Adrian S. Hamers
I present a numerical fit to the peak harmonic gravitational wave frequency emitted by an eccentric binary system in the post-Newtonian approximation. This fit significantly improves upon a previous commonly-used fit in population synthesis studies, in particular for eccentricities $\lesssim 0.8$.
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Identifying Eccentricity in Binary Black Hole mergers using a Harmonic Decomposition of the Gravitational Waveform
本文通过将偏心双黑洞并合引力波分解为谐波，提出利用主要谐波振幅估计轨道偏心率的方法，并验证了其有效性。
Most of the inspiralling compact binaries are expected to be circularized by the time their gravitational-wave signals enter the frequency band of ground-based detectors such as LIGO or VIRGO. However, it is not excluded that some of these binaries might still possess a significant eccentricity at a few tens of hertz. Despite this possibility, current search pipelines based on matched filtering techniques consider only non-eccentric templates. The effect of such an approximation on the loss of signal-to-noise ratio (SNR) has been investigated by Martel and Poisson (1999 Phys. Rev. D 60 124008)…
Data-driven extraction, phenomenology and modeling of eccentric harmonics in binary black hole merger waveforms
提出基于奇异值分解的数据驱动框架，从有效单体形式论波形中提取偏心谐波，并给出解析拟合公式，用于高效搜索和参数估计偏心并合。
gwharmone: first data-driven surrogate for eccentric harmonics in binary black hole merger waveforms
该研究提出首个针对偏心无自旋双黑洞并合主导四极模式偏心谐波的数据驱动替代模型gwharmone，基于173个波形训练，覆盖特定质量比与偏心率范围，通过SVD和GPR构建，评估快且误差低，可助力偏心并合搜索与参数估计。
Data-driven extraction and phenomenology of eccentric harmonics in eccentric spinning binary black hole mergers
本文利用数据驱动框架gwMiner从偏心双黑洞并合波形中提取偏心谐波，揭示其相位结构并关联到有效单体动力学，为偏心波形建模提供新见解。
Spin effects in Spherical Harmonic Modes of Gravitational Waves from Eccentric Compact Binary Inspirals
本文首次完整解析推导了非圆轨道致密双星引力波球谐模式中直至2PN阶的自旋-轨道和自旋-自旋效应，为偏心并合建模和参数估计提供了闭合形式表达式。
Line-of-sight acceleration in compact binaries with higher harmonics and eccentricity
重新推导了致密双星中的视线加速度效应，并在含进动和高阶模式的准圆形波形模型及偏心波形模型中一致实现，用于探测环境对双星形成的影响。
Adding higher-order spherical harmonics in non-spinning eccentric binary black hole merger waveform models
利用gwNRHME框架将多模态准圆形波形模型与四极偏心波形模型结合，构建多模态非自旋偏心模型，并通过数值相对论模拟验证其准确性。
Universal phenomenological relations between spherical harmonic modes in non-precessing eccentric binary black hole merger waveforms
基于数值相对论模拟，发现非进动偏心双黑洞合并中不同球谐模态的振幅和频率调制由单一时间序列决定，并建立框架gwNRXHME利用四极偏心波形和多模态准环形非进动波形计算多模态偏心波形。
We study the possibility of pre-merger localization of eccentric compact binary coalescences by second-generation gravitational-wave detector networks. Gravitational waves from eccentric binaries can be regarded as a sequence of pulses, which are composed of various higher harmonic modes than ones with twice the orbital frequency. The higher harmonic modes from a very early inspiral phase will not only contribute to the signal-to-noise ratio, but also allow us to localize the gravitational-wave source before the merger sets in. This is due to the fact that high-frequency gravitational waves ar…
We compute the non-linear memory contributions to the gravitational-wave amplitudes for compact binaries in eccentric orbits at the third post-Newtonian (3PN) order in general relativity. These contributions are hereditary in nature as they are sourced by gravitational waves emitted during the binary's entire dynamical past. Combining these with already available instantaneous and tail contributions we get the complete 3PN accurate gravitational waveform.
Compact binaries that emit gravitational waves in the sensitivity band of ground-based detectors can have non-negligible eccentricities just prior to merger, depending on the formation scenario. We develop a purely analytic, frequency-domain model for gravitational waves emitted by compact binaries on orbits with small eccentricity, which reduces to the quasi-circular post-Newtonian approximant TaylorF2 at zero eccentricity and to the post-circular approximation of Yunes et al. (2009) at small eccentricity. Our model uses a spectral approximation to the (post-Newtonian) Kepler problem to model…
We obtain an approximate solution for the motion of a charged particle around a Schwarzschild black hole immersed in a weak dipolar magnetic field. We focus on eccentric bound orbits in the equatorial plane of the Schwarzschild black hole and derive an analytic expression for the spectral distribution of the electromagnetic emission from a charged particle on such an orbit. Two sets of harmonic contributions appear, with specific frequency spacing. The expression can be written in compact form, if it is truncated up to the lowest order harmonic contributions.
A quasi-Keplerian parameterisation for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin-spin and next-to-leading order spin-orbit interactions. Rotational deformation of the compact objects is incorporated. For arbitrary mass ratios the spin orientations are taken to be parallel or anti-parallel to the orbital angular momentum vector. The emitted gravitational wave forms are given in analytic form up to 2PN point particle, 1.5PN spin orbit and 1PN spin-spin contributions, where the spins are counted …
Eccentricity or spin precession? Distinguishing subdominant effects in gravitational-wave data
研究通过模拟分析，探讨了引力波数据中偏心率与自转进动的区分条件，发现对于某些源类型，无法可靠区分两者。
The article provides full-analytic gravitational wave (GW) forms for eccentric nonspinning compact binaries of arbitrary mass ratio in the time Fourier domain. The semi-analytical property of recent descriptions, i.e. the demand of inverting the higher-order Kepler equation numerically but keeping all other computations analytic, is avoided for the first time. The article is a completion of a previous one (Tessmer and Schäfer, Phys. Rev. D 82, 124064 (2010)) to second post-Newtonian (2PN) order in the harmonic GW amplitude and conservative orbital dynamics. A fully analytical inversion formula…
Straightforward mode hierarchy in eccentric binary black hole mergers and associated waveform model
本研究利用SXS合作组的模拟数据，发现偏心双黑洞并合中各球谐模式的偏心调制可由单一时间序列建模，据此提出 gwNRHME 模型，将准圆波形转换为偏心波形，大幅降低了建模复杂度且误差极低。
Most of compact binary systems are expected to circularize before the frequency of emitted gravitational waves (GWs) enters the sensitivity band of the ground based interferometric detectors. However, several mechanisms have been proposed for the formation of binary systems, which retain eccentricity throughout their lifetimes. Since no matched-filtering algorithm has been developed to extract continuous GW signals from compact binaries on orbits with low to moderate values of eccentricity, and available algorithms to detect binaries on quasi-circular orbits are sub-optimal to recover these ev…
We compute here the spin-orbit and spin-spin couplings needed for an accurate computation of the phasing of gravitational waves emitted by comparable-mass binaries on eccentric orbits at the second post-Newtonian (PN) order. We use a quasi-Keplerian parametrization of the orbit free of divergencies in the zero eccentricity limit. We find that spin-spin couplings induce a residual eccentricity for coalescing binaries at 2PN, of the order of $10^{-4}$-$10^{-3}$ for supermassive black hole binaries in the LISA band. Spin-orbit precession also induces a non-trivial pattern in the evolution of the …
A parametrized test of general relativity for inspiralling eccentric binaries in LISA
本文针对LISA观测的偏心旋近黑洞双星，构建两种含偏差参数δα的频域偏心波形模型，经lisabeta的贝叶斯分析表明，LISA可对δα施加严格约束，且偏心率增大可强化该约束。
We study the orbital evolution of eccentric binary neutron stars. The orbit is described as a Quasi-Keplarian orbit with perturbations due to tidal couplings. We find that the tidal interaction between stars contributes to orbital precession, in addition to the Post-Newtonian procession. The coupling between the angular and radial motion of the binary also excites a series of harmonics in the stars' oscillation. In the small eccentricity limit, this coupling mainly gives rise to an additional orbital resonance, with the orbital frequency being one third of the f-mode frequency. For a binary wi…
Enhancing Early Detection and Localization of Gravitational Waves via Eccentricity-Induced Higher Harmonic Modes with 2G Detector Networks
研究通过偏心性诱导的高阶谐波模式提升引力波早期检测与定位能力，分析信号噪声比和定位精度随时间的变化，为多信使天文学提供改进方案。
Gravitational waves radiated during binary black hole coalescence is a perfect probe for studying the characteristics of strong gravity. Advanced techniques for creating numerical relativity substitute models for eccentric binary black hole systems are presumed to become more crucial in existing and anticipated gravitational wave detectors. The imprint on the observation data of the gravitational wave emitted by the binary coalescence enhances the two body system studies. The aim of this study is to present an overview of the change in characteristics behaviours of hierarchical massive astroph…
The population of stellar-mass, compact object binaries that merge with non-negligible eccentricity may be large enough to motivate searches with ground-based gravitational wave detectors. Such events could be exceptional laboratories to test General Relativity in the dynamical, strong-field regime, as a larger fraction of the energy is emitted at high-velocities, compared to quasi-circular inspirals. A serious obstacle here, however, is the challenge of computing theoretical waveforms for eccentric systems with the requisite accuracy for use in a matched-filter search. The corresponding wavef…
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 …
This article presents the calculation of gravitational and electromagnetic radiation emitted from a classical simple harmonic oscillator (SHO). Here we show only the selected formulae and apply them to a toy problem without rigorous derivation. First, we calculate the explicit expressions for the gravitational waves polarizations and then obtain the power radiated away in gravitational waves using Brans-Dicke theory (BD). We also calculate the electromagnetic dipole and quadrupole power emitted by the SHO and compare them with their gravitational counterparts.
We provide a method for analytically constructing high-accuracy templates for the gravitational wave signals emitted by compact binaries moving in inspiralling eccentric orbits. By contrast to the simpler problem of modeling the gravitational wave signals emitted by inspiralling {\it circular} orbits, which contain only two different time scales, namely those associated with the orbital motion and the radiation reaction, the case of {\it inspiralling eccentric} orbits involves {\it three different time scales}: orbital period, periastron precession and radiation-reaction time scales. By using …
In a globular cluster, hierarchical triple black hole systems can be produced through binary-binary interaction. It has been proposed recently that the Kozai mechanism could drive the inner binary of the triple system to merge before it is interrupted by interactions with other field stars. We investigate qualitatively and numerically the evolution of the eccentricities in these binaries under gravitational radiation (GR) reaction. We predict that ~ 30 % of the systems will possess eccentricities >0.1 when their emitted gravitational waves pass through 10 Hz frequency. The implications for gra…
Binary systems emit gravitational waves in a well-known pattern; for binaries in circular orbits, the emitted radiation has a frequency that is twice the orbital frequency. Systems in eccentric orbits, however, emit gravitational radiation in the higher harmonics too. In this paper, we are concerned with the stochastic background of gravitational waves generated by double neutron star systems of cosmological origin in eccentric orbits. We consider in particular the long-lived systems, that is, those binaries for which the time to coalescence is longer than the Hubble time ($\sim 10$Gyr). Thus,…
Compact object binaries formed from dynamics interactions will generically have non-zero orbital eccentricity. The gravitational waves from such binaries can change drastically depending on how large the eccentricity is, ranging from emitted in small a subset of orbital harmonics at low eccentricities, to being concentrated into intense bursts of radiation from each pericenter passage at large eccentricities. Gravitational waves from such highly eccentric binaries present themselves an intriguing systems for probing fundamental physics, but also present interesting challenges in terms of detec…
The article provides ready-to-use 1pN-accurate frequency-domain gravitational wave forms for eccentric nonspinning compact binaries of arbitrary mass ratio including the first post-Newtonian (1pN) point particle corrections to the far-zone gravitational wave amplitude, given in terms of tensor spherical harmonics. The averaged equations for the decay of the eccentricity and growth of radial frequency due to radiation reaction are used to provide stationary phase approximations to the frequency-domain wave forms.
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…
Inspiraling supermassive black hole binary systems with high orbital eccentricity are important sources for space-based gravitational wave (GW) observatories like the Laser Interferometer Space Antenna (LISA). Eccentricity adds orbital harmonics to the Fourier transform of the GW signal and relativistic pericenter precession leads to a three-way splitting of each harmonic peak. We study the parameter estimation accuracy for such waveforms with different initial eccentricity using the Fisher matrix method and a Monte Carlo sampling of the initial binary orientation. The eccentricity improves th…
ESIGMAHM: An Eccentric, Spinning inspiral-merger-ringdown waveform model with Higher Modes for the detection and characterization of binary black holes
本文提出了时域波形模型ESIGMAHM，通过结合后牛顿理论与数值相对论模拟，对中等偏心自旋双黑洞的旋进、并合和铃宕过程及高阶谐波进行建模，并证实其在提升下一代探测器引力波探测精度与降低信噪比损失方面的关键作用。
Binary Black Hole inspirals cannot hide their eccentricity
本文提出了一种快速且准确的偏心率估计方法，利用时频域中的有效啁啾质量模型和改进的像素收集方法，能够在短时间内对双黑洞并合事件的偏心率进行有效约束。
Including higher-order modes in a quadrupolar eccentric numerical relativity surrogate using universal eccentric modulation functions
本文提出一种框架，利用通用谐振调制函数将多模准圆波形转换为偏心波形，结合NR替代模型与四极非自转偏心替代模型，构建多模非自转偏心模型，实现九种模式的高精度模拟。
Line-of-sight Acceleration Driven Effects in Eccentric Compact Binary Coalescences
本研究针对偏心致密双星并合中视线加速度与轨道偏心率的简并问题，提出在波形模板中同时建模两种效应，并通过类似GW170817的注入实验证明该方法能在90%置信区间内准确恢复参数。
Effective-one-body modelling of eccentric supermassive black hole binaries for Pulsar Timing Array
本文提出基于EOB方法的偏心双星引力波模型，用于PTA数据中的连续引力波搜索，揭示偏心双星对脉冲星定时残差的显著影响。
Modeling Gravitational Wave Modes from the Inspiral of Binaries with Arbitrary Eccentricity
本研究提出后牛顿框架，计算任意偏心率双星旋近引力波的傅里叶振幅，分析各模式贡献并确定最小模式集，为高效建模偏心波形提供理论与工具。
Highly eccentric non-spinning binary black hole mergers: quadrupolar post-merger waveforms
本文基于数值模拟，提出非自转二黑洞高偏心并合的后并波形模型，通过贝叶斯方法构建多项式模型，用于参数估计和信号源特性研究。
Periastron precession effect of $f$-mode dynamical tides on gravitational waves from eccentric double white dwarfs
针对偏心双白矮星系统，研究动力学潮汐的近星点进动效应，分析共振、混沌等不同情形下的表现及LISA的可探测性，明确不同质量系统中该效应的测量条件。
While the expectation is that the majority of gravitational wave events observable by ground-based detectors will be emitted by compact binaries in quasi-circular orbits, the growing number of detections suggests the possibility of detecting waves from binaries with non-negligible orbital eccentricity in the near future. Several gravitational wave models incorporate the effects of small orbital eccentricities ($e \lesssim 0.2$), but these models may not be sufficient to analyze waves from systems with moderate eccentricity. We recently developed a gravitational wave model that faithfully accou…
We lay the foundations for the construction of analytic expressions for Fourier-domain gravitational waveforms produced by eccentric, inspiraling compact binaries in a post-circular or small-eccentricity approximation. The time-dependent, "plus" and "cross" polarizations are expanded in Bessel functions, which are then self-consistently re-expanded in a power series about zero initial eccentricity to eighth order. The stationary phase approximation is then employed to obtain explicit analytic expressions for the Fourier transform of the post-circular expanded, time-domain signal. We exemplify …
Eccentric compact binaries pose not only a challenge for gravitational wave detectors, but also provide a probe into the nuclear equation of state if one of the objects is a neutron star. At the short pericenter passage, tidal interactions excite f-modes on the star, which in turn emit their own gravitational waves. We derive an analytic waveform for these stellar oscillations within the effective fly-by framework, modeling the emission to leading post-Newtonian order. At this order, the f-mode response can be written in a Fourier decomposition in terms of orbital harmonics, with the amplitude…
A study of the Inspiral-Merger-Ringdown Consistency Test with gravitational-wave signals from compact binaries in eccentric orbits
本研究通过注入实验表明，偏心引力波信号在残余偏心率≥0.04时会导致准圆形波形下的IMRCT虚假违反，凸显了精确偏心波形模型在广义相对论检验中的必要性。
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…
Periodic line-of-sight velocity-driven modulations to gravitational waves emitted by compact binaries in Keplerian outer orbits
研究超大质量黑洞附近致密双星并合质心因周期性视线速度产生的引力波调制，给出波形相位和幅度校正，通过费希尔矩阵分析预测探测器对相关环境的约束，相比近似方法，所得约束显著改善。
Recent gravitational wave observations have allowed stringent new constraints on modifications to General Relativity (GR) in the extreme gravity regime. Although these observations were consistent with compact binaries with no orbital eccentricity, gravitational waves emitted in mildly eccentric binaries may be observed once detectors reach their design sensitivity. In this paper, we study the effect of eccentricity in gravitational wave constraints of modified gravity, focusing on Jordan-Brans- Dicke-Fierz theory as an example. Using the stationary phase approximation and the post-circular ap…
We present a numerical code for calculating the local gravitational self-force acting on a pointlike particle in a generic (bound) geodesic orbit around a Schwarzschild black hole. The calculation is carried out in the Lorenz gauge: For a given geodesic orbit, we decompose the Lorenz-gauge metric perturbation equations (sourced by the delta-function particle) into tensorial harmonics, and solve for each harmonic using numerical evolution in the time domain (in 1+1 dimensions). The physical self-force along the orbit is then obtained via mode-sum regularization. The total self-force contains a …
Evidence for eccentricity in the population of binary black holes observed by LIGO-Virgo-KAGRA
本研究利用机器学习代码DINGO分析LVK观测的57个引力波事件，通过含偏心参数的波形模型发现部分事件存在显著轨道偏心率证据，证实了动力学双星形成通道并强调了偏心参数在双黑洞特征描述中的重要性。
Exact Results On the Number of Gravitons Radiated During Binary Inspiral
本研究推导了双黑洞非相对论并合中引力子数目与角动量的精确公式$F(e)$，验证拓展Page结果，证实$ν(1)$的Page猜想，并给出$F(e)$的积分表示形式。
Can the gravitational waves emitted by Eta Carinae be detected?
本文提出利用脉冲星计时技术搜索船底座η星这一孤立强源发出的引力波，通过选择特定脉冲星并利用其高偏心率轨道产生的谐波来识别信号，并分析已有数据以验证探测可行性。
Mapping eccentricity evolutions between numerical relativity and effective-one-body gravitational waveforms
本研究针对偏心率定义模糊导致测量不一致的问题，通过28组偏心双黑洞数值相对论模拟，开发了偏心率演化测量流程，实现了模拟数据与有效单体模型间的偏心率可靠映射，助力偏心波形模型精度提升。
Extracting Astrophysical Information of Highly-Eccentric Binaries in the Millihertz Gravitational Wave Band
本研究通过分析高偏心致密双星在毫赫兹频段的引力波信号，展示了如何精确测量其轨道参数，并评估了LISA探测器的实际可探测性。
This paper is to introduce a new software called CBwaves which provides a fast and accurate computational tool to determine the gravitational waveforms yielded by generic spinning binaries of neutron stars and/or black holes on eccentric orbits. This is done within the post-Newtonian (PN) framework by integrating the equations of motion and the spin precession equations while the radiation field is determined by a simultaneous evaluation of the analytic waveforms. In applying CBwaves various physically interesting scenarios have been investigated. In particular, we have studied the appropriate…
Gravitational waves allow us to test general relativity in the highly dynamical regime. While current observations have been consistent with waves emitted by quasi-circular binaries, eccentric binaries may also produce detectable signals in the near future with ground- and space-based detectors. We here explore how tests of general relativity scale with the orbital eccentricity of the source during the inspiral of compact objects up to $e \sim 0.8$. We use a new, 3rd post-Newtonian-accurate, eccentric waveform model for the inspiral of compact objects, which is fast enough for Bayesian paramet…
Eccentric Pairs: Analytic Gravitational Waves from Binary Black Holes in Elliptic Orbits
本文在 Wolfram Mathematica 中实现偏心双黑洞并合的全解析引力波模板，结合六阶PN旋近与BoB并合模型，改进低偏心率匹配并修正高偏心率振幅。
We develop a numerical code to compute gravitational waves induced by a particle moving on eccentric inclined orbits around a Kerr black hole. For such systems, the black hole perturbation method is applicable. The gravitational waves can be evaluated by solving the Teukolsky equation with a point like source term, which is computed from the stress-energy tensor of a test particle moving on generic bound geodesic orbits. In our previous papers, we computed the homogeneous solutions of the Teukolsky equation using a formalism developed by Mano, Suzuki and Takasugi and showed that we could compu…
Parameter control for eccentric, precessing binary black hole simulations with SpEC
本研究针对双黑洞数值模拟难以达到目标参数的问题，扩展现有零偏心率方法，提出基于迭代演化、后牛顿拟合的参数控制循环，用SpEC实现轨道与自旋参数的高精度收敛，可用于参数空间稀疏区域模拟及相对论双黑洞动力学研究。
Frequency space derivation of linear and non-linear memory gravitational wave signals from eccentric binary orbits
本研究利用场论方法计算偏心椭圆与双曲线双星轨道的散射振幅，直接在频域得到线性与非线性记忆引力波信号的波形及能谱，发现双曲线轨道线性记忆含log(ω)项，为引力波数据信号提取提供了频域模板。
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