Gravitational wave (GW) radiations from numerous cosmic stellar-compact-binaries form a stochastic GW background (GWB), which is expected to be detected by ground and space GW detectors in future. Theoretical predictions of this GWB were mostly obtained by assuming either circular binaries and/or a specific channel for binary formation, which may have some uncertainties. In this paper, we estimate the GWB and its spectrum by using simple models for the formation of both stellar mass binary black holes (sBBHs) and binary neutron stars (BNSs). We consider that the dynamically originated sBBHs have relatively larger masses and higher eccentricities compared with those from field binary stars and its possible effect on the GWB spectrum. We find that the GWB spectrum may have a turnover in the low-frequency (Laser Interferometer Space Antenna; LISA) band and may be better described by a broken double power-law than a single power-law with the unique index $2/3$, and the low-frequency slope depends on the significance of the dynamically originated sBBHs with high eccentricities. We further generate mock samples of sBBHs and BNSs, and simulate the mock GWB strain in the time domain. We find that GWB can be detected with signal-to-noise ratio (SNR) $\gtrsim274/255/21$ by LISA/Taiji/TianQin over $5$-years' observation and $\gtrsim3$ by LIGO over $2$-years' observation. Furthermore, we estimate that the number of sBBHs that may be detected by LISA/Taiji/TianQin individually with SNR $\gtrsim8$ is $\sim5$-$221$/$7$-$365$/$3$-$223$ over $5$-years' observation.
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 study precession dynamics of generic binary black holes in eccentric orbits using an effective potential based formalism derived in [M. Kesden et al., PRL {\bf 114}, 081103 (2015)]. This effective potential is used to classify binary black holes into three mutually exclusive spin morphologies. During the inspiral phase, binaries make transitions from one morphology to others. We evolve a population of binary black holes from an initial separation of $1000\mathbf{M}$ to a final separation of $10\mathbf{M}$ using post-Newtonian accurate evolution equations. We find that, given suitable initia…
[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…
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 determine the ability of Cosmic Explorer, a proposed third-generation gravitational-wave observatory, to detect eccentric binary neutron stars and to measure their eccentricity. We find that for a matched-filter search, template banks constructed using binaries in quasi-circular orbits are effectual for eccentric neutron star binaries with $e_{7} \leq 0.004$ ($e_{7} \leq 0.003$) for CE1 (CE2), where $e_7$ is the binary's eccentricity at a gravitational-wave frequency of 7~Hz. We show that stochastic template placement can be used to construct a matched-filter search for binaries with larger…
We present new numerical-relativity simulations of eccentric merging black holes with initially antiparallel spins lying in the orbital plane (the so-called \emph{superkick} configuration). Binary eccentricity boosts the recoil of the merger remnant by up to $25\%$. The increase in the energy flux is much more modest, and therefore this kick enhancement is mainly due to asymmetry in the binary dynamics. Our findings might have important consequences for the retention of stellar-mass black holes in star clusters and supermassive black holes in galactic hosts.
Due to their small mass, subsolar mass black hole binaries would have to be primordial in origin instead of the result of stellar evolution. Soon after formation in the early universe, primordial black holes can form binaries after decoupling from the cosmic expansion. Alternatively, primordial black holes as dark matter could also form binaries in the late universe due to dynamical encounters and gravitational-wave braking. A significant feature for this channel is the possibility that some sources retain nonzero eccentricity in the LIGO/Virgo band. Assuming all dark matter is primordial blac…
We develop a method to compute low-eccentricity initial data of black hole--neutron star binaries in the puncture framework extending previous work on other types of compact binaries. In addition to adjusting the orbital angular velocity of the binary, the approaching velocity of a neutron star is incorporated by modifying the helical Killing vector used to derive equations of the hydrostationary equilibrium. The approaching velocity of the black hole is then induced by requiring the vanishing of the total linear momentum of the system, differently from the case of binary black holes in the pu…
The gravitational-wave (GW) detection of GW190521 has provided new insights on the mass distribution of black holes and new constraints for astrophysical formation channels. With independent claims of GW190521 having significant pre-merger eccentricity, we investigate what this implies for GW190521-like binaries that form dynamically. The Laser Interferometer Space Antenna (LISA) will also be sensitive to GW190521-like binaries if they are circular from an isolated formation channel. We show, however, that GW190521-like binaries that form dynamically may skip the LISA band entirely. To this en…
We study the dynamics of merging compact binaries near a rotating supermassive black hole (SMBH) in a hierarchical triple configuration. We include various general relativistic effects that couple the inner orbit, the outer orbit and the spin of the SMBH. During the orbital decay due to gravitational radiation, the inner binary can encounter an "apsidal precession resonance" and experience eccentricity excitation. This resonance occurs when the apsidal precession rate of the inner binary matches that of the outer binary, with the precessions driven by both Newtonian interactions and various po…
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 …
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 …
Ultralight bosons can be abundantly produced through superradiance process by a spinning black hole and form a bound state with hydrogen-like spectrum. We show that such a "gravitational atom" typically possesses anomalously large mass quadrupole and leads to significant orbital precession when it forms an eccentric binary with a second compact object. Dynamically formed black hole binaries or pulsar-black hole binaries are typically eccentric during their early inspirals. We show that the large orbital precession can generate distinct and observable signature in their gravitational wave or pu…
Up to hundreds of black hole binaries individually resolvable by eLISA will coalesce in the Advanced LIGO/Virgo band within ten years, allowing for multi-band gravitational wave observations. Binaries formed via dynamical interactions in dense star clusters are expected to have eccentricities $e_0\sim 10^{-3}$-$10^{-1}$ at the frequencies $f_0=10^{-2}$ Hz where eLISA is most sensitive, while binaries formed in the field should have negligible eccentricity in both frequency bands. We estimate that eLISA should always be able to detect a nonzero $e_0$ whenever $e_0\gtrsim 10^{-2}$; if $e_0\sim 1…
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…
Gravitational waves from binary black hole mergers have allowed us to directly observe stellar-mass black hole binaries for the first time, and therefore explore their formation channels. One of the ways to infer how a binary system is assembled is by measuring the system's orbital eccentricity. Current methods of parameter estimation do not include all physical effects of eccentric systems such as spin-induced precession, higher-order modes, and the initial argument of periapsis: an angle describing the orientation of the orbital ellipse. We explore how varying the argument of periapsis chang…
In this paper, we derive a set of equations of motions for binaries on eccentric orbits undergoing spin-induced precession that can efficiently be integrated on the radiation-reaction timescale. We find a family of solutions with a computation cost improved by a factor $10$ - $50$ down to $\sim 10$ ms per waveform evaluation compared to waveforms obtained by directly integrating the precession equations, that maintain a mismatch of the order $10^{-4}$ - $10^{-6}$ for waveforms lasting a million orbital cycles and a thousand spin-induced precession cycles. We express it in terms of parameters t…
Detection of gravitational waves (GW) from highly eccentric binary black hole (BBH) systems can provide insight into their dynamics and formation. To date, all of the LIGO-Virgo BBH detections have been made using quasi-circular templates in their initial discovery. However, recent studies have found some of these systems to be compatible with high eccentricity in the LIGO band, $e_{10 \textrm{Hz}} > 0.1$, possibly pointing to a population of sources that are challenging to detect. Current low-latency search methods used with ground-based GW detector data are not well equipped to detect highly…
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）；CEICO, FZU-Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所FZU-CEICO）
We show how the observable number of binaries in LISA is affected by eccentricity through its influence on the peak gravitational wave frequency, enhanced binary number density required to produce the LIGO observed rate, and the reduced signal-to-noise ratio for an eccentric event. We also demonstrate how these effects should make it possible to learn about the eccentricity distribution and formation channels by counting the number of binaries as a function of frequency, even with no explicit detection of eccentricity. We also provide a simplified calculation for signal-to-noise ratio of eccen…
Using high-resolution hydrodynamics simulations, we show that equal-mass binaries accreting from a circumbinary disk evolve toward an orbital eccentricity of $e \simeq 0.45$, unless they are initialized on a nearly circular orbit with $e \lesssim 0.08$, in which case they further circularize. The implied bi-modal eccentricity distribution resembles that seen in post-AGB stellar binaries. Large accretion spikes around periapse impart a tell-tale, quasi-periodic, bursty signature on the light curves of eccentric binaries. We predict that intermediate-mass and massive black hole binaries at $z \l…
Eccentricity evolution of spinning binaries and its dependence on the equation of state of the components
Gran Sasso Science Institute (GSSI)（格兰萨索科学研究所）；INFN, Laboratori Nazionali del Gran Sasso（意大利国家核物理研究所，格兰萨索国家实验室）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理学研究所（爱因斯坦研究所））；Leibniz Universität Hannover（汉诺威莱布尼茨大学）
Stochastic Gravitational Wave Background from Highly-Eccentric Stellar-Mass Binaries in the Milli-hertz Band
UCLA（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, UCLA（加州大学洛杉矶分校物理与天文学系马尼·L·巴乌米克理论物理研究所）；Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford（牛津大学鲁道夫·派尔斯理论物理中心）
We present a suite of high resolution hydrodynamic simulations of binaries immersed in circumbinary accretion disks (CBDs). For the first time, we investigate the preferential accretion rate as a function of both eccentricity $e_{\rm b}$ and mass ratio $q_{\rm b}$ in a densely sampled parameter space, finding that when compared with circular binaries, mass ratios grow more efficiently in binaries on moderately eccentric orbits ($0.0 \lesssim e_{\rm b} \lesssim 0.4$), and high eccentricities ($e_{\rm b} \gtrsim 0.6 $) suppress mass ratio growth. We suggest that this non-monotonic preferential a…
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…
Many gravitational wave (GW) sources in the LISA band are expected to have non-negligible eccentricity. Furthermore, many of them can undergo acceleration because they reside in the presence of a tertiary. Here we develop analytical and numerical methods to quantify how the compact binary's eccentricity enhances the detection of its peculiar acceleration. We show that the general relativistic precession pattern can disentangle the binary's acceleration-induced frequency shift from the chirp-mass-induced frequency shift in GW template fitting, thus relaxing the signal-to-noise ratio requirement…
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…
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…
In a recent paper, we determined the measurement accuracy of physical parameters for eccentric, precessing, non-spinning, inspiraling, stellar-mass black hole - black hole (BH-BH) binaries for the upcoming second-generation LIGO/VIRGO/KAGRA detector network at design sensitivity using the Fisher matrix method. Here we extend that study to a wide range of binary masses including neutron star - neutron star (NS-NS), NS-BH, and BH-BH binaries with BH masses up to $110 \, M_{\odot}$. The measurement error of eccentricity $e_{10 \,\rm Hz}$ at a gravitational-wave (GW) frequency of $10 \, {\rm Hz}$ …
Type I outbursts in Be/X-ray binaries are usually associated with the eccentricity of the binary orbit. The neutron star accretes gas from the outer parts of the decretion disk around the Be star at each periastron passage. However, this mechanism cannot explain type I outbursts that have been observed in nearly circular orbit Be/X-ray binaries. With hydrodynamical simulations and analytic estimates we find that in a circular orbit binary, a nearly coplanar disk around the Be star can become eccentric. The extreme mass ratio of the binary leads to the presence of the 3:1 Lindblad resonance ins…
Extracting Astrophysical Information of Highly-Eccentric Binaries in the Millihertz Gravitational Wave Band
UCLA（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, UCLA（加州大学洛杉矶分校物理与天文学系马尼·L·巴乌米克理论物理研究所）；LIGO Laboratory, California Institute of Technology（加州理工学院LIGO实验室）；Department of Physics, The Chinese University of Hong Kong（香港中文大学物理系）；RESCEU, The University of Tokyo（东京大学RESCEU）；Rudolf Peierls Centre for Theoretical Physics, Parks Road, Oxford（牛津大学鲁道夫·派尔斯理论物理中心）；Department of Physics and Astronomy, University of British Columbia（不列颠哥伦比亚大学物理与天文学系）；Department of Astronomy and Astrophysics, University of California, San Diego（加州大学圣地亚哥分校天文与天体物理学系）；Center for Computational Astrophysics, Flatiron Institute（西蒙斯基金会平顿研究所计算天体物理中心）
We solve the equations of two-dimensional hydrodynamics describing a circumbinary disk accreting onto an eccentric, equal-mass binary. We compute the time rate of change of the binary semimajor axis $a$ and eccentricity $e$ over a continuous range of eccentricities spanning $e=0$ to $e=0.9$. We find that binaries with initial eccentricities $e_0 \lesssim 0.1$ tend to $e=0$, where the binary semimajor axis expands. All others are attracted to $e \approx 0.4$, where the binary semimajor axis decays. The $e \approx 0.4$ attractor is caused by a rapid change in the disk response from a nearly orig…
The tidal force from a third body near a binary system could introduce long-term oscillations in the binary's eccentricity, known as Kozai-Lidov oscillations. We show that the Kozai-Lidov oscillations of stellar-mass black hole binaries have the potential to be observed by LISA. Detections of such binaries will give insights into binary formation channels and also provide an important benchmark of observing Kozai-Lidov oscillations directly.
Binary millisecond pulsars (MSPs) are believed to have descended from low-mass X-ray binaries (LMXBs), which have experienced substantial mass transfer and tidal circularization. Therefore, they should have very circular orbits. However, the discovery of several eccentric binary MSPs (with eccentricity $e\sim 0.01-0.1$) challenges this standard picture. Three models have been proposed thus far based on accretion-induced collapse of massive white dwarfs (WDs), neutron star-strange star transition, and formation of circumbinary disks. All of them are subject to various uncertainties, and are not…
Distance Estimation and Sky Localization of Eccentric Double White Dwarf Binaries from Gravitational Wave Observations inside Globular Clusters
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of physics and astronomy, Beijing Normal University（北京师范大学物理与天文学院）；Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天体物理中心）；Department of Physics, Centre for Extragalactic Astronomy, Durham University（杜伦大学系外天文学中心物理系）；School of Astronomy and Space Sciences, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；International Centre of Supernovae (ICESUN), Yunnan Key Laboratory of Supernova Research, Yunnan Observatories, CAS（中国科学院云南天文台超新星研究云南省重点实验室国际超新星中心）
Mergers of compact binaries, such as binary neutron stars (BNSs), neutron star-black hole binaries (NSBHs), and binary black holes (BBHs), are expected to be the best candidates for the sources of gravitational waves (GWs) and the leading theoretical models for short gamma-ray bursts (SGRBs). Based on the observations of SGRBs, we could derive the merger rates of these compact binaries, and study the stochastic GW backgrounds (SGWBs) or the co-detection rates of GWs associate with SGRBs (GW-SGRBs). But before that, the most important thing is to derive the GW spectrum from a single GW source. …
Nuclear star clusters around massive black holes are expected to be abundant in stellar mass black holes and black hole binaries. These binaries form a hierarchical triple system with the massive black hole at the center. Gravitational perturbations from the massive black hole can cause high eccentricity excitation. During this process, the eccentricity may approach unity, and the pericenter distance may become sufficiently small that gravitational wave emission drives the binary to merge. In this paper, we consider a simple proof of concept and explore the effect of the eccentric Kozai-Lidov …
