Gravitational power from cosmic string loops with many kinks

We investigate the effect of a large number of kinks on the gravitational power radiated by cosmic string loops. We show that the total power radiated by a loop with N left-moving and right-moving kinks is proportional to N and increases with the typical kink angle. We then apply these results to loops containing junctions which give rise to a proliferation of the number of sharp kinks. We show that the time of gravitational decay of these loops is smaller than previously assumed. In light of this we revisit the gravitational wave burst predictions from a network containing such loops. We find there is no parameter regime in which the rate of individual kink bursts is enhanced with respect to standard networks. By contrast, there remains a region of parameter space for which the kink-kink bursts dominate the stochastic background. Finally, we discuss the order of magnitude of the typical number of sharp kinks resulting from kink proliferation on loops with junctions.Comment: 20 pages, 1 figur

Conservative Dynamics of Binary Systems of Compact Objects at the Fourth Post-Newtonian Order

We review our recent derivation of a Fokker action describing the conservative dynamics of a compact binary system at the fourth post-Newtonian (4PN) approximation of general relativity. The two bodies are modeled by point particles, which induces ultraviolet (UV) divergences that are cured by means of dimensional regularization combined with a renormalization of the particle's wordlines. Associated with the propagation of wave tails at infinity is the appearance of a non-local-in-time conservative tail effect at the 4PN order in the Lagrangian. In turn this implies the appearance of infrared (IR) divergent integrals which are also regularized by means of dimensional regularization. We compute the Noetherian conserved energy and periastron advance for circular orbits at 4PN order, paying special attention to the treatment of the non-local terms. One ambiguity parameter remaining in the current formalism is determined by comparing those quantities, expressed as functions of the orbital frequency, with self-force results valid in the small mass ratio limit.Comment: 7 pages; contribution to the proceedings of the 52nd Rencontres de Moriond, "Gravitation

Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order

The Fokker action of point-particle binaries at the fourth post-Newtonian (4PN) approximation of general relativity has been determined previously. However two ambiguity parameters associated with infra-red (IR) divergencies of spatial integrals had to be introduced. These two parameters were fixed by comparison with gravitational self-force (GSF) calculations of the conserved energy and periastron advance for circular orbits in the test-mass limit. In the present paper together with a companion paper, we determine both these ambiguities from first principle, by means of dimensional regularization. Our computation is thus entirely defined within the dimensional regularization scheme, for treating at once the IR and ultra-violet (UV) divergencies. In particular, we obtain crucial contributions coming from the Einstein-Hilbert part of the action and from the non-local tail term in arbitrary dimensions, which resolve the ambiguities.Comment: 25 pages, published versio

Fokker action of non-spinning 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.Comment: 47 pages; references added; Sec. VD enhanced; a few more minor improvement

Enriching the Symphony of Gravitational Waves from Binary Black Holes by Tuning Higher Harmonics

For the first time, we construct an inspiral-merger-ringdown waveform model within the effective-one-body formalism for spinning, nonprecessing binary black holes that includes gravitational modes beyond the dominant $(\ell,|m|) = (2,2)$ mode, specifically $(\ell,|m|)=(2,1),(3,3),(4,4),(5,5)$. Our multipolar waveform model incorporates recent (resummed) post-Newtonian results for the inspiral and information from 157 numerical-relativity simulations, and 13 waveforms from black-hole perturbation theory for the (plunge-)merger and ringdown. We quantify the improved accuracy including higher-order modes by computing the faithfulness of the waveform model against the numerical-relativity waveforms used to construct the model. We define the faithfulness as the match maximized over time, phase of arrival, gravitational-wave polarization and sky position of the waveform model, and averaged over binary orientation, gravitational-wave polarization and sky position of the numerical-relativity waveform. When the waveform model contains only the $(2,2)$ mode, we find that the averaged faithfulness to numerical-relativity waveforms containing all modes with $\ell \leq$ 5 ranges from $90\%$ to $99.9\%$ for binaries with total mass $20-200 M_\odot$ (using the Advanced LIGO's design noise curve). By contrast, when the $(2,1),(3,3),(4,4),(5,5)$ modes are also included in the model, the faithfulness improves to $99\%$ for all but four configurations in the numerical-relativity catalog, for which the faithfulness is greater than $98.5\%$. Using our results, we also develop also a (stand-alone) waveform model for the merger-ringdown signal, calibrated to numerical-relativity waveforms, which can be used to measure multiple quasi-normal modes. The multipolar waveform model can be extended to include spin-precession, and will be employed in upcoming observing runs of Advanced LIGO and Virgo.Comment: 28 page

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 non-precessing (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 $|a/m| \sim 0.85$ ($0.98$ 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 \emph{any} merger-ringdown waveform model is accurate outside its calibration region. As an example, we note that an alternative non-precessing 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.Comment: 27 pages, 21 figures, Updated coefficients tabl

Frequency-domain gravitational waves from non-precessing 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 non-precessing 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.Comment: 17 pages, 18 figures ,minor edits to tex

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 binary’s 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, χp. 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 model’s 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

Searching for gravitational waves from compact binaries with precessing spins

Current searches for gravitational waves from compact-object binaries with the LIGO and Virgo observatories employ waveform models with spins aligned (or anti-aligned) with the orbital angular momentum. Here, we derive a new statistic to search for compact objects carrying generic (precessing) spins. Applying this statistic, we construct banks of both aligned- and generic-spin templates for binary black holes and neutron-star--black-hole binaries, and compare the effectualness of these banks towards simulated populations of generic-spin systems. We then use these banks in a pipeline analysis of Gaussian noise to measure the increase in background incurred by using generic- instead of aligned-spin banks. Although the generic-spin banks have a factor of ten to twenty more templates than the aligned-spin banks, we find an overall improvement in signal recovery at fixed false-alarm rate for systems with high-mass ratio and highly precessing spins ---up to 60\% for neutron-star--black-hole mergers. This gain in sensitivity comes at a small loss of sensitivity ($\lesssim$4\%) for systems that are already well-covered by aligned-spin templates. Since the observation of even a single binary merger with misalinged spins could provide unique astrophysical insights into the formation of these sources, we recommend that the method described here be developed further to mount a viable search for generic-spin binary mergers in LIGO/Virgo data