We present the first application of deep learning forecasting for binary neutron stars, neutron star - black hole systems, and binary black hole mergers that span an eccentricity range e <= 0.9. We train neural networks that describe these astrophysical populations, and then test their performance by injecting simulated eccentric signals in advanced LIGO noise available at the \texttt{Gravitational Wave Open Science Center} to: 1) quantify how fast neural networks identify these signals before the binary components merge; 2) quantify how accurately neural networks estimate the time to merger once gravitational waves are identified; and 3) estimate the time-dependent sky localization of these events from early detection to merger. Our findings show that deep learning can identify eccentric signals from a few seconds (for binary black holes) up to tens of seconds (for binary neutron stars) prior to merger. A quantized version of our neural networks achieves 4x reduction in model size, and up to 2.5x inference speed up. These novel algorithms may be used to facilitate time-sensitive multi-messenger astrophysics observations of compact binaries in dense stellar environments.
Compact binary coalescences are a promising source of gravitational waves for second-generation interferometric gravitational-wave detectors such as advanced LIGO and advanced Virgo. While most binaries are expected to possess circular orbits, some may be eccentric, for example, if they are formed through dynamical capture. Eccentric orbits can create difficulty for matched filtering searches due to the challenges of creating effective template banks to detect these signals. In previous work, we showed how seedless clustering can be used to detect low-mass ($M_\text{total}\leq10M_\odot$) compa…
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…
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…
Compact binary coalescences are a promising source of gravitational waves for second-generation interferometric gravitational-wave detectors. Although matched filtering is the optimal search method for well-modeled systems, alternative detection strategies can be used to guard against theoretical errors (e.g., involving new physics and/or assumptions about spin/eccentricity) while providing a measure of redundancy. In previous work, we showed how "seedless clustering" can be used to detect long-lived gravitational-wave transients in both targeted and all-sky searches. In this paper, we apply s…
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…
Compact binary systems coalesce over time due to the radiation of gravitational waves, following the field equations of general relativity. Conservation of energy and angular momentum gives a mathematical description for the evolution of separation between the orbiting objects and eccentricity ($e$) of the orbit. We develop an improved analytical solution to the coalescence time for a circular binary system with an arbitrary semi-major axis, to the first post-Newtonian (1PN) accuracy. The results from the quadruple approximation and 1PN approximation are compared for a circular orbit ($e=0$).
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…
Effective-one-body (EOB) numerical-relativity (NR) waveform models for spin-aligned binary black holes (BBHs), known as the SEOBNR waveform models, are based on the EOB theoretical framework and NR simulations. SEOBNR models have played an important role in the LIGO scientific collaboration (LSC) gravitational wave (GW) data analysis for both signal search and parameter estimation. SEOBNR models for quasi-circular orbits have evolved through version 1 to version 4 by extending their validity domain and including more NR results. Along another direction, we recently extended SEOBNRv1 model to S…
We present a new effective-one-body (EOB) model for eccentric binary coalescences. The model stems from the state-of-the-art model TEOBResumS$\_$SM for circularized coalescing black-hole binaries, that is modified to explicitly incorporate eccentricity effects both in the radiation reaction and in the waveform. Using Regge-Wheeler-Zerilli type calculations of the gravitational wave losses as benchmarks, we find that a rather accurate ($\sim 1\%$) expression for the radiation reaction along mildly eccentric orbits ($e \sim 0.3$) is given by dressing the current, EOB-resummed, circularized angul…
We present a search for gravitational waves from the coalescence of sub-solar mass black hole binaries using data from the first half of Advanced LIGO and Virgo's third observing run. The observation of a sub-solar mass black hole merger may be an indication of primordial origin; primordial black holes may contribute to the dark matter distribution. We search for black hole mergers where the primary mass is $0.1-7 M_{\odot}$ and the secondary mass is $0.1-1 M_{\odot}$. A variety of models predict the production and coalescence of binaries containing primordial black holes; some involve dynamic…
We outline the eccentricity evolution of sub-parsec massive black hole binaries (MBHBs) forming in galaxy mergers. In both stellar and gaseous environments, MBHBs are expected to grow large orbital eccentricities before they enter the gravitational wave (GW) observational domain. We re--visit the predicted eccentricities detectable by space based laser interferometers (as the proposed ELISA/NGO) for both environments. Close to coalescence, many MBHBs will still maintain detectable eccentricities, spanning a broad range from <10^{-5} up to <~ 0.5. Stellar and gas driven dynamics lead to distinc…
A large number of theoretically predicted waveforms are required by matched-filtering searches for the gravitational-wave signals produced by compact binary coalescence. In order to substantially alleviate the computational burden in gravitational-wave searches and parameter estimation without degrading the signal detectability, we propose a novel reduced-order-model (ROM) approach with applications to adiabatic 3PN-accurate inspiral waveforms of sources that evolve on either highly or slightly eccentric orbits. We provide a singular-value decomposition-based reduced-basis method in the freque…
Dynamically formed compact object binaries may still be eccentric while in the LIGO/Virgo band. For a neutron star (NS) in an eccentric binary, the fundamental modes (f-modes) are excited at pericenter, transferring energy from the orbit to oscillations in the NS. We model this system by coupling the evolution of the NS f-modes to the orbital evolution of the binary as it circularizes and moves toward coalescence. NS f-mode excitation generally speeds up the orbital decay and advances the phase of the gravitational wave signal from the system. We calculate how this effect changes the timing of…
We describe the methodology and novel techniques used to construct a set of waveforms, or template bank, applicable to searches for compact binary coalescences in Advanced LIGO's second observing run. This template bank is suitable for observing systems composed of two neutron stars, two black holes, or a neutron star and a black hole. The Post-Newtonian formulation is used to model waveforms with total mass less than 4 $M_{\odot}$ and the most recent effective-one-body model, calibrated to numerical relativity to include the merger and ringdown, is used for total masses greater than 4 $M_{\od…
The problem of gravitational wave parameter estimation and source localization is crucial in gravitational wave astronomy. Gravitational waves emitted by compact binary coalescences in the sensitivity band of second-generation ground-based detectors could have non-negligible eccentricities. Thus it is an interesting topic to study how the eccentricity of a binary source affects and improves the accuracy of its localization (and the signal-to-noise ratio). In this work we continue to investigate this effect with the enhanced postcircular waveform model. Using the Fisher information matrix metho…
We investigate a purely stellar dynamical solution to the Final Parsec Problem. Galactic nuclei resulting from major mergers are not spherical, but show some degree of triaxiality. With $N$-body simulations, we show that massive black hole binaries (MBHB) hosted by them will continuously interact with stars on centrophilic orbits and will thus inspiral---in much less than a Hubble time---down to separations at which gravitational wave (GW) emission is strong enough to drive them to coalescence. Such coalescences will be important sources of GWs for future space-borne detectors such as the {\it…
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…
A generic, non-eccentric binary black hole (BBH) system emits gravitational waves (GWs) that are completely described by 7 intrinsic parameters: the black hole spin vectors and the ratio of their masses. Simulating a BBH coalescence by solving Einstein's equations numerically is computationally expensive, requiring days to months of computing resources for a single set of parameter values. Since theoretical predictions of the GWs are often needed for many different source parameters, a fast and accurate model is essential. We present the first surrogate model for GWs from the coalescence of BB…
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 e…
Coalescing massive black hole binaries (MBHBs) of $10^{4-7} \rm M_{\odot}$, forming in the aftermath of galaxy mergers, are primary targets of the space mission LISA, the {\it Laser Interferometer Space Antenna}. An assessment of LISA detection prospects requires an estimate of the abundance and properties of MBHBs that form and evolve during the assembly of cosmic structures. To this aim, we employ a semi-analytic model to follow the co-evolution of MBHBs within their host galaxies. We identify three major evolutionary channels driving the binaries to coalescence: two standard paths along whi…
Eccentricity or spin precession? Distinguishing subdominant effects in gravitational-wave data
Department of Applied Mathematics and Theoretical Physics, Cambridge（剑桥大学应用数学与理论物理系）；School of Physics and Astronomy, Monash University（蒙纳士大学物理与天文学院）；OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery（引力波发现ARC卓越中心）；Dipartimento di Fisica “G. Occhialini”, Universitá degli Studi di Milano-Bicocca（米兰比可卡大学“G. Oc恰利尼”物理系）；INFN, Sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）；School of Physics and Astronomy & 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学研究所）；Dipartimento di Fisica, “Sapienza” Università di Roma & Sezione INFN Roma1（罗马智慧大学物理系及意大利国家核物理研究所罗马一分部）
Searches for gravitational waves from compact binaries focus mostly on quasi-circular motion, with the rationale that wave emission circularizes the orbit. Here, we study the generality of this result, when astrophysical environments (e.g., accretion disks) or other fundamental interactions are taken into account. We are motivated by possible electromagnetic counterparts to binary black hole coalescences and orbits, but also by the possible use of eccentricity as a smoking-gun for new physics. We find that: i) backreaction from radiative mechanisms, including scalars, vectors and gravitational…
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,…
We derive fourth post-Newtonian (4PN) contributions to the Keplerian-type parametric solution associated with the conservative dynamics of eccentric, non-spinning compact binaries. The solution has been computed while ignoring certain zero-average, oscillatory terms arising due to 4PN tail effects. We provide explicit expressions for the parametric solution and various orbital elements in terms of the conserved energy, angular momentum and symmetric mass ratio. Canonical perturbation theory (along with the technique of Pade approximant) is used to incorporate the 4PN nonlocal-in-time tail effe…
Impact of eccentricity on the population properties of neutron star - black hole mergers
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学院及引力波天文研究所）
Deep Learning Search for Gravitational Waves from Compact Binary Coalescence
Università degli Studi di Urbino Carlo Bo（乌尔比诺卡洛·博大学）；INFN, Sezione di Firenze（意大利国家核物理研究所佛罗伦萨分部）；Université Paris-Saclay, CNRS/IN2P3, IJCLab（巴黎萨克雷大学、法国国家科学研究中心/法国国家粒子物理研究所、IJCLab）
We compute the gravitational wave background (GWB) generated by a cosmological population of (BH-BH) binaries using hybrid waveforms recently produced by numerical simulations of (BH-BH) coalescence, which include the inspiral, merger and ring-down contributions. A large sample of binary systems is simulated using the population synthesis code SeBa, and we extract fundamental statistical information on (BH-BH) physical parameters (primary and secondary BH masses, orbital separations and eccentricities, formation and merger timescales). We then derive the binary birth and merger rates using the…
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…
If binary intermediate-mass black holes (IMBHs; with masses between 100 and $10^4 \Msun$) form in dense stellar clusters, their inspiral will be detectable with the planned Laser Interferometer Space Antenna (LISA) out to several Gpc. Here we present a study of the dynamical evolution of such binaries using a combination of direct $N$-body techniques (when the binaries are well separated) and three-body relativistic scattering experiments (when the binaries are tight enough that interactions with stars occur one at a time). We find that for reasonable IMBH masses there is only a mild effect on…
We study the transition from inspiral to plunge in general relativity by computing gravitational waveforms of non-spinning, equal-mass black-hole binaries. We consider three sequences of simulations, starting with a quasi-circular inspiral completing 1.5, 2.3 and 9.6 orbits, respectively, prior to coalescence of the holes. For each sequence, the binding energy of the system is kept constant and the orbital angular momentum is progressively reduced, producing orbits of increasing eccentricity and eventually a head-on collision. We analyze in detail the radiation of energy and angular momentum i…
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 …
Surface abundance observations of halo stars hint at the occurrence of $r$-process nucleosynthesis at low metallicity ($\rm{[Fe/H]< -3}$), possibly within the first $10^8$ yr after the formation of the first stars. Possible loci of early-Universe $r$-process nucleosynthesis are the ejecta of either black hole--neutron star or neutron star--neutron star binary mergers. Here we study the effect of the inclination--eccentricity oscillations raised by a tertiary (e.g. a star) on the coalescence time scale of the inner compact object binaries. Our results are highly sensitive to the assumed initial…
We study black hole MACHO binary formation through three-body interactions in the early universe at $t\sim 10^{-5}$s. The probability distribution functions of the eccentricity and the semimajor axis of binaries as well as of the coalescence time are obtained assuming that the black holes are randomly formed in space. We confirm that the previous order-of-magnitude estimate for the binary parameters is valid within $\sim 50%$ error. We find that the coalescence rate of the black hole MACHO binaries is $\sim 5 \times 10^{-2} \times 2^{\pm 1}$ events/year/galaxy taking into consideration several…
Observations suggest that star clusters often form in binaries or larger bound groups. Therefore, mergers between two clusters are likely to occur. If these clusters both harbor an intermediate-mass black hole (IMBH; 10^{2-4} Msun) in their center, they can become a strong source of gravitational waves when the black holes merge with each other. In order to understand the dynamical processes that operate in such a scenario, one has to study the evolution of the merger of two such young massive star clusters, and more specifically, their respective IMBHs. We employ the direct-summation Nbody4 n…
The coalescence of two neutron stars is an important gravitational wave source for LIGO and other detectors. Numerous studies have considered the precision with which binary parameters (masses, spins, Love numbers) can be measured. Here I consider the accuracy with which these parameters can be determined in the presence of systematic errors due to waveform approximations. These approximations include truncation of the post-Newtonian (PN) series and neglect of neutron star (NS) spin, tidal deformation, or orbital eccentricity. All of these effects can yield systematic errors that exceed statis…
Eccentricity constraints disfavor single-single capture in nuclear star clusters as the origin of all LIGO-Virgo-KAGRA binary black holes
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）；University of British Columbia（不列颠哥伦比亚大学）；California Institute of Technology（加州理工学院）；LIGO Laboratory（LIGO实验室）；Universitá degli Studi di Milano-Bicocca（米兰比可卡大学）；INFN, Sezione di Milano-Bicocca（意大利国家核物理研究所米兰比可卡分部）
Early Warning From Eccentric Compact Binaries: Template Initialization And Sub-dominant Mode Effects
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Gravity Exploration Institute, School of Physics and Astronomy, Cardiff University（引力探索研究所，卡迪夫大学物理与天文学院）；Department of Physics, Indian Institute of Technology Madras（印度马德拉斯理工学院物理系）；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）
We explore the performance of an updated effective-one-body (EOB) model for spin-aligned coalescing black hole binaries designed to deal with any orbital configuration. The model stems from previous work involving the \TEOBResumS{} waveform model, but incorporates recently computed analytical information up to fifth post-Newtonian (PN) order in the EOB potentials. The dynamics is then informed by Numerical Relativity (NR) quasi-circular simulations (incorporating also recently computed 4PN spin-spin and, optionally, 4.5PN spin-orbit terms). The so-constructed model(s) are then compared to vari…
The environment near super massive black holes (SMBHs) in galactic nuclei contain a large number of stars and compact objects. A fraction of these are likely to be members of binaries. Here we discuss the binary population of stellar black holes and neutron stars near SMBHs and focus on the secular evolution of such binaries, due to the perturbation by the SMBH. Binaries with highly inclined orbits in respect to their orbit around the SMBH are strongly affected by secular Kozai processes, which periodically change their eccentricities and inclinations (Kozai-cycles). During periapsis approach,…
Massive black hole binaries (MBHBs) are expected to form at the centre of merging galaxies during the hierarchical assembly of the cosmic structure, and are expected to be the loudest sources of gravitational waves (GWs) in the low frequency domain. However, because of the dearth of energy exchanges with background stars and gas, many of these MBHBs may stall at separations too large for GW emission to drive them to coalescence in less than a Hubble time. Triple MBH systems are then bound to form after a further galaxy merger, triggering a complex and rich dynamics that can eventually lead to …
The supermassive black holes originally in the nuclei of two merging galaxies will form a binary in the remnant core. The early evolution of the massive binary is driven by dynamical friction before the binary becomes "hard" and eventually reaches coalescence through gravitational wave emission. { We consider the dynamical friction evolution of massive binaries consisting of a secondary hole orbiting inside a stellar cusp dominated by a more massive central black hole.} In our treatment we include the frictional force from stars moving faster than the inspiralling object which is neglected in …
The detection of GW190521 gains huge attention because it is the most massive binary that LIGO and Virgo ever confidently detected until the release of GWTC-3 (GW190426_190642 is more massive), and it is the first black hole merger whose remnant is believed to be an intermediate mass black hole. Furthermore, the primary black hole mass falls in the black hole mass gap, where the pair-instability supernova prevents the formation of astrophysical black holes in this range. In this paper, we systematically explore the prospect of TianQin on detecting GW190521-like sources. For sources with small …
