Prototype effective-one-body model for nonprecessing spinning inspiral-merger-ringdown waveforms

We first use five non-spinning and two mildly spinning (chi_i \simeq -0.44, +0.44) numerical-relativity waveforms of black-hole binaries and calibrate an effective-one-body (EOB) model for non-precessing spinning binaries, notably its dynamics and the dominant (2,2) gravitational-wave mode. Then, we combine the above results with recent outcomes of small-mass-ratio simulations produced by the Teukolsky equation and build a prototype EOB model for detection purposes, which is capable of generating inspiral-merger-ringdown waveforms for non-precessing spinning black-hole binaries with any mass ratio and individual black-hole spins -1 \leq chi_i \lesssim 0.7. We compare the prototype EOB model to two equal-mass highly spinning numerical-relativity waveforms of black holes with spins chi_i = -0.95, +0.97, which were not available at the time the EOB model was calibrated. In the case of Advanced LIGO we find that the mismatch between prototype-EOB and numerical-relativity waveforms is always smaller than 0.003 for total mass 20-200 M_\odot, the mismatch being computed by maximizing only over the initial phase and time. To successfully generate merger waveforms for individual black-hole spins chi_i \gtrsim 0.7, the prototype-EOB model needs to be improved by (i) better modeling the plunge dynamics and (ii) including higher-order PN spin terms in the gravitational-wave modes and radiation-reaction force.Comment: 20 pages, 8 figures. Minor changes to match version accepted for publication in PR

Relating gravitational wave constraints from primordial nucleosynthesis, pulsar timing, laser interferometers, and the CMB: implications for the early universe

We derive a general master equation relating the gravitational-wave observables r and Omega_gw(f). Here r is the tensor-to-scalar ratio, constrained by cosmic-microwave-background (CMB) experiments; and Omega_gw(f) is the energy spectrum of primordial gravitational-waves, constrained e.g. by pulsar-timing measurements, laser-interferometer experiments, and Big Bang Nucleosynthesis (BBN). Differentiating the master equation yields a new expression for the tilt d(ln Omega_gw(f))/d(ln f). The relationship between r and Omega_gw(f) depends sensitively on the uncertain physics of the early universe, and we show that this uncertainty may be encapsulated (in a model-independent way) by two quantities: w_hat(f) and nt_hat(f), where nt_hat(f) is a certain logarithmic average over nt(k) (the primordial tensor spectral index); and w_hat(f) is a certain logarithmic average over w_tilde(a) (the effective equation-of-state in the early universe, after horizon re-entry). Here the effective equation-of-state parameter w_tilde(a) is a combination of the ordinary equation-of-state parameter w(a) and the bulk viscosity zeta(a). Thus, by comparing constraints on r and Omega_gw(f), one can obtain (remarkably tight) constraints in the [w_hat(f), nt_hat(f)] plane. In particular, this is the best way to constrain (or detect) the presence of a ``stiff'' energy component (with w > 1/3) in the early universe, prior to BBN. Finally, although most of our analysis does not assume inflation, we point out that if CMB experiments detect a non-zero value for r, then we will immediately obtain (as a free by-product) a new upper bound w_hat < 0.55 on the logarithmically averaged effective equation-of-state parameter during the ``primordial dark age'' between the end of inflation and the start of BBN.Comment: v1: 12 + 6 pages (main text + appendices), 7 figures; v2: fonts fixed in figure

Observational Constraints on Theories with a Blue Spectrum of Tensor Modes

Motivated by the string gas cosmological model, which predicts a blue tilt of the primordial gravitational wave spectrum, we examine the constraints imposed by current and planned observations on a blue tilted tensor spectrum. Starting from an expression for the primordial gravitational wave spectrum normalized using cosmic microwave background observations, pulsar timing, direct detection and nucleosynthesis bounds are examined. If we assume a tensor to scalar ratio on scales of the CMB which equals the current observational upper bound, we obtain from these current observations constraints on the tensor spectral index of $n_{T} \lesssim 0.79$, $n_{T} \lesssim 0.53$, and $n_{T} \lesssim 0.15$ respectively.Comment: 12 pages, 1 figure, 2 references added, relationship of this work with Ref. 20 adde

High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants

Expressions for the gravitational wave (GW) energy flux and center-of-mass energy of a compact binary are integral building blocks of post-Newtonian (PN) waveforms. In this paper, we compute the GW energy flux and GW frequency derivative from a highly accurate numerical simulation of an equal-mass, non-spinning black hole binary. We also estimate the (derivative of the) center-of-mass energy from the simulation by assuming energy balance. We compare these quantities with the predictions of various PN approximants (adiabatic Taylor and Pade models; non-adiabatic effective-one-body (EOB) models). We find that Pade summation of the energy flux does not accelerate the convergence of the flux series; nevertheless, the Pade flux is markedly closer to the numerical result for the whole range of the simulation (about 30 GW cycles). Taylor and Pade models overestimate the increase in flux and frequency derivative close to merger, whereas EOB models reproduce more faithfully the shape of and are closer to the numerical flux, frequency derivative and derivative of energy. We also compare the GW phase of the numerical simulation with Pade and EOB models. Matching numerical and untuned 3.5 PN order waveforms, we find that the phase difference accumulated until $M \omega = 0.1$ is -0.12 radians for Pade approximants, and 0.50 (0.45) radians for an EOB approximant with Keplerian (non-Keplerian) flux. We fit free parameters within the EOB models to minimize the phase difference, and confirm degeneracies among these parameters. By tuning pseudo 4PN order coefficients in the radial potential or in the flux, or, if present, the location of the pole in the flux, we find that the accumulated phase difference can be reduced - if desired - to much less than the estimated numerical phase error (0.02 radians).Comment: modified non-Keplerian flux improves agreement with NR; updated error bound of NR-PN comparison; added ref

Inspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism

We calibrate an effective-one-body (EOB) model to numerical-relativity simulations of mass ratios 1, 2, 3, 4, and 6, by maximizing phase and amplitude agreement of the leading (2,2) mode and of the subleading modes (2,1), (3,3), (4,4) and (5,5). Aligning the calibrated EOB waveforms and the numerical waveforms at low frequency, the phase difference of the (2,2) mode between model and numerical simulation remains below 0.1 rad throughout the evolution for all mass ratios considered. The fractional amplitude difference at peak amplitude of the (2,2) mode is 2% and grows to 12% during the ringdown. Using the Advanced LIGO noise curve we study the effectualness and measurement accuracy of the EOB model, and stress the relevance of modeling the higher-order modes for parameter estimation. We find that the effectualness, measured by the mismatch, between the EOB and numerical-relativity polarizations which include only the (2,2) mode is smaller than 0.2% for binaries with total mass 20-200 Msun and mass ratios 1, 2, 3, 4, and 6. When numerical-relativity polarizations contain the strongest seven modes, and stellar-mass black holes with masses less than 50Msun are considered, the mismatch for mass ratio 6 (1) can be as high as 5% (0.2%) when only the EOB (2,2) mode is included, and an upper bound of the mismatch is 0.5% (0.07%) when all the four subleading EOB modes calibrated in this paper are taken into account. For binaries with intermediate-mass black holes with masses greater than 50Msun the mismatches are larger. We also determine for which signal-to-noise ratios the EOB model developed here can be used to measure binary parameters with systematic biases smaller than statistical errors due to detector noise.Comment: 26 pages, 25 figures, published Phys. Rev. D versio

Analytic approximations, perturbation methods, and their applications

The paper summarizes the parallel session B3 {\em Analytic approximations, perturbation methods, and their applications} of the GR18 conference. The talks in the session reported notably recent advances in black hole perturbations and post-Newtonian approximations as applied to sources of gravitational waves.Comment: Summary of the B3 parallel session of the GR18 conferenc

Thermal Inflation and the Gravitational Wave Background

We consider the impact of thermal inflation -- a short, secondary period of inflation that can arise in supersymmetric scenarios -- on the stochastic gravitational wave background. We show that while the primordial inflationary gravitational wave background is essentially unchanged at CMB scales, it is massively diluted at solar system scales and would be unobservable by a BBO style experiment. Conversely, bubble collisions at the end of thermal inflation can generate a new stochastic background. We calculate the likely properties of the bubbles created during this phase transition, and show that the expected amplitude and frequency of this signal would fall within the BBO range.Comment: 21 pages, 4 figures; accepted for JCAP; a reference added; table reformatte

Comparison of high-accuracy numerical simulations of black-hole binaries with stationary phase post-Newtonian template waveforms for Initial and Advanced LIGO

We study the effectiveness of stationary-phase approximated post-Newtonian waveforms currently used by ground-based gravitational-wave detectors to search for the coalescence of binary black holes by comparing them to an accurate waveform obtained from numerical simulation of an equal-mass non-spinning binary black hole inspiral, merger and ringdown. We perform this study for the Initial- and Advanced-LIGO detectors. We find that overlaps between the templates and signal can be improved by integrating the match filter to higher frequencies than used currently. We propose simple analytic frequency cutoffs for both Initial and Advanced LIGO, which achieve nearly optimal matches, and can easily be extended to unequal-mass, spinning systems. We also find that templates that include terms in the phase evolution up to 3.5 pN order are nearly always better, and rarely significantly worse, than 2.0 pN templates currently in use. For Initial LIGO we recommend a strategy using templates that include a recently introduced pseudo-4.0 pN term in the low-mass (M \leq 35 \MSun) region, and 3.5 pN templates allowing unphysical values of the symmetric reduced mass $\eta$ above this. This strategy always achieves overlaps within 0.3% of the optimum, for the data used here. For Advanced LIGO we recommend a strategy using 3.5 pN templates up to M=12 \MSun, 2.0 pN templates up to M=21 \MSun, pseudo-4.0 pN templates up to 65 \MSun, and 3.5 pN templates with unphysical $\eta$ for higher masses. This strategy always achieves overlaps within 0.7% of the optimum for Advanced LIGO.Comment: 20 pages, 11 figures. Presented at NRDA 200

Gravitational waveforms from spectral Einstein code simulations: Neutron star-neutron star and low-mass black hole-neutron star binaries

Gravitational waveforms from numerical simulations are a critical tool to test and analytically calibrate the waveform models used to study the properties of merging compact objects. In this paper, we present a series of high-accuracy waveforms produced with the spectral Einstein code (SpEC) for systems involving at least one neutron star. We provide for the first time waveforms with subradian accuracy over more than twenty cycles for low-mass black hole-neutron star binaries, including binaries with nonspinning objects, and binaries with rapidly spinning neutron stars that maximize the impact on the gravitational wave signal of the near-resonant growth of the fundamental excitation mode of the neutron star (f-mode). We also provide for the first time with SpEC a high-accuracy neutron star-neutron star waveform. These waveforms are made publicly available as part of the SxS catalogue. We compare our results to analytical waveform models currently implemented in data analysis pipelines. For most simulations, the models lie outside of the predicted numerical errors in the last few orbits before merger, but do not show systematic deviations from the numerical results: comparing different models appears to provide reasonable estimates of the modeling errors. The sole exception is the equal-mass simulation using a rapidly counterrotating neutron star to maximize the impact of the excitation of the f-mode, for which all models perform poorly. This is however expected, as even the single model that takes f-mode excitation into account ignores the significant impact of the neutron star spin on the f-mode excitation frequency