Binaries In Eccentric Orbits Research Articles

A study of the inspiral-merger-ringdown consistency test with gravitational-wave signals from compact binaries in eccentric orbits

A study of the inspiral-merger-ringdown consistency test with gravitational-wave signals from compact binaries in eccentric orbits

Inferring eccentricity evolution from observations of coalescing binary black holes

The origin and formation of stellar-mass binary black holes remains an open question that can be addressed by precise measurements of the binary and orbital parameters from their gravitational-wave signal. Such binaries are expected to circularize due to the emission of gravitational waves as they approach merger. However, depending on their formation channel, some binaries could have a non-negligible eccentricity when entering the frequency band of current gravitational-wave detectors. In order to measure eccentricity in an observed gravitational-wave signal, accurate waveform models that describe binaries in eccentric orbits are necessary. In this work we demonstrate the efficacy of the improved TEOBResumS waveform model for eccentric coalescing binaries with aligned spins. We first validate the model against mock signals of aligned-spin binary black hole mergers and quantify the impact of eccentricity on the estimation of other intrinsic binary parameters. We then perform a fully Bayesian reanalysis of GW150914 with the eccentric waveform model. We find (i) that the model is reliable for aligned-spin binary black holes and (ii) that GW150914 is consistent with a non-eccentric merger although we cannot rule out small values of initial eccentricity at a reference frequency of $20$ Hz. Finally, we present a systematic method to measure the eccentricity and its evolution directly from the gravitational-wave posterior samples. Such an estimator is useful when comparing results from different analyses as the definition of eccentricity may differ between models. Our scheme can be applied even in the case of small eccentricities and can be adopted straightforwardly in post-processing to allow for direct comparison between models.

High accuracy post-Newtonian and numerical relativity comparisons involving higher modes for eccentric binary black holes and a dominant mode eccentric inspiral-merger-ringdown model

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 simple extension to a multi-mode model based on this dominant mode model is also presented. Overlaps with quasi-circular IMR waveform models including the effect of higher modes, maximized over a time- and phase-shift, hint at the importance (mismatches $>1\%$) of including eccentricity in gravitational waveforms when analysing BBHs lighter than $\sim 80 M_{\odot}$, irrespective of the binary's eccentricity (as it enters the LIGO bands), or mass-ratio. Combined impact of eccentricity and higher modes seems to become more apparent through smaller overlaps with increasing inclination angles and mass ratios. Additionally, we show that the state-of-the-art quasi-circular models including the effect of higher modes will not be adequate in extracting source properties for signals with initial eccentricities $e_0$ $\gtrsim0.1$.

Orbital and physical parameters of eclipsing binaries from the Optical Gravitational Lensing Experiment catalogue: testing the tidal circularization

ABSTRACT Tidal forces are an important process in the pre-main-sequence phase (as reported by Zahn and Bouchet in their now well-known paper) and throughout the main-sequence phase of stellar evolution. Nevertheless, uncertainty over tidal forces affects estimates obtained from models of the circularization and synchronization of the orbit by tidal interactions. Here, we search for evidence of tidal circularization in close binaries using a large sample of well-characterized eclipsing systems. We searched Optical Gravitational Lensing Experiment (OGLE) photometric catalogue for the Southern hemisphere from the Southern hemisphere for eclipsing binaries in eccentric orbits. We present precise values of the eccentricity and orbital and stellar parameters of eight detached, eclipsing stars from the OGLE catalogue that were determined by jointly modelling light curves and spectral analysis. The temperatures and relative radii of their components, as well as their mass ratios, were also calculated with high accuracy. We find a clear dependence of the components' relative radii and orbital period on the eccentricity. The determination of eccentricities as a function of period potentially allows us to infer the role of tidal circularization. The (P, r1,2) distribution of the known eccentric binaries exhibits a rough trend of increasing eccentricity with period. This suggests that the secondary components in binaries with longer orbital periods may be tidally circularized significantly more efficiently than is usually assumed. Observing this effect is challenging because it requires large and well-characterized samples that include many types of systems. Here we seek evidence of the predicted dependence of circularization on the relative radii using a sample of eclipsing binaries observed by OGLE.

Gravitational-wave amplitudes for compact binaries in eccentric orbits at the third post-Newtonian order: Memory contributions

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.

Gravitational-wave amplitudes for compact binaries in eccentric orbits at the third post-Newtonian order: Tail contributions and postadiabatic corrections

We compute the tail contributions to the gravitational-wave mode amplitudes for compact binaries in eccentric orbits at the third post-Newtonian order of general relativity. We combine them with the already available instantaneous pieces and include the post-adiabatic corrections required to fully account for the effects of radiation-reaction forces on the motion. We compare the resulting waveform in the small eccentricity limit to the circular one, finding perfect agreement.

Solving post-Newtonian accurate Kepler equation

We provide an elegant way of solving analytically the third post-Newtonian (3PN) accurate Kepler equation, associated with the 3PN-accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits. An additional analytic solution is presented to check the correctness of our compact solution and we perform comparisons between our PN-accurate analytic solution and a very accurate numerical solution of the PN-accurate Kepler equation. We adapt our approach to compute crucial 3PN-accurate inputs that will be required to compute analytically both the time and frequency domain ready-to-use amplitude-corrected PN-accurate search templates for compact binaries in inspiralling eccentric orbits.

Third post-Newtonian gravitational waveforms for compact binary systems in general orbits: Instantaneous terms

We compute the instantaneous contributions to the spherical harmonic modes of gravitational waveforms from compact binary systems in general orbits up to the third post-Newtonian order. We further extend these results for compact binaries in quasi-elliptical orbits using the 3PN quasi-Keplerian representation of the conserved dynamics of compact binaries in eccentric orbits. Using the multipolar post-Minkowskian formalism, starting from the different mass and current type multipole moments, we compute the spin weighted spherical harmonic decomposition of the instantaneous part of the gravitational waveform. These are terms which are functions of the retarded time and do not depend on the history of the binary evolution. Together with the hereditary part, which depends on the binary's dynamical history, these waveforms form the basis for construction of accurate templates for the detection of gravitational wave signals from binaries moving in quasi-elliptical orbits.

Characterizing spinning black hole binaries in eccentric orbits with LISA

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 17 parameter waveform model that includes the effects of orbital eccentricity, spin precession, and higher harmonics, we investigate how well the source parameters can be inferred from simulated LISA data. Defining the reference eccentricity as the value one year before merger, we find that for typical LISA sources, it will be possible to measure the eccentricity to an accuracy of parts in a thousand. The accuracy with which the eccentricity can be measured depends only very weakly on the eccentricity, making it possible to distinguish circular orbits from those with very small eccentricities. LISA measurements of the orbital eccentricity can help constraints theories of galaxy mergers in the early universe. Failing to account for the eccentricity in the waveform modeling can lead to a loss of signal power and bias the estimation of parameters such as the black hole masses and spins.

Measuring eccentricity in binary black-hole initial data

Initial data for evolving black-hole binaries can be constructed via many techniques, and can represent a wide range of physical scenarios. However, because of the way that different schemes parametrize the physical aspects of a configuration, it is not always clear what a given set of initial data actually represents. This is especially important for quasiequilibrium data constructed using the conformal thin-sandwich approach. Most initial-data studies have focused on identifying data sets that represent binaries in quasicircular orbits. In this paper, we consider initial-data sets representing equal-mass black-hole binaries in eccentric orbits. We will show that effective-potential techniques can be used to calibrate initial data for black-hole binaries in eccentric orbits. We will also examine several different approaches, including post-Newtonian diagnostics, for measuring the eccentricity of an orbit. Finally, we propose the use of the ``Komar-mass difference'' as a useful, invariant means of parametrizing the eccentricity of relativistic orbits.

Determination of tidal distortion in the eclipsing binary system V621 Cen by means of deviations from the third Kepler law

In this paper we determine the tidal distortion parameter k m of the secondary partner (mass loser) of the semi-detached eclipsing binary system V621 Cen by comparing the phenomenologically determined orbital period P b = 3.683549 ( 11 ) d to the Keplerian one P Kep computed with the values of the relevant system’s parameters determined independently of the third Kepler law itself. Our result is k m = - 1.5 ± 0.6 . Using the periastron precession, as traditionally done with other eclipsing binaries in eccentric orbits, would have not been possible because of the circularity of the V621 Cen path.

Accurate and efficient gravitational waveforms for certain galactic compact binaries

Stellar-mass compact binaries in eccentric orbits are almost guaranteed sources of gravitational waves for the Laser Interferometer Space Antenna. We present a prescription to compute accurate and efficient gravitational-wave polarizations associated with bound compact binaries of arbitrary eccentricity and mass ratio moving in slowly precessing orbits. We compare our approach with those existing in the literature and present its advantages.

Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction

We derive Keplerian-type parametrization for the solution of post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The PN accurate dynamics that we consider consists of the third post-Newtonian accurate conservative orbital dynamics influenced by the leading order spin effects, namely the leading order spin-orbit interactions. The orbital elements of the representation are explicitly given in terms of the conserved orbital energy, angular momentum and a quantity that characterizes the leading order spin-orbit interactions in Arnowitt, Deser, and Misner-type coordinates. Our parametric solution is applicable in the following two distinct cases: (i) the binary consists of equal mass compact objects, having two arbitrary spins, and (ii) the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. As an application of our parametrization, we present gravitational wave polarizations, whose amplitudes are restricted to the leading quadrupolar order, suitable to describe gravitational radiation from spinning compact binaries moving in eccentric orbits. The present parametrization will be required to construct `ready to use' reference templates for gravitational waves from spinning compact binaries in inspiralling eccentric orbits. Our parametric solution for the post-Newtonian accurate conservative dynamics of spinning compact binaries clearly indicates, for the cases considered, the absence of chaos in these systems. Finally, we note that our parametrization provides the first step in deriving a fully second post-Newtonian accurate `timing formula', that may be useful for the radio observations of relativistic binary pulsars like J0737-3039.

Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits

We present Keplerian-type parametrization for the solution of third post-Newtonian (3PN) accurate equations of motion for two nonspinning compact objects moving in an eccentric orbit. The orbital elements of the parametrization are explicitly given in terms of the 3PN accurate conserved orbital energy and angular momentum in both Arnowitt-Deser-Misner--type and harmonic coordinates. Our representation will be required to construct post-Newtonian accurate ``ready to use'' search templates for the detection of gravitational waves from compact binaries in inspiralling eccentric orbits. Because of the presence of certain 3PN accurate gauge invariant orbital elements, the parametrization should be useful to analyze the compatibility of general relativistic numerical simulations involving compact binaries with the corresponding post-Newtonian descriptions. If required, the present parametrization will also be needed to compute post-Newtonian corrections to the currently employed ``timing formula'' for the radio observations of relativistic binary pulsars.

An analytical study of stable planetary orbits in the circular restricted problem

In this article we treat analytically the problem of finding stability limits ofP-type orbits (=direct nearly circular orbits surrounding both primaries) in double stars. The model used is the circular restricted three body problem; in that sense the results are not valid for binaries in eccentric orbits. But as the chosen model is often used in dynamical descriptions of the problem we can compare our results with other ones derived in earlier studies with semianalytical or just numerical methods.