A. Bohe

Low-frequency gravitational-wave science with eLISA/NGO

We review the expected science performance of the New Gravitational-Wave Observatory (NGO, a.k.a. eLISA), a mission under study by the European Space Agency for launch in the early 2020s. eLISA will survey the low-frequency gravitational-wave sky (from 0.1 mHz to 1 Hz), detecting and characterizing a broad variety of systems and events throughout the Universe, including the coalescences of massive black holes brought together by galaxy mergers; the inspirals of stellar-mass black holes and compact stars into central galactic black holes; several millions of ultra-compact binaries, both detached and mass transferring, in the Galaxy; and possibly unforeseen sources such as the relic gravitational-wave radiation from the early Universe. eLISAs high signal-to-noise measurements will provide new insight into the structure and history of the Universe, and they will test general relativity in its strong-field dynamical regime.

Frequency-domain gravitational waves from non-precessing black-hole binaries. II. A phenomenological model for the advanced detector era

We present a new frequency-domain phenomenological model of the gravitational-wave signal from the inspiral, merger and ringdown of nonprecessing (aligned-spin) black-hole binaries. The model is calibrated to 19 hybrid effective-one-body–numerical-relativity waveforms up to mass ratios of 1∶18 and black-hole spins of |a/m|∼0.85 (0.98 for equal-mass systems). The inspiral part of the model consists of an extension of frequency-domain post-Newtonian expressions, using higher-order terms fit to the hybrids. The merger ringdown is based on a phenomenological ansatz that has been significantly improved over previous models. The model exhibits mismatches of typically less than 1% against all 19 calibration hybrids and an additional 29 verification hybrids, which provide strong evidence that, over the calibration region, the model is sufficiently accurate for all relevant gravitational-wave astronomy applications with the Advanced LIGO and Virgo detectors. Beyond the calibration region the model produces physically reasonable results, although we recommend caution in assuming that any merger-ringdown waveform model is accurate outside its calibration region. As an example, we note that an alternative nonprecessing model, SEOBNRv2 (calibrated up to spins of only 0.5 for unequal-mass systems), exhibits mismatch errors of up to 10% for high spins outside its calibration region. We conclude that waveform models would benefit most from a larger number of numerical-relativity simulations of high-aligned-spin unequal-mass binaries.

Simple model of complete precessing black-hole-binary gravitational waveforms

The construction of a model of the gravitational-wave (GW) signal from generic configurations of spinning-black-hole binaries, through inspiral, merger, and ringdown, is one of the most pressing theoretical problems in the buildup to the era of GW astronomy. We present the first such model in the frequency domain, PhenomP, which captures the basic phenomenology of the seven-dimensional parameter space of binary configurations with only three key physical parameters. Two of these (the binarys mass ratio and an effective total spin parallel to the orbital angular momentum, which determines the inspiral rate) define an underlying nonprecessing-binary model. The nonprecessing-binary waveforms are then twisted up with approximate expressions for the precessional motion, which require only one additional physical parameter, an effective precession spin, χ(p). All other parameters (total mass, sky location, orientation and polarization, and initial phase) can be specified trivially. The model is constructed in the frequency domain, which will be essential for efficient GW searches and source measurements. We have tested the models fidelity for GW applications by comparison against hybrid post-Newtonian-numerical-relativity waveforms at a variety of configurations--although we did not use these numerical simulations in the construction of the model. Our model can be used to develop GW searches, to study the implications for astrophysical measurements, and as a simple conceptual framework to form the basis of generic-binary waveform modeling in the advanced-detector era.

Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal

In this paper we discuss the anatomy of frequency-domain gravitational-wave signals from nonprecessing black-hole coalescences with the goal of constructing accurate phenomenological waveform models. We first present new numerical-relativity simulations for mass ratios up to 18, including spins. From a comparison of different post-Newtonian approximants with numerical-relativity data we select the uncalibrated SEOBNRv2 model as the most appropriate for the purpose of constructing hybrid post-Newtonian/numerical-relativity waveforms, and we discuss how we prepare time-domain and frequency-domain hybrid data sets. We then use our data together with results in the literature to calibrate simple explicit expressions for the final spin and radiated energy. Equipped with our prediction for the final state we then develop a simple and accurate merger-ringdown model based on modified Lorentzians in the gravitational-wave amplitude and phase, and we discuss a simple method to represent the low frequency signal augmenting the TaylorF2 post-Newtonian approximant with terms corresponding to higher orders in the post-Newtonian expansion. We finally discuss different options for modelling the small intermediate frequency regime between inspiral and merger ringdown. A complete phenomenological model based on the present work is presented in a companion paper [S. Khan et al., following paper, Phys. Rev. D 93 044007 (2016)].

Improved effective-one-body model of spinning, nonprecessing binary black holes for the era of gravitational-wave astrophysics with advanced detectors

We improve the accuracy of the effective-one-body (EOB) waveforms that were employed during the first observing run of Advanced LIGO for binaries of spinning, nonprecessing black holes by calibrating them to a set of 141 numerical-relativity (NR) waveforms. The NR simulations expand the domain of calibration toward larger mass ratios and spins, as compared to the previous EOBNR model. Merger-ringdown waveforms computed in black-hole perturbation theory for Kerr spins close to extremal provide additional inputs to the calibration. For the inspiral-plunge phase, we use a Markov-chain Monte Carlo algorithm to efficiently explore the calibration space. For the merger-ringdown phase, we fit the NR signals with phenomenological formulae. After extrapolation of the calibrated model to arbitrary mass ratios and spins, the (dominant-mode) EOBNR waveforms have faithfulness—at design Advanced-LIGO sensitivity—above 99% against all the NR waveforms, including 16 additional waveforms used for validation, when maximizing only on initial phase and time. This implies a negligible loss in event rate due to modeling for these binary configurations. We find that future NR simulations at mass ratios ≳4 and double spin ≳0.8 will be crucial to resolving discrepancies between different ways of extrapolating waveform models. We also find that some of the NR simulations that already exist in such region of parameter space are too short to constrain the low-frequency portion of the models. Finally, we build a reduced-order version of the EOBNR model to speed up waveform generation by orders of magnitude, thus enabling intensive data-analysis applications during the upcoming observation runs of Advanced LIGO.

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. Schafer, Phys. Rev. D 89, 064058 (2014)]. More work is needed to understand this discrepancy.

Next-to-next-to-leading order spin–orbit effects in the near-zone metric and precession equations of compact binaries

We extend our previous work devoted to the computation of the next-to-next-to-leading order spin–orbit correction (corresponding to 3.5PN order) in the equations of motion of spinning compact binaries by (i) deriving the corresponding spin–orbit terms in the evolution equations for the spins, the conserved integrals of the motion and the metric regularized at the location of the particles (obtaining also the metric all over the near zone but with some lower precision); (ii) performing the orbital reduction of the precession equations, near-zone metric and conserved integrals to the center-of-mass frame and then further assuming quasi-circular orbits (neglecting gravitational radiation reaction). The results are systematically expressed in terms of the spin variables with a conserved Euclidean norm instead of the original antisymmetric spin tensors of the pole–dipole formalism. This work paves the way to the future computation of the next-to-next-to-leading order spin–orbit terms in the gravitational-wave phasing of spinning compact binaries.

Next-to-next-to-leading order spin–orbit effects in the gravitational wave flux and orbital phasing of compact binaries

We compute the next-to-next-to-leading order spin–orbit contributions in the total energy flux emitted in gravitational waves by compact binary systems. Such contributions correspond to the post-Newtonian order 3.5PN for maximally spinning compact objects. Continuing our recent work on the next-to-next-to-leading spin–orbit terms at the 3.5PN order in the equations of motion, we obtain the spin–orbit terms in the multipole moments of the compact binary system up to the same order within the multipolar post-Newtonian wave generation formalism. Our calculation of the multipole moments is valid for general orbits and in an arbitrary frame, the moments are then reduced to the center-of-mass frame and the resulting energy flux is specialized to quasi-circular orbits. The test-mass limit of our final result for the flux agrees with the already known Kerr black hole perturbation limit. Furthermore, the various multipole moments of the compact binary reduce in the one-body case to those of a single-boosted Kerr black hole. We briefly discuss the implications of our result for the gravitational wave flux in terms of the binary’s phase evolution, and address its importance for the future detection and parameter estimation of signals in gravitational wave detectors.

Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order

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 Hamiltonian computed on shell, which was not taken into account in our previous work. We also provide a direct derivation of the periastron advance by taking carefully into account this non-locality. We then argue that the infra-red (IR) divergences in the calculation of the gravitational part of the action are problematic, which motivates us to introduce a second ambiguity parameter, in addition to the one already assumed previously. After fixing these two ambiguity parameters by requiring that the conserved energy and the relativistic periastron precession for circular orbits are in agreement with numerical and analytical gravitational self-force calculations, valid in the limiting case of small mass ratio, we find that our resulting Lagrangian is physically equivalent to the one obtained in the ADM Hamiltonian approach.

Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order

We investigate the dynamics of spinning binaries of compact objects at the next-to-leading order in the quadratic-in-spin effects, which corresponds to the third post-Newtonian order (3PN). Using a Dixon-type multipolar formalism for spinning point particles endowed with spin-induced quadrupoles and computing iteratively in harmonic coordinates the relevant pieces of the PN metric within the near zone, we derive the post-Newtonian equations of motion as well as the equations of spin precession. We find full equivalence with available results. We then focus on the far-zone field produced by those systems and obtain the previously unknown 3PN spin contributions to the gravitational-wave energy flux by means of the multipolar post-Minkowskian (MPM) wave generation formalism. Our results are presented in the center-of-mass frame for generic orbits, before being further specialized to the case of spin-aligned, circular orbits. We derive the orbital phase of the binary based on the energy balance equation and briefly discuss the relevance of the new terms.