We compare different methods of computing the orbital eccentricity of quasi-circular binary black hole systems using the orbital variables and gravitational wave phase and frequency. For eccentricities of about a per cent, most methods work satisfactorily. For small eccentricity, however, the gravitational wave phase allows a particularly clean and reliable measurement of the eccentricity. Furthermore, we measure the decay of the orbital eccentricity during the inspiral and find reasonable agreement with post-Newtonian results. Finally, we measure the periastron advance of non-spinning binary black holes, and we compare them to post-Newtonian approximations. With the low uncertainty in the measurement of the periastron advance, we positively detect deviations between fully numerical simulations and post-Newtonian calculations.
In this paper, we revisit and complete our preceding work on the Fokker Lagrangian describing the dynamics of compact binary systems at the fourth post-Newtonian (4PN) order in harmonic coordinates. We clarify the impact of the non-local character of the Fokker Lagrangian or the associated Hamiltonian on both the conserved energy and the relativistic periastron precession for circular orbits. We show that the non-locality of the action, due to the presence of the tail effect at the 4PN order, gives rise to an extra contribution to the conserved integral of energy with respect to the Hamiltonia…
The inclination of low-eccentricity orbits is shown to significantly affect the orbital parameters, in particular, the Keplerian, nodal precession, and periastron rotation frequencies, which are interpreted in terms of observable quantities. For the nodal precession and periastron rotation frequencies of low-eccentricity orbits in a Kerr field, we derive a Taylor expansion in terms of the Kerr parameter at arbitrary orbital inclinations to the black-hole spin axis and at arbitrary radial coordinates. The particle radius, energy, and angular momentum in the marginally stable circular orbits are…
We will comment on the perihelion/periastron advance of celestial bodies due to the cosmological constant $Λ$. It is well known that the cosmological constant $Λ$ causes the perihelion/periastron shift; however, there seems to still exist a discrepancy among the various derived precession formulae. We will point out that the expression $Δω_Λ = (πc^2 Λa^3/(GM))\sqrt{1 - e^2}$ is the general formula for any orbital eccentricity $e$ and the expression $Δω_Λ = (πc^2 Λa^3/(GM))(1 - e^2)^3$ comes from the nearly circular ($e \ll 1$) approximation.
We study the Kozai-Lidov mechanism in a hierarchical triple system in detail by the direct integration of the first-order post Newtonian equations of motion. We analyse a variety of models with a pulsar to evaluate the cumulative shift of the periastron time of a binary pulsar caused by the gravitational wave emission in a hierarchical triple system with Kozai-Lidov mechanism. We compare our results with those by the double-averaging method. The deviation in the eccentricity, even if small, is important in the evaluation of the emission of the gravitational waves. We also calculate the cumulat…
We present the first analytical computation of the (conservative) gravitational self-force correction to the periastron advance around a spinning black hole. Our result is accurate to the second order in the rotational parameter and through the 9.5 post-Newtonian level. It has been obtained as the circular limit of the correction to the gyroscope precession invariant along slightly eccentric equatorial orbits in the Kerr spacetime. The latter result is also new and we anticipate here the first few terms only of the corresponding post-Newtonian expansion.
Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data cl…
We study a hierarchical triple system with the Kozai-Lidov mechanism, and analyse the cumulative shift of periastron time of a binary pulsar by the emission of gravitational waves. Time evolution of the osculating orbital elements of the triple system is calculated by directly integrating the first-order post-Newtonian equations of motion. The Kozai-Lidov mechanism will bend the evolution curve of the cumulative shift when the eccentricity becomes large. We also investigate the parameter range of mass and semi-major axis of the third companion with which the bending of the cumulative-shift cur…
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）
We compute the periastron advance using the effective-one-body formalism for binary black holes moving on quasi-circular orbits and having spins collinear with the orbital angular momentum. We compare the predictions with the periastron advance recently computed in accurate numerical-relativity simulations and find remarkable agreement for a wide range of spins and mass ratios. These results do not use any numerical-relativity calibration of the effective-one-body model, and stem from two key ingredients in the effective-one-body Hamiltonian: (i) the mapping of the two-body dynamics of spinnin…
We present simple procedures to construct quasi-circular initial data for numerical evolutions of binary black hole spacetimes. Our method consists of using Post-Newtonian theory in three ways: first to provide an initial guess for the initial momenta at 3.5PN order that implies low residual eccentricity, second to measure the resulting eccentricity, and third to calculate corrections to the momenta or initial separation which further reduce the eccentricity. Regarding the initial guess, we compare numerical evolutions in post-Newtonian theory to the post-circular and post-post-circular analyt…
We examine the evolution, under gravitational radiation reaction, of slightly eccentric equatorial orbits of point particles around Kerr black holes. Our method involves numerical integration of the Sasaki-Nakamura equation. It is discovered that such orbits decrease in eccentricity throughout most of the inspiral, until shortly before the innermost stable circular orbit (ISCO), when a critical radius $r_{\text{crit}}$ is reached beyond which the inspiralling orbits increase in eccentricity. It is shown that the number of orbits remaining in this last (eccentricity increasing) phase of the ins…
We study the general relativistic periastron advance in spinning black hole binaries on quasi-circular orbits, with spins aligned or anti-aligned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies' labels, we devise an improved version of the perturbative result, and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the perias…
We derive the first law of binary point-particle mechanics for generic bound (i.e. eccentric) orbits at the fourth post-Newtonian (4PN) order, accounting for the non-locality in time of the dynamics due to the occurence of a gravitational-wave tail effect at that order. Using this first law, we show how the periastron advance of the binary system can be related to the averaged redshift of one of the two bodies for a slightly non-circular orbit, in the limit where the eccentricity vanishes. Combining this expression with existing analytical self-force results for the averaged redshift, we recov…
Standard choices of quasi-circular orbit parameters for black-hole binary evolutions result in eccentric inspiral. We introduce a conceptually simple method, which is to integrate the post-Newtonian equations of motion through hundreds of orbits, and read off the values of the momenta at the separation at which we wish to start a fully general relativistic numerical evolution. For the particular case of non-spinning equal-mass inspiral with an initial coordinate separation of $D = 11M$ we show that this approach reduces the eccentricity by at least a factor of five to $e < 0.002$ as compared t…
The Cost of Circularity: Quantifying Eccentricity-Induced Biases in Binary Black Hole Inference
University of Wisconsin–Milwaukee（威斯康星大学密尔沃基分校）；The Pennsylvania State University（宾夕法尼亚州立大学）；University of California, Berkeley（加州大学伯克利分校）；University of Florida（佛罗里达大学）
While current gravitational wave observations with ground based detectors have been consistent with compact binaries in quasi-circular orbits, eccentric binaries may be detectable by ground-based and space-based instruments in the near future. Eccentricity significantly complicates the gravitational wave signal, and we currently lack fast and accurate models that are valid in the moderate to large eccentricity range. In a previous paper, we built a Fourier domain, eccentric waveform model at leading order in the post-Newtonian approximation, i.e. as an expansion in small velocities and weak fi…
In the present work, our main objective is to investigate the orbits of spinning test particles around a Schwarzschild black hole under the influence of a quintessence matter field (SQBH). We begin with the dynamics of the spinning test particles around SQBH which is governed by the Mathisson-Papapetrou-Dixon (MPD) equations under the pole-dipole approximation, where the gravitational field and the higher multipoles of the particle are neglected. Depending on the types of saddle points,the effective potential are classified and the possibility of chaotic orbits is discussed. The inner most sta…
The modelling of unequal mass binary black hole systems is of high importance to detect and estimate parameters from these systems. Numerical relativity (NR) is well suited to study systems with comparable component masses, $m_1\sim m_2$, whereas small mass ratio (SMR) perturbation theory applies to binaries where $q=m_2/m_1<< 1$. This work investigates the applicability for NR and SMR as a function of mass ratio for eccentric non-spinning binary black holes. We produce $52$ NR simulations with mass ratios between $1:10$ and $1:1$ and initial eccentricities up to $0.7$. From these we extract q…
It is demonstrated that, in the adiabatic approximation, non-Equatorial circular orbits of particles in the Kerr metric (i.e. orbits of constant Boyer-Lindquist radius) remain circular under the influence of gravitational radiation reaction. A brief discussion is given of conditions for breakdown of adiabaticity and of whether slightly non-circular orbits are stable against the growth of eccentricity.
The second post-Newtonian (2PN) contribution to the `plus' and `cross' gravitational wave polarizations associated with gravitational radiation from non-spinning, compact binaries moving in elliptic orbits is computed. The computation starts from our earlier results on 2PN generation, crucially employs the 2PN accurate generalized quasi-Keplerian parametrization of elliptic orbits by Damour, Schäfer and Wex and provides 2PN accurate expressions modulo the tail terms for gravitational wave polarizations incorporating effects of eccentricity and periastron precession.
Given the absence of observations of black hole binaries, it is critical that the full range of accessible parameter space be explored in anticipation of future observation with gravitational wave detectors. To this end, we compile the Hamiltonian equations of motion describing the conservative dynamics of the most general black hole binaries, as computed by Will and collaborators, and incorporate an effective treatment of dissipation through gravitational radiation. We evolve these equations for systems with orbital eccentricity and precessing spins. We find that, while spin-spin coupling cor…
Building upon recent work, we present an improved effective-one-body (EOB) model for spin-aligned, coalescing, black hole binaries with generic orbital configurations, i.e. quasi-circular, eccentric or hyperbolic orbits. The model relies on the idea of incorporating general Newtonian prefactors, instead of the usual quasi-circular ones, in both radiation reaction and waveform. The major advance with respect to previous work is that the quasi-circular limit of the model is now correctly informed by numerical relativity (NR) quasi-circular simulation. This provides EOB/NR unfaithfulness for the …
One of the major assumptions in the search for gravitational wave signatures from massive and supermassive black hole binaries with LISA, is that these systems will have circularized before entering the LISA bandwidth. Current astrophysical simulations now suggest that systems could have a non-negligible eccentricity in the LISA band, and an important level of eccentricity in the Pulsar Timing regime. In this work, we use a set of source catalogues from astrophysically motivated models of massive black hole binary formation and assume a one year LISA mission lifetime. Depending on the model in…
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…
Binary neutron stars (BNSs) are the primary source of gravitational waves for the Laser Interferometer Gravitational-Wave Observatory (LIGO) and its international partners Virgo and KAGRA. Current BNS searches target field binaries whose orbits will have circularized by radiation reaction before their gravitational waves enter the Advanced LIGO sensitive band at 15 Hz. It has been suggested that a population of BNSs may form by n-body interactions near supermassive black holes or in globular clusters and that these systems may have non-negligible eccentricity in the Advanced LIGO band. We show…
Two binary neutron star mergers, GW170817 and GW190425, have been detected by Advanced LIGO and Virgo. These signals were detected by matched-filter searches that assume the star's orbit has circularized by the time their gravitational-wave emission is observable. This suggests that their eccentricity is low, but full parameter estimation of their eccentricity has not yet been performed. We use gravitational-wave observations to measure the eccentricity of GW170817 and GW190425. We find that the eccentricity at a gravitational-wave frequency of 10 Hz is $e \leq 0.024$ and $e \leq 0.048$ for GW…
Future Gaia and Legacy Survey of Space and Time data releases, together with wide area spectroscopic surveys, will deliver large samples of resolved binary stars with phase space coordinates, albeit with low-cadence. Given an eccentricity law $f(ε)$, we derive properties of (i) the velocity distribution $v/\sqrt{G M/r}$ normalised by the value for a circular orbit at the measured separation $r$; (ii) the astrometric acceleration distributions $a/\left(G M/r^2\right)$ again normalised to the circular orbit value. Our formulation yields analytic predictions for the full statistical distribution …
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 …
The Laser Interferometer Space Antenna (LISA) is designed to detect gravitational wave signals from astrophysical sources, including those from coalescing binary systems of compact objects such as black holes. Colliding galaxies have central black holes that sink to the center of the merged galaxy and begin to orbit one another and emit gravitational waves. Some galaxy evolution models predict that the binary black hole system will enter the LISA band with significant orbital eccentricity, while other models suggest that the orbits will already have circularized. Using a full seventeen paramet…
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）
We investigate the stable circular orbits of the spinning test particles around the accelerating Kerr black hole on the equatorial plane. To this end, we first calculate the equations of motion and analyze the parameter space for the particles. We study the effect of the particle's spin and the black hole's acceleration on the conserved angular momentum, conserved energy and radius of the spinning test particle on the innermost stable circular orbit. We find that the effect of the particle's spin on the orbit parameters is almost linear, the effect of the black hole's acceleration on those par…
Gravitational-wave observations provide a unique opportunity to test general relativity (GR) in the strong-field and highly dynamical regime of the theory. Parametrized tests of GR are one well-known approach for quantifying violations of GR. This approach constrains deviations in the coefficients of the post-Newtonian phasing formula, which describes the gravitational-wave phase evolution of a compact binary as it inspirals. Current bounds from this test using LIGO/Virgo observations assume that binaries are circularized by the time they enter the detector frequency band. Here, we investigate…
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…
Biased parameter inference of eccentric, spin-precessing binary black holes
Cardiff University（卡迪夫大学）；Indian Institute of Technology Madras（马德拉斯印度理工学院）；Penn State University（宾夕法尼亚州立大学）；Tata Institute of Fundamental Research（塔塔基础研究所）
