Electromagnetic fields in compact binaries: a post-Newtonian approach
Quentin Henry, François Larrouturou, Christophe Le Poncin-Lafitte
备注：
23 pages, no figure, supplementary material attached. v2: references and acknowledgments updated. v3: post-referee version (Eq. (3.3b) and typos corrected, discussions added)
银河系双星，尤其是双白矮星系统，将成为未来 LISA 和 Einstein Telescope 探测器的重要引力波源。与当前 LIGO-Virgo-KAGRA 网络观测到的黑洞不同，这些天体携带着强磁场，人们自然预期这些磁场会在引力波辐射中留下某些印记。因此，本工作的目的是在特别适用于双白矮星系统的后牛顿（PN）框架内研究这些印记。为此，我们构建了一个考虑恒星完整电磁结构的有效作用量，随后将其具体化到偶极阶。利用这一作用量，我们在相对 2PN 阶计算了一般电偶极子和磁偶极子的加速度及 Noether 量。最后，通过聚焦于物理上相关的系统，我们表明磁场对轨道频率、能量和角动量的影响是显著的，这证实了以往工作的结论。
英文摘要：
Galactic binaries, and notably double white dwarfs systems, will be a prominent source for the future LISA and Einstein Telescope detectors. Contrarily to the black holes observed by the current LIGO-Virgo-KAGRA network, such objects bear intense magnetic fields, that are naturally expected to leave some imprints on the gravitational wave emission. The purpose of this work is thus to study those imprints within the post-Newtonian (PN) framework, particularly adapted to double white dwarfs systems. To this end, we construct an effective action that takes into account the whole electromagnetic structure of a star, and then specify it to dipolar order. With this action at hand, we compute the acceleration and Noetherian quantities for generic electric and magnetic dipoles, at a relative 2PN order. Finally, focusing on physically relevant systems, we show that the magnetic effects on the orbital frequency, energy and angular momentum is significant, confirming previous works conclusions.
We present the next-to-next-to-leading order post-Newtonian (PN) spin(1)-spin(2) Hamiltonian for two self-gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincare algebra with the center-of-mass vector uniquely determined by an ansatz.
We present the next-to-next-to-leading order post-Newtonian (PN) spin-orbit Hamiltonian for two self-gravitating spinning compact objects. If at least one of the objects is rapidly rotating, then the corresponding interaction is comparable in strength to a 3.5PN effect. The result in the present paper in fact completes the knowledge of the post-Newtonian Hamiltonian for binary spinning black holes up to and including 3.5PN. The Hamiltonian is checked via known results for the test-spin case and via the global Poincare algebra with the center-of-mass vector uniquely determined by an ansatz.
The set up of matched filters for the detection of gravitational waves from in-spiraling compact binaries is usually carried out using the restricted post-Newtonian approximation: the filter phase is modelled including post-Newtonian corrections, whereas the amplitude is retained at the Newtonian order. Here we investigate the effects of the introduction of post-Newtonian corrections also to the amplitude and we discuss some of the implications for signal detection and parameter estimation.
The accuracy of the post-Newtonian waveforms, both in standard and Pade form, is determined by computing their matched-filtering overlap integral with a reference waveform obtained from black-hole perturbation theory.
We develop a semi-analytical approach, based on the post-Newtonian expansion and on the affine approximation, to model the tidal deformation of neutron stars in the coalescence of black hole-neutron star or neutron star-neutron star binaries. Our equations describe, in a unified framework, both the system orbital evolution, and the neutron star deformations. These are driven by the tidal tensor, which we expand at 1/c^3 post-Newtonian order, including spin terms. We test the theoretical framework by simulating black hole-neutron star coalescence up to the onset of mass shedding, which we deter…
We present further evidence that the second post-Newtonian (pN) approximation to the gravitational waves emitted by inspiraling compact binaries is sufficient for the detection of these systems. This is established by comparing the 2-pN wave forms to signals calculated from black hole perturbation theory. Results are presented for different detector noise curves. We also discuss the validity of this type of analysis.
Emission of anisotropic gravitational radiation from compact binary system leads to a flux of linear momentum. This results in the recoil of the system. We investigate the rate of loss of Linear momentum flux in the far zone of the source using various mass type and current type multipole moments for inspiralling compact binary mergers in quasi-elliptical orbits at 2.5 Post Newtonian order. We compute the linear momentum flux accurate up to $\mathcal{O}(e_t)$ in harmonic coordinate. A 2.5 Post Newtonian Quasi-Keplarian representation of the parametric solution to the Post Newtonian equation of…
The increasing sophistication and accuracy of numerical simulations of compact binaries (especially binary black holes) presents the opportunity to test the regime in which post-Newtonian (PN) predictions for the emitted gravitational waves are accurate. In order to confront numerical results with those of post-Newtonian theory, it is convenient to compare multipolar decompositions of the two waveforms. It is pointed out here that the individual modes can be computed to higher post-Newtonian order by examining the radiative multipole moments of the system, rather than by decomposing the 2.5PN …
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.
A brief review is given of all the Hamiltonians and effective potentials calculated hitherto covering the post-Newtonian (pN) dynamics of a two body system. A method is presented to compare (conservative) reduced Hamiltonians with nonreduced potentials directly at least up to the next-to-leading-pN order.
The leading-order spin-orbit coupling is included in a post-Newtonian Lagrangian formulation of spinning compact binaries, which consists of the Newtonian term, first post-Newtonian (1PN) and 2PN non-spin terms and 2PN spin-spin coupling. This makes a 3PN spin-spin coupling occur in the derived Hamiltonian. The spin-spin couplings are mainly responsible for chaos in the Hamiltonians. However, the 3PN spin-spin Hamiltonian is small and has different signs, compared with the 2PN spin-spin Hamiltonian equivalent to the 2PN spin-spin Lagrangian. As a result, the probability of the occurrence of ch…
This is an extended summary of the two parallel sessions held at MG11: PPN1 ``Strong Gravity and Binaries'' (chaired by L.B. and L.G.) and PPN2 ``Post-Newtonian Dynamics in Binary Objects'' (chaired by G.S.). The aims and contents of these sessions were close to each other and overlapping. It is natural to review both sessions in one joint contribution to the MG11 Proceedings. The summary places the delivered talks in a broader perspective of current studies in this area. One can find more details in individual contributions of the respective authors.
We use the Effective Field Theory (EFT) framework to compute the mass quadrupole moment, the equation of motion, and the power loss of inspiralling compact binaries at the second order in the Post-Newtonian (PN) approximation. We present expressions for the stress-energy pseudo-tensor components of the binary system in higher PN orders. The 2PN correction to the mass quadrupole moment as well as to the acceleration computed in the linearized harmonic gauge presented here are the ingredients needed for the calculation of the next-to-next-to leading order radiation reaction force, which will be …
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.
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 gravitatio…
The Laser Interferometer Space Antenna (LISA) will observe black hole binaries of stellar origin during their gravitational wave inspiral, months to years before coalescence. Due to the long duration of the signal in the LISA band, a faithful waveform is necessary in order to keep track of the binary phase. This is crucial to extract the signal from the data and to perform an unbiased estimation of the source parameters. We consider Post-Newtonian (PN) waveforms, and analyze the PN order needed to keep the bias caused by the PN approximation negligible relative to the statistical parameter est…
We present Keplerian-type parametrization for the solution of third post-Newtonian (3PN) accurate equations of motion for two non-spinning 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, and 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. Due to…
Coalescing binary systems are one of the most promising sources of gravitational waves. The technique of matched filtering used in the detection of gravitational waves from coalescing binaries relies on the construction of accurate templates. Until recently filters modelled on the quadrupole or the Newtonian approximation were deemed sufficient. Recently it was shown that post-Newtonian effects contribute to a secular growth in the phase difference between the actual signal and its corresponding Newtonian template. In this paper we investigate the possibility of compensating for the phase diff…
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.
The two independent ``plus" and ``cross" polarization waveforms associated with the gravitational waves emitted by inspiralling, non-spinning, compact binaries are presented, ready for use in the data analysis of signals received by future laser interferometer gravitational-wave detectors such as LIGO and VIRGO. The computation is based on a recently derived expression of the gravitational field at the second-post-Newtonian approximation of general relativity beyond the dominant (Newtonian) quadrupolar field. The use of these theoretical waveforms to make measurements of astrophysical paramete…
We derive the equation of motion for the relativistic compact binaries in the post-Newtonian approximation taking explicitly their strong internal gravity into account. For this purpose we adopt the method of the point particle limit where the equation of motion is expressed in terms of the surface integrals. We examine carefully the behavior of the surface integrals in the derivation. As a result, we obtain the Einstein-Infeld-Hoffman equation of motion at the first post-Newtonian (1PN) order, and a part of the 2PN order which depends on the quadrupole moments and the spins of component stars…
The post-post-Newtonian (2PN) accurate mass quadrupole moment, for compact binaries of arbitrary mass ratio, moving in general orbits is obtained by the multi-polar post Minkowskian approach of Blanchet, Damour, and Iyer (BDI). Using this, for binaries in general orbits, the 2PN contributions to the gravitational waveform, and the associated far-zone energy and angular momentum fluxes are computed. For quasi-elliptic orbits, the energy and angular momentum fluxes are averaged over an orbital period, and employed to determine the 2PN corrections to the rate of decay of the orbital elements.
We consider LISA observations of in-spiral signals emitted by massive black hole binary systems in circular orbit and with negligible spins. We study the accuracy with which the source parameters can be extracted from the data stream. We show that the use of waveforms retaining post-Newtonian corrections not only to the phase but also the amplitude can drastically improve the estimation of some parameters.
The spin memory effect is a recently predicted relativistic phenomenon in asymptotically flat spacetimes that become nonradiative infinitely far in the past and future. Between these early and late times, the magnetic-parity part of the time integral of the gravitational-wave strain can undergo a nonzero change; this difference is the spin memory effect. Families of freely falling observers around an isolated source can measure this effect, in principle, and fluxes of angular momentum per unit solid angle (or changes in superspin charges) generate the effect. The spin memory effect had not bee…
We calculate the gravitational waveform for spinning, precessing compact binary inspirals through second post-Newtonian order in the amplitude. When spins are collinear with the orbital angular momentum and the orbits are quasi-circular, we further provide explicit expressions for the gravitational-wave polarizations and the decomposition into spin-weighted spherical-harmonic modes. Knowledge of the second post-Newtonian spin terms in the waveform could be used to improve the physical content of analytical templates for data analysis of compact binary inspirals and for more accurate comparison…
The orbital motion of inspiralling and coalescing black hole binaries can be investigated using a variety of approximation schemes and numerical methods within general relativity: post-Newtonian expansions, black hole perturbation theory, numerical relativity, and the effective-one-body formalism. We review two recent comparisons of the predictions from these various techniques. Both comparisons rely on the calculation of a coordinate invariant relation, in the case of non-spinning binary black holes on quasi-circular orbits. All methods are shown to agree very well in their common domain of v…
We compute the spin-tidal couplings that affect the dynamics of two orbiting bodies at the leading order in the post-Newtonian (PN) framework and to linear order in the spin. These corrections belong to two classes: (i) terms arising from the coupling between the ordinary tidal terms and the point-particle terms, which depend on the standard tidal Love numbers of order $l$ and affect the gravitational-wave (GW) phase at $(2l+5/2)$PN order and (ii) terms depending on the rotational tidal Love numbers, recently introduced in previous work, that affect the GW phase at $(2l+1/2+δ_{2l})$PN order. F…
We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, an…
A third post-Newtonian (3 PN) equation of motion for two spherical compact stars in a harmonic coordinate has been derived based on the surface integral approach and the strong field point particle limit. The strong field point particle limit enables us to incorporate a notion of a self-gravitating regular star into general relativity. The resulting 3 PN equation of motion is Lorentz invariant, unambiguous, and conserves an energy of the binary orbital motion.
This paper is motivated by the need to improve the post-Newtonian (PN) amplitude accuracy of waveforms for gravitational waves generated by inspiralling compact binaries, both for use in data analysis and in the comparison between post-Newtonian approximations and numerical relativity computations. It presents: (i) the non-linear couplings between multipole moments of general post-Newtonian matter sources up to order 3.5PN, including all contributions from tails, tails-of-tails and the non-linear memory effect; and (ii) the source mass-type octupole moment of (non-spinning) compact binaries up…
We present analytic computations of gauge invariant quantities for a point mass in a circular orbit around a Schwarzschild black hole, giving results up to 15.5 post-Newtonian order in this paper and up to 21.5 post-Newtonian order in an online repository. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi (MST) and a recent series of results by Bini and Damour. We develop an optimised method for generating post-Newtonian expansions of the MST series, enabling significantly faster computations. We also clarify the structure of the expansions for large values …
We present a new phenomenological gravitational waveform model for the inspiral and coalescence of non-precessing spinning black hole binaries. Our approach is based on a frequency domain matching of post-Newtonian inspiral waveforms with numerical relativity based binary black hole coalescence waveforms. We quantify the various possible sources of systematic errors that arise in matching post-Newtonian and numerical relativity waveforms, and we use a matching criteria based on minimizing these errors; we find that the dominant source of errors are those in the post-Newtonian waveforms near th…
The gravitational radiation from point particle binaries is computed at the third post-Newtonian (3PN) approximation of general relativity. Three previously introduced ambiguity parameters, coming from the Hadamard self-field regularization of the 3PN source-type mass quadrupole moment, are consistently determined by means of dimensional regularization, and proved to have the values xi = -9871/9240, kappa = 0 and zeta = -7/33. These results complete the derivation of the general relativistic prediction for compact binary inspiral up to 3.5PN order, and should be of use for searching and deciph…
Recent perturbative self-force computations (Shah, Friedman & Whiting, submitted to Phys. Rev. {\bf D}, arXiv:1312.1952 [gr-qc]), both numerical and analytical, have determined that half-integral post-Newtonian terms arise in the conservative dynamics of black-hole binaries moving on exactly circular orbits. We look at the possible origin of these terms within the post-Newtonian approximation, find that they essentially originate from non-linear "tail-of-tail" integrals and show that, as demonstrated in the previous paper, their first occurrence is at the 5.5PN order. The post-Newtonian method…
We ascertain the effectiveness of the second post-Newtonian approximation to the gravitational waves emitted during the adiabatic inspiral of a compact binary system as templates for signal searches with kilometer-scale interferometric detectors. The reference signal is obtained by solving the Teukolsky equation for a small mass moving on a circular orbit around a large nonrotating black hole. Fitting factors computed from this signal and these templates, for various types of binary systems, are all above the 90% mark. According to Apostolatos' criterion, second post-Newtonian waveforms should…
We present our 3.5PN computation of the (2,2) mode of the gravitational wave amplitude emitted by compact binaries, on quasi-circular orbits and in the absence of spins. We use the multipolar post-Newtonian wave generation formalism, extending and building on previous works which computed the 3PN order. This calculation required the extension of the multipolar post-Minkowskian algorithm, as well as the computation of the mass source quadrupole at 3.5PN order. Our result will allow more accurate comparisons to numerical relativity, and is a first step towards the computation of the full 3.5PN w…
We compute the overlap function between Post-Newtonian (PN) templates and gravitational signals emitted by binary systems composed of one neutron star and one point mass, obtained by a perturbative approach. The calculations are performed for different stellar models and for different detectors, to estimate how effectual and faithful the PN templates are, and to establish whether effects related to the internal structure of neutron stars may possibly be extracted by the matched filtering technique.
The radiative evolution of the relative orientations of the spin and orbital angular momentum vectors ${\bf S}_{\bf 1}, {\bf S}_{\bf 2}$ and ${\bf L}$, characterizing a binary system on eccentric orbit is studied up to the second post-Newtonian order. As an intermediate result, all Burke-Thorne type instantaneous radiative changes in the spins are shown to average out over a radial period. It is proved that spin-orbit and spin-spin terms contribute to the radiative angular evolution equations, while Newtonian, first and second post-Newtonian terms together with the leading order tail terms do …
We derive spin-orbit coupling effects on the gravitational field and equations of motion of compact binaries in the 2.5 post-Newtonian approximation to general relativity, one PN order beyond where spin effects first appear. Our method is based on that of Blanchet, Faye, and Ponsot, who use a post-Newtonian metric valid for general (continuous) fluids and represent pointlike compact objects with a delta-function stress-energy tensor, regularizing divergent terms by taking the Hadamard finite part. To obtain post-Newtonian spin effects, we use a different delta-function stress-energy tensor int…
Compact binaries inspiralling along eccentric orbits are plausible gravitational wave (GW) sources for the ground-based laser interferometers. We explore the losses in the event rates incurred when searching for GWs from compact binaries inspiralling along post-Newtonian accurate eccentric orbits with certain obvious non-optimal search templates. For the present analysis, GW signals having 2.5 post-Newtonian accurate orbital evolution are modeled following the phasing formalism, presented in [T. Damour, A. Gopakumar, and B. R. Iyer, Phys. Rev. D \textbf{70}, 064028 (2004)]. We demonstrate that…
We derive the gravitational field and equations of motion of compact binary systems up to the 5/2 post-Newtonian approximation of general relativity (where radiation-reaction effects first appear). The approximate post-Newtonian gravitational field might be used in the problem of initial conditions for the numerical evolution of binary black-hole space-times. On the other hand we recover the Damour-Deruelle 2.5PN equations of motion of compact binary systems. Our method is based on an expression of the post-Newtonian metric valid for general (continuous) fluids. We substitute into the fluid me…
We compute the quadrupole mode of the gravitational waveform of inspiralling compact binaries at the third and a half post-Newtonian (3.5PN) approximation of general relativity. The computation is performed using the multipolar post-Newtonian formalism, and restricted to binaries without spins moving on quasi-circular orbits. The new inputs mainly include the 3.5PN terms in the mass quadrupole moment of the source, and the control of required subdominant corrections to the contributions of hereditary integrals (tails and non-linear memory effect). The result is given in the form of the quadrup…
In this paper, we compare the waveforms from the post-Newtonian (PN) approach with the numerical simulations of generic black-hole binaries which have mass ratio $q\sim0.8$, arbitrarily oriented spins with magnitudes $S_1/m_1^2\sim0.6$ and $S_2/m_2^2\sim0.4$, and orbit 9 times from an initial orbital separation of $r\approx11M$ prior to merger. We observe a reasonably good agreement between the PN and numerical waveforms, with an overlap of over 98% for the first six cycles of the $(\ell=2,m=\pm2)$ mode and over 90% for the $(\ell=2,m=1)$ and $(\ell=3,m=3)$ modes.
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 \textbf{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…
The angular momentum flux from an inspiralling binary system of compact objects moving in quasi-elliptical orbits is computed at the third post-Newtonian (3PN) order using the multipolar post-Minkowskian wave generation formalism. The 3PN angular momentum flux involves the instantaneous, tail, and tail-of-tails contributions as for the 3PN energy flux, and in addition a contribution due to non-linear memory. We average the angular momentum flux over the binary's orbit using the 3PN quasi-Keplerian representation of elliptical orbits. The averaged angular momentum flux provides the final input …
We use a post-Newtonian diagnostic tool to examine numerically generated quasiequilibrium initial data sets for non-spinning double neutron star and neutron star-black hole binary systems. The PN equations include the effects of tidal interactions, parametrized by the compactness of the neutron stars and by suitable values of ``apsidal'' constants, which measure the degree of distortion of stars subjected to tidal forces. We find that the post-Newtonian diagnostic agrees well with the double neutron star initial data, typically to better than half a percent except where tidal distortions are b…
Gravitational waves from inspiralling binaries are expected to be detected using a data analysis technique known as {\it matched filtering.} This technique is applicable whenever the form of the signal is known accurately. Though we know the form of the signal precisely, we will not know {\it a priori} its parameters. Hence it is essential to filter the raw output through a host of search templates each corresponding to different values of the parameters. The number of search templates needed in detecting the Newtonian waveform characterized by three independent parameters is itself several th…
We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field point particle limit to describe self-gravitating stars instead of the Dirac delta functional. The computation is done in harmonic coordinates. Our equations of motion describe the orbital motion of the binary consisting of spherically symmetric non-rotating stars. The resulting equations of motion fully agree with the 3.5 PN equations of motion derived in the previous works. We also show th…
The inspiral and merger of supermassive black hole binary systems with high orbital eccentricity are among the promising sources of the advanced gravitational wave observatories. In this paper we derive analytic ready-to-use first post-Newtonian eccentric waveform in Fourier domain with the use of Hansen coefficients. Introducing generic perturbations of celestial mechanics we have generalized the Hansen expansion to the first post-Newtonian order which are then used to express the waveforms. Taking into account the high eccentricity of the orbit leads to the appearance of secular terms in the…
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…
A precessing source frame, constructed using the Newtonian orbital angular momentum ${\bf L_{\rm N}}$, can be invoked to model inspiral gravitational waves from generic spinning compact binaries. An attractive feature of such a precessing convention is its ability to remove all spin precession induced modulations from the orbital phase evolution. However, this convention usually employs a post-Newtonian (PN) accurate precessional equation, appropriate for the PN accurate orbital angular momentum ${\bf L}$, to evolve the ${\bf L_{\rm N}}$-based precessing source frame. This influenced us to dev…
The parameters of inspiralling compact binaries can be estimated using matched filtering of gravitational-waveform templates against the output of laser-interferometric gravitational-wave detectors. Using a recently calculated formula, accurate to second post-Newtonian (2PN) order [order $(v/c)^4$, where $v$ is the orbital velocity], for the frequency sweep ($dF/dt$) induced by gravitational radiation damping, we study the statistical errors in the determination of such source parameters as the ``chirp mass'' $\cal M$, reduced mass $μ$, and spin parameters $β$ and $σ$ (related to spin-orbit an…
The paper deals with the estimation of parameters of gravitational waves from coalescing binaries. It explains the discrepancy between the Monte carlo simulations and the covariance matrix. We include the post-Newtonian as well as the Newtonian case.
The Christodoulou memory is a nonlinear contribution to the gravitational-wave field that is sourced by the gravitational-wave stress-energy tensor. For quasicircular, inspiralling binaries, the Christodoulou memory produces a growing, nonoscillatory change in the gravitational-wave "plus" polarization, resulting in the permanent displacement of a pair of freely-falling test masses after the wave has passed. In addition to its nonoscillatory behavior, the Christodoulou memory is interesting because even though it originates from 2.5 post-Newtonian (PN) order multipole interactions, it affects …
