Non-spinning Compact Binaries Research Articles

Gravitational-wave flux and quadrupole modes from quasicircular nonspinning compact binaries to the fourth post-Newtonian order

Gravitational-wave flux and quadrupole modes from quasicircular nonspinning compact binaries to the fourth post-Newtonian order

Gravitational Waveforms for Compact Binaries from Second-Order Self-Force Theory.

We produce gravitational waveforms for nonspinning compact binaries undergoing a quasicircular inspiral. Our approach is based on a two-timescale expansion of the Einstein equations in second-order self-force theory, which allows first-principles waveform production in tens of milliseconds. Although the approach is designed for extreme mass ratios, our waveforms agree remarkably well with those from full numerical relativity, even for comparable-mass systems. Our results will be invaluable in accurately modeling extreme-mass-ratio inspirals for the LISA mission and intermediate-mass-ratio systems currently being observed by the LIGO-Virgo-KAGRA Collaboration.

Complete gravitational-waveform amplitude modes for quasicircular compact binaries to the 3.5PN order

We complete the computation of the gravitational waveform amplitude for non-spinning compact binaries to the third and a half post-Newtonian (PN) order in the quasi-circular case. This is done by performing a spin-weighted spherical harmonics decomposition of the amplitude. This computation is achieved using the post-Newtonian-Multipolar-post-Minkowskian formalism. The amplitude modes are written in a PN expanded way as well as a factorized form suitable for EOB template building. Combining this work with previous ones, we provide in the supplemental materials the expressions of the modes including all non-spinning and spinning effects to the 3.5PN order for non-precessing quasi-circular binaries.

Generalized quasi-Keplerian solution for eccentric, nonspinning compact binaries at 4PN order and the associated inspiral-merger-ringdown waveform

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 effects within the action-angles framework. We then employ the resulting solution to obtain an updated inspiral-merger-ringdown (IMR) waveform that models the coalescence of non-spinning, moderately eccentric black hole binaries, influenced by arXiv:1709.02007. Our updated waveform is expected to be valid over similar parameter range as the above reference. We also present a related waveform which makes use of only the post-Newtonian equations and thus is valid only for the inspiral stage. This waveform is expected to work for a much larger range of eccentricity ($e_t \lesssim 0.85$) than our full IMR waveform (which assumes circularization of the binaries close to merger). We finally pursue preliminary data analysis studies to probe the importance of including the 4PN contributions to the binary dynamics while constructing gravitational waveform templates for eccentric mergers.

Testing the multipole structure and conservative dynamics of compact binaries using gravitational wave observations: The spinning case

In an earlier work [S. Kastha et al., Phys. Rev. D 98, 124033 (2018)], we developed the parametrized multipolar gravitational wave phasing formula to test general relativity, for the nonspinning compact binaries in quasicircular orbit. In this paper, we extend the method and include the important effect of spins in the inspiral dynamics. Furthermore, we consider parametric scaling of post-Newtonian (PN) coefficients of the conserved energy for the compact binary, resulting in the parametrized phasing formula for nonprecessing spinning compact binaries in quasicircular orbit. We also compute the projected accuracies with which the second and third generation ground-based gravitational wave detector networks as well as the planned space-based detector LISA will be able to measure the multipole deformation parameters and the binding energy parameters. Based on different source configurations, we find that a network of third-generation detectors would have comparable ability to that of LISA in constraining the conservative and dissipative dynamics of the compact binary systems. This parametrized multipolar waveform would be extremely useful not only in deriving the first upper limits on any deviations of the multipole and the binding energy coefficients from general relativity using the gravitational wave detections, but also for science case studies of next generation gravitational wave detectors.

Testing the multipole structure of compact binaries using gravitational wave observations

We propose a novel method to test the consistency of the multipole moments of compact binary systems with the predictions of General Relativity (GR). The multipole moments of a compact binary system, known in terms of symmetric and trace-free tensors, are used to calculate the gravitational waveforms from compact binaries within the post-Newtonian (PN) formalism. For nonspinning compact binaries, we derive the gravitational wave phasing formula, in the frequency domain, parametrizing each PN order term in terms of the multipole moments which contribute to that order. Using GW observations, this {\it{parametrized multipolar phasing}} would allow us to derive the bounds on possible departures from the multipole structure of GR and hence constrain the parameter space of alternative theories of gravity. We compute the projected accuracies with which the second generation ground-based detectors, such as Advanced Laser Interferometer Gravitational-wave Observatory (LIGO), the third generation detectors such as Einstein Telescope and Cosmic Explorer, as well as space-based detector Laser Interferometer Space Antenna (LISA) will be able to measure these multipole parameters. We find that while Advanced LIGO can measure the first two or three multipole coefficients with good accuracy, Cosmic Explorer and Einstein Telescope may be able to measure the first four multipole coefficients which enter the phasing formula. Intermediate mass ratio inspirals, with mass ratio of several tens, in the frequency band of planned space-based LISA mission should be able to measure all the seven multipole coefficients which appear in the 3.5PN phasing formula. Our finding highlights the importance of this class of sources for probing the strong-field gravity regime. The proposed test will facilitate the first probe of the multipolar structure of Einstein's general relativity.

Gravitational waves from compact binaries in post-Newtonian accurate hyperbolic orbits

We derive from first principles third post-Newtonian (3PN) accurate Keplerian-type parametric solution to describe PN-accurate dynamics of non-spinning compact binaries in hyperbolic orbits. Orbital elements and functions of the parametric solution are obtained in terms of the conserved orbital energy and angular momentum in both Arnowitt-Deser-Misner type and modified harmonic coordinates. Elegant checks are provided that include a modified analytic continuation prescription to obtain our independent hyperbolic parametric solution from its eccentric version. A prescription to model gravitational wave polarization states for hyperbolic compact binaries experiencing 3.5PN-accurate orbital motion is presented that employs our 3PN-accurate parametric solution.

Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation

The Fokker action governing the motion of compact binary systems without spins is derived in harmonic coordinates at the fourth post-Newtonian approximation (4PN) of general relativity. Dimensional regularization is used for treating the local ultraviolet (UV) divergences associated with point particles, followed by a renormalization of the poles into a redefinition of the trajectories of the point masses. Effects at the 4PN order associated with wave tails propagating at infinity are included consistently at the level of the action. A finite part procedure based on analytic continuation deals with the infrared (IR) divergencies at spatial infinity, which are shown to be fully consistent with the presence of near-zone tails. Our end result at 4PN order is Lorentz invariant and has the correct self-force limit for the energy of circular orbits. However, we find that it differs from the recently published result derived within the ADM Hamiltonian formulation of general relativity [T. Damour, P. Jaranowski, and G. Sch\"afer, Phys. Rev. D 89, 064058 (2014)]. More work is needed to understand this discrepancy.

The remains of a spinning, hyperbolic encounter

We review a recently proposed approach to construct gravitational wave (GW) polarization states of unbound spinning compact binaries. Through this rather simple method, we are able to include corrections due to the dominant order spin-orbit interactions, in the quadrupolar approximation and in a semi-analytic way. We invoke the 1.5 post-Newtonian (PN) accurate quasi-Keplerian parametrization for the radial part of the dynamics and impose its temporal evolution in the PN accurate polarization states equations. Further, we compute 1PN accurate amplitude corrections for the polarization states of non-spinning compact binaries on hyperbolic orbits. As an interesting application, we perform comparisons with previously available results for both the GW signals in the case of non-spinning binaries and the theoretical prediction for the amplitude of the memory effect on the metric after the hyperbolic passage.

Gravitational waves from spinning compact binaries in hyperbolic orbits

Compact binaries in hyperbolic orbits are plausible gravitational wave (GW) sources for the upcoming and planned GW observatories. We develop an efficient prescription to compute post-Newtonian (PN) accurate ready-to-use GW polarization states for spinning compact binaries, influenced by the dominant order spin-orbit interactions, in hyperbolic orbits. This is achieved by invoking the 1.5PN accurate quasi-Keplerian parameterization for the radial sector of the orbital dynamics. We probe the influences of spins and gravitational radiation reaction on $h_+$ and $h_{\times}$ during the hyperbolic passage. It turns out that both polarization states exhibit the memory effect for GWs from spinning compact binaries in hyperbolic orbits. In contrast, only cross polarization state exhibits the memory effect for GWs from non-spinning compact binaries. Additionally, we compute 1PN accurate amplitude corrected GW polarization states for hyperbolic non-spinning compact binaries in a fully parametric manner and perform initial comparisons with the existing waveforms.

Singular value decomposition in parametrized tests of post-Newtonian theory

Various coefficients of the 3.5 post-Newtonian (PN) phasing formula of non-spinning compact binaries moving in circular orbits is fully characterized by the two component masses. If two of these coefficients are independently measured, the masses can be estimated. Future gravitational wave observations may measure most of the eight independent PN coefficients calculated to date. These additional measurements can be used to test the PN predictions of the underlying theory of gravity with a similar PN structure. Since all of these parameters are functions of the two component masses, there is a strong correlation between the parameters when treated independently. Using singular value decomposition of the Fisher information matrix, we remove these correlations and obtain a new set of parameters which are a linear combination of the original phasing coefficients. We show that the new set of parameters can be estimated with significantly improved accuracies which have implications for the ongoing efforts to implement parametrized tests of PN theory in the data analysis pipelines.

Gravitational wave phasing for spinning compact binaries in inspiraling eccentric orbits

We present a semi-analytic prescription to obtain gravitational wave (GW) phasing for spinning compact binaries in inspiraling eccentric orbits, while restricting the spin effects to the leading order spin-orbit coupling. We demonstrate that only the radial part of the orbital dynamics is amenable for a Keplerian-type solution that is compatible with the standard post-Newtonian (PN) accurate quasi-Keplerian parametrization for nonspinning compact binaries. We also derive PN-accurate equations governing the evolution of the Eulerian angles that are crucial to obtain temporally evolving GW polarization states and compute the associated fully 1PN accurate amplitude corrected GW polarization states. We show that it is not possible to obtain a Keplerian-type parametric solution for the angular part of the above dynamics in a noninertial frame that follows the precessing orbital plane [N. J. Cornish and J. S. Key, Phys. Rev. D 82, 044028 (2010)]. Further, we point out certain undesirable features present in their approach for doing GW phasing, like the use of precessing polarization vectors to construct the polarization states.

Full-analytic frequency-domain gravitational wave forms from eccentric compact binaries to 2PN accuracy

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 Sch\"afer, 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 of the Kepler equation in harmonic coordinates is provided, as well as the analytic time Fourier expansion of trigonometric functions of the eccentric anomaly in terms of sines and cosines of the mean anomaly. Tail terms are not considered.

Full-analytic frequency-domain first-post-Newtonian-accurate gravitational wave forms from eccentric compact binaries

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.

Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope

General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitationalwave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44 Msun. The choice of the lower frequency cut off is important for testing post-Newtonian theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.

Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order

We obtain an efficient description for the dynamics of nonspinning compact binaries moving in inspiralling eccentric orbits to implement the phasing of gravitational waves from such binaries at the 3.5 post-Newtonian (PN) order. Our computation heavily depends on the phasing formalism, presented in [T. Damour, A. Gopakumar, and B. R. Iyer, Phys. Rev. D 70, 064028 (2004)], and the 3PN accurate generalized quasi-Keplerian parametric solution to the conservative dynamics of nonspinning compact binaries moving in eccentric orbits, available in [R.-M. Memmesheimer, A. Gopakumar, and G. Sch\"afer, Phys. Rev. D 70, 104011 (2004)]. The gravitational-wave (GW) polarizations ${h}_{+}$ and ${h}_{\ifmmode\times\else\texttimes\fi{}}$ with 3.5PN accurate phasing should be useful for the earth-based GW interferometers, current and advanced, if they plan to search for gravitational waves from inspiralling eccentric binaries. Our results will be required to do astrophysics with the proposed space-based GW interferometers like LISA, BBO, and DECIGO.

Erratum: Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The nonspinning case [Phys. Rev. D71, 084008 (2005)

(Abridged) We revisit the problem of parameter estimation of gravitational-wave chirp signals from inspiralling non-spinning compact binaries in the light of the recent extension of the post-Newtonian (PN) phasing formula to order $(v/c)^7$ beyond the leading Newtonian order. We study in detail the implications of higher post-Newtonian orders from 1PN up to 3.5PN in steps of 0.5PN ($\sim v/c$), and examine their convergence. In both initial and advanced detectors the estimation of the chirp mass (${\cal M}$) and symmetric mass ratio ($\eta$) improve at higher PN orders but oscillate with every half-a-PN order. We compare parameter estimation in different detectors and assess their relative performance in two different ways: at a {\it fixed SNR,} with the aim of understanding how the bandwidth improves parameter estimation, and for a {\it fixed source}, to gauge the importance of sensitivity. Errors in parameter estimation at a fixed SNR are smaller for VIRGO than for both initial and advanced LIGO. However, for sources at a fixed distance it is advanced LIGO that achieves the lowest errors owing to its greater sensitivity. Finally, we compute the amplitude corrections due to the `frequency-sweep' in the Fourier domain representation of the waveform within the stationary phase approximation and discuss its implication on parameter estimation.

Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The nonspinning case

We revisit the problem of parameter estimation of gravitational-wave chirp signals from inspiralling nonspinning compact binaries in the light of the recent extension of the post-Newtonian (PN) phasing formula to order $(v/c{)}^{7}$ beyond the leading Newtonian order. We study in detail the implications of higher post-Newtonian orders from 1PN up to 3.5PN in steps of 0.5PN ($\ensuremath{\sim}v/c$), and examine their convergence. In both initial and advanced detectors the estimation of the chirp mass ($\mathcal{M}$) and symmetric mass ratio ($\ensuremath{\eta}$) improve at higher PN orders but oscillate with every half-a-PN order. In initial LIGO, for a $10{M}_{\ensuremath{\bigodot}}--10{M}_{\ensuremath{\bigodot}}$ binary at a signal-to-noise ratio (SNR) of 10, the improvement in the estimation of $\mathcal{M}$ ($\ensuremath{\eta}$) at 3.5PN relative to 2PN is $\ensuremath{\sim}19%$ (52%). We compare parameter estimation in different detectors and assess their relative performance in two different ways: at a fixed SNR, with the aim of understanding how the bandwidth improves parameter estimation, and for a fixed source, to gauge the importance of sensitivity. Errors in parameter estimation at a fixed SNR are smaller for VIRGO than for both initial and advanced LIGO. This is because of the larger bandwidth over which it observes the signals. However, for sources at a fixed distance it is advanced LIGO that achieves the lowest errors owing to its greater sensitivity. Finally, we compute the amplitude corrections due to the ``frequency-sweep'' in the Fourier domain representation of the waveform within the stationary phase approximation and discuss its implication on parameter estimation. We find that the amplitude corrections change the errors in $\mathcal{M}$ and $\ensuremath{\eta}$ by less than 10% for initial LIGO at a signal-to-noise ratio of 10. Our analysis makes explicit the significance of higher PN order modeling of the inspiralling compact binary on parameter estimation.