used to analyze the LIGO-Virgo's gravitational wave data by several groups. The accuracy of this model has been validated by comparing it with numerical relativity. However, SEOBNRE is a time-domain model, and the efficiency for generating waveforms is a bottleneck in data analysis. To overcome this disadvantage, we offer a reduced-order surrogate model for eccentric binary black holes based on the SEOBNRE waveforms. This surrogate model (SEOBNRE\_S) can simulate the complete inspiral-merger-ringdown waves with enough…
The coalescence of a stellar-mass compact object together with an intermediate-mass black hole, also known as intermediate-mass-ratio inspiral, is usually not expected to be a viable gravitational wave source for the current ground-based gravitational wave detectors, due to the generally lower frequency of such source. In this paper, we adopt the effective-one-body formalism as the equation of motion, and obtain the accurately calculated gravitational waveforms by solving the Teukolsky equation in frequency-domain. We point out that high frequency modes of gravitational waves can be excited by…
In general relativity, there is no dispersion in gravitational waves, while some modified gravity theories predict dispersion phenomena in the propagation of gravitational waves. In this paper, we demonstrate that this dispersion will induce an observable deviation of waveforms if the orbits have large eccentricities. The mechanism is that the waveform modes with different frequencies will be emitted at the same time due to the existence of eccentricity. During the propagation, because of the dispersion, the arrival time of different modes will be different, then produce the deviation and deph…
While there has been much success in understanding the orbital dynamics and gravitational wave emission of eccentric compact binaries in the post-Newtonian formalism, some problems still remain. The largest of these concerns hereditary effects: non-linear phenomena related to the scattering off of the background curved spacetime (tails) and to the generation of gravitational waves by gravitational waves (memory). Currently, these hereditary effects are only known numerically for arbitrary eccentricity through infinite sums of Bessel functions, with closed-form, analytic results only available …
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 for computing gravitational waveforms for the inspiral, merger and ringdown of non-spinning eccentric binary black hole systems. The inspiral waveform is computed using the post-Newtonian expansion and the merger waveform is computed by interpolating a small number of quasi-circular NR waveforms. The use of circular merger waveforms is possible because eccentric binaries circularize in the last few cycles before the merger, which we demonstrate up to mass ratio $q = m_1/m_2 = 3$. The complete model is calibrated to 23 numerical relativity (NR) simulations starting ~20…
Constraining initial orbital eccentricity of inspiral-dominated gravitational-wave events with an analytic approximant
The Chinese University of Hong Kong（香港中文大学）；Tata Institute of Fundamental Research（塔塔基础研究所）；Nikhef—National Institute for Subatomic Physics（NIKHEF-国家亚原子物理研究所）；KU Leuven（荷语鲁汶大学）；The Inter-University Centre for Astronomy and Astrophysics（大学间天文学与天体物理学中心）
Numerical simulations of low-mass black hole-neutron star mergers with moderate eccentricities
Institut für Physik und Astronomie, Universität Potsdam（波茨坦大学物理与天文学研究所）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理学研究所（爱因斯坦研究所））
Although the gravitational waves observed by advanced LIGO and Virgo are consistent with compact binaries in a quasi-circular inspiral prior to coalescence, eccentric inspirals are also expected to occur in Nature. Due to their complexity, we currently lack ready-to-use, analytic waveforms in the Fourier domain valid for sufficiently high eccentricity, and such models are crucial to coherently extract weak signals from the noise. We here take the first steps to derive and properly validate an analytic waveform model in the Fourier domain that is valid for inspirals of arbitrary orbital eccentr…
We present $\texttt{ENIGMA}$, a time domain, inspiral-merger-ringdown waveform model that describes non-spinning binary black holes systems that evolve on moderately eccentric orbits. The inspiral evolution is described using a consistent combination of post-Newtonian theory, self-force and black hole perturbation theory. Assuming eccentric binaries that circularize prior to coalescence, we smoothly match the eccentric inspiral with a stand-alone, quasi-circular merger, which is constructed using machine learning algorithms that are trained with quasi-circular numerical relativity waveforms. W…
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 …
It was recently suggested that the merger of $\sim30\,M_\odot$ primordial black holes (PBHs) may provide a significant number of events in gravitational-wave observatories over the next decade, if they make up an appreciable fraction of the dark matter. Here we show that measurement of the eccentricities of the inspiralling binary black holes can be used to distinguish these binaries from those produced by more traditional astrophysical mechanisms. These PBH binaries are formed on highly eccentric orbits and can then merge on timescales that in some cases are years or less, retaining some ecce…
Extreme Mass Ratio Inspirals (EMRIs) are important sources for space-borne gravitational wave detectors, such as LISA (Laser Interferometer Space Antenna) and TianQin. Previous EMRI rate studies have focused on the "loss cone" scenario, where stellar-mass black holes (sBHs) are scattered into highly eccentric orbits near the central massive black hole (MBH) via multi-body interaction. In this work, we calculate the rate of EMRIs of an alternative formation channel: EMRI formation assisted by the accretion flow around accreting massive black holes. In this scenario, sBHs and stars on inclined o…
[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 expression…
We study the stellar binary black holes (BBHs) inspiralling/merging in galactic nuclei based on our numerical method GNC. We find that $3-40\%$ of all new born BBHs will finally merge due to various dynamical effects. In a five year's mission, up to $10^4$, $10^5$, $\sim100$ of BBHs inspiralling/merging in galactic nuclei can be detected with SNR$>8$ in aLIGO, Einstein/DECIGO, TianQin/LISA/TaiJi, respectively. About tens are detectable in both LISA/TaiJi/TianQin and aLIGO. These BBHs have two unique characteristics: (1) Significant eccentricities. $1-3\%$, $2-7\%$, or $30-90\%$ of them is with…
Relativistic effects in extreme-mass-ratio inspirals within scalar clouds: Eccentric and inclined orbits
CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学高级技术学院物理系中心）；Gravitation Astroparticle Physics Amsterdam (GRAPPA), University of Amsterdam（阿姆斯特丹大学引力天体粒子物理学中心）
The localization and distance inference of gravitational waves are two crucial factors for dark sirens as precise probes of cosmology, astrophysics, and fundamental physics. In this Letter, for the first time we investigate the parameter estimation of gravitational waves emitted by the eccentric compact binaries in the mid-frequency (0.1--10 Hz) band. Based on the configuration of one cluster of DECIGO (B-DECIGO), we simulate five types of typical compact binaries in GWTC-3 with component mass ranging from $\mathcal{O}(1\sim100)~M_{\odot}$. For each type of binaries, we assign discrete eccentr…
Spin precession effects in the phasing formula of eccentric compact binary inspirals up to the second post-Newtonian order
Indian Institute of Technology Madras（印度马德拉斯理工学院）；Centre for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras（印度马德拉斯理工学院物理系弦、引力和宇宙学中心）；Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University（西北大学天体物理学交叉探索与研究中心）
Post-Newtonian inspiral waveform model for eccentric precessing binaries with higher-order modes and matter effects
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid（马德里自治大学理论物理研究所）；School of Physics and Astronomy and Institute for Gravitational Wave Astronomy, University of Birmingham（伯明翰大学物理与天文学院及引力波天文研究所）；Department of Physics, University of Maryland, College Park（马里兰大学帕克分校物理系）
The detection of a gravitational capture of a stellar-mass compact object by a massive black hole (MBH) will allow us to test gravity in the strong regime. These sources form via two-body relaxation, by exchanging energy and angular momentum, and inspiral in a slow, progressive way down to the final merger. The range of frequencies is localised in the range of millihertz in the case of MBH of masses $\sim 10^6\,M_{\odot}$, i.e. that of space-borne gravitational-wave observatories such as LISA. In this article I show that, depending on their orbital parameters, intermediate-mass ratios (IMRIs) …
The Fast and the Frame-Dragging: Efficient waveforms for asymmetric-mass eccentric equatorial inspirals into rapidly-spinning black holes
University of Birmingham（伯明翰大学）；University of Glasgow（格拉斯哥大学）；European Space Agency (ESA)（欧洲航天局（ESA））；University of Southampton（南安普顿大学）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）；NASA Marshall Space Flight Center（美国宇航局马歇尔太空飞行中心）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；National University of Singapore（新加坡国立大学）
本文提出了一种高效方法，用于生成非对称质量偏心赤道 inspirals 进入快速旋转黑洞的波形，支持偏心率 e < 0.9 和半焦距参数 p < 200，生成长时程 IMRI 波形，且在 100 毫秒内完成，具有 10^-5 的匹配度。
We present a new set of 95 numerical relativity simulations of non-precessing binary black holes (BBHs). The simulations sample comprehensively both black-hole spins up to spin magnitude of 0.9, and cover mass ratios 1 to 3. The simulations cover on average 24 inspiral orbits, plus merger and ringdown, with low initial orbital eccentricities $e<10^{-4}$. A subset of the simulations extends the coverage of non-spinning BBHs up to mass ratio $q=10$. Gravitational waveforms at asymptotic infinity are computed with two independent techniques, extrapolation, and Cauchy characteristic extraction. An…
Efficient Eccentric Effective-One-Body Dynamics via Near-Identity Averaging Transformations
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；University of Maryland（马里兰大学）；Niels Bohr Institute（尼尔斯·玻尔研究所）
We present the first systematic study of strong binary-single and binary-binary black hole interactions with the inclusion of general relativity. When including general relativistic effects in strong encounters, dissipation of orbital energy from gravitational waves (GWs) can lead to captures and subsequent inspirals with appreciable eccentricities when entering the sensitive frequency ranges of the LIGO and Virgo GW detectors. In this study, we perform binary-binary and binary-single scattering experiments with general relativistic dynamics up through the 2.5 post-Newtonian order included, bo…
The space gravitational wave detector LISA is expected to detect $\sim10^4$ of nearly monochromatic binaries, after $\sim 10$yr operation. We propose to measure the inspiral/outspiral binary fluxes in the frequency space, by processing tiny frequency drifts of these numerous binaries. Rich astrophysical information is encoded in the frequency dependencies of the two fluxes, and we can read the long-term evolution of white dwarf binaries, resulting in metamorphoses or disappearances. This measurement will thus help us to deepen our understanding on the strongly interacting exotic objects. Using…
The environment surrounding supermassive black holes (SMBHs) in galactic nuclei (GNs) is expected to harbour stellar-mass binary black hole (BBH) populations. These binaries were suggested to form a hierarchical triple system with the SMBH, and gravitational perturbations from the SMBH can enhance the mergers of BBHs through Lidov-Kozai (LK) oscillations. Previous studies determined the expected binary parameter distribution for this merger channel in single GNs. Here we account for the different spatial distribution and mass distribution models of BBHs around SMBHs and perform direct high-pre…
