Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order

Faye, Guillaume; Blanchet, Luc; Iyer, B. R.

doi:10.1088/0264-9381/32/4/045016

Cited by 59 publications

(64 citation statements)

References 61 publications

(191 reference statements)

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“…We assume m ⩾ 0; the modes having m < 0 are easily deduced using . The dominant mode , which is primarily important for numerical relativity comparisons, is known at 3.5PN order and reads [74, 197] Similarly, we report the subdominant modes and also known at 3.5PN order [195] The other modes are known with a precision consistent with 3PN order in the full waveform [74]: Notice that the modes with m = 0 are zero except for the DC (zero-frequency) non-linear memory contributions. We already know that this effect arises at Newtonian order [see Eq.…”

Section: Gravitational Waves From Compact Binariesmentioning

confidence: 99%

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Blanchet

2014

Living Rev. Relativ.

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1,428

1,617

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To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (eLISA, etc.), inspiralling compact binaries — binary star systems composed of neutron stars and/or black holes in their late stage of evolution — require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary’s orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries — moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.

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Section: Gravitational Waves From Compact Binariesmentioning

confidence: 99%

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Blanchet

2014

Living Rev. Relativ.

Self Cite

1,428

1,617

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“…These integrals, although somewhat complicated, can be evaluated numerically (as was done in [35]). Alternately, the integral can be recast in terms of symmetric-tracefree tensors or scalar spherical harmonics and evaluated analytically (in terms of Clebsch-Gordon coefficients or Wigner 3-j symbols) [15,54,57].…”

Section: Computing the Nonlinear Gw Memorymentioning

confidence: 99%

Forecasts for detecting the gravitational-wave memory effect with Advanced LIGO and Virgo

2020

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The detection of gravitational waves (GWs) from binary black holes (BBHs) has allowed the theory of general relativity to be tested in a previously unstudied regime: that of strong curvature and high GW luminosities. One distinctive and measurable effect associated with this aspect of the theory is the nonlinear GW memory effect. The GW memory effect is characterized by its effect on freely falling observers: the proper distance between their locations differs before and after a burst of GWs passes by their locations. Gravitational-wave interferometers, like the LIGO and Virgo detectors, can measure features of this effect from a single BBH merger, but previous work has shown that it will require an event that is significantly more massive and closer than any previously detected GW event. Finding evidence for the GW memory effect within the entire population of BBH mergers detected by LIGO and Virgo is more likely to occur sooner. A prior study has shown that the GW memory effect could be detected in a population of BBHs consisting of binaries like the first GW150914 event after roughly one-hundred events. In this paper, we compute forecasts of the time it will take the advanced LIGO and Virgo detectors (when the detectors are operating at their design sensitivities) to find evidence for the GW memory effect in a population of BBHs that is consistent with the measured population of events in the first two observing runs of the LIGO detectors. We find that after five years of data collected by the advanced LIGO and Virgo detectors the signal-to-noise ratio for the nonlinear GW memory effect in the population will be about three (near a previously used threshold for detection). We point out that the different approximation methods used to compute the GW memory effect can lead to notably different signal-to-noise ratios.

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“…III, provides the ideal tool to compute all the logarithmic terms coming from simple tails, the only limitation being the knowledge of the multipole moments of the binary constituents, at the desired PN order. Given that the current knowledge is limited to 3PN for the mass quadrupole moment [44][45][46], we are presently able to provide such terms up to 7PN order.…”

Section: A Simple Tail Termsmentioning

confidence: 99%

Logarithmic tail contributions to the energy function of circular compact binaries

et al. 2020

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We combine different techniques to extract information about the logarithmic contributions to the two-body conservative dynamics within the post-Newtonian (PN) approximation of General Relativity. The logarithms come from the conservative part of non linear gravitational-wave tails and their iterations. Explicit, original expressions are found for conservative dynamics logarithmic tail terms up to 6PN order by adopting both traditional PN calculations and effective field theory (EFT) methods. We also determine all logarithmic terms at 7PN order, fixing a sub-leading logarithm from a tail-of-tail-of-tail process by comparison with self-force (SF) results. Moreover, we use renormalization group techniques to obtain the leading logarithmic terms to generic power n, appearing at (3n + 1)PN order, and we resum the infinite series in a closed form. Half-integer PN orders enter the conservative dynamics starting at 5.5PN, but they do not generate logarithmic contributions up to next-to-next-to-leading order included. We nevertheless present their contribution at leading order in the small mass ratio limit. I. MOTIVATIONS AND OVERVIEWThe post-Newtonian (PN) approximation to General Relativity (GR) has been a largely successful framework to perturbatively solve Einstein's equations, widely adopted and approached with a variety of methods, see Refs. [1][2][3][4][5] for recent reviews. Among the most important methods we mention the ADM Hamiltonian approach [6-8], the Multipolar-post-Minkowskian framework with PN matching (MPM-PN) [9,10], the direct integration of the relaxed field equations (DIRE) [11], the surface-integral approach [12] and the Effective Field Theory (EFT) approach pioneered by Ref. [13]. In particular we want to highlight here the great synergies existing today between the EFT approach and more traditional PN methods.Within the two-body dynamics, we focus in the present work on tail processes, which arise from the back-scattering of gravitational waves (GW) off the quasi-static curvature sourced by the total mass of the binary system. Tail effects are known from a long time (see e.g. [14,15]) but were first identified and investigated in the present context in [16][17][18]. They are present in both the conservative and dissipative sectors of the theory. The conservative tail effect at 4PN order [19,20] has been recently fully incorporated into the 4PN equations of motion using the ADM Hamiltonian method [21][22][23][24], the Fokker Lagrangian in harmonic coordinates [25][26][27][28] and the EFT approach [29][30][31][32]. Moreover the leading and next-to-leading logarithmic tail terms in the energy function of compact binaries on circular orbits have been derived [33][34][35][36].Tails present themselves with a characteristic logarithmic and hereditary nature, i.e., which depends of the entire history of the source rather than its state at the retarded time, corresponding to wave propagation inside the retarded light-cone. We focus our investigation in the present work to such tail logarithmic contributio...

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Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order

Cited by 59 publications

References 61 publications

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Forecasts for detecting the gravitational-wave memory effect with Advanced LIGO and Virgo

Logarithmic tail contributions to the energy function of circular compact binaries

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