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Register a new userAccuracy of binary black hole waveform models for aligned-spin binaries
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Coalescing binary black holes are among the primary science targets for second generation ground-based gravitational wave (GW) detectors. Reliable GW models are central to detection of such systems and subsequent parameter estimation. This paper performs a comprehensive analysis of the accuracy of recent waveform models for binary black holes with aligned spins, utilizing a new set of $84$ high-accuracy numerical relativity simulations. Our analysis covers comparable mass binaries ($1le m_1/m_2le 3$), and samples independently both black hole spins up to dimensionless spin-magnitude of $0.9$ for equal-mass binaries and $0.85$ for unequal mass binaries. Furthermore, we focus on the high-mass regime (total mass $gtrsim 50M_odot$). The two most recent waveform models considered (PhenomD and SEOBNRv2) both perform very well for signal detection, losing less than 0.5% of the recoverable signal-to-noise ratio $rho$, except that SEOBNRv2s efficiency drops mildly for both black hole spins aligned with large magnitude. For parameter estimation, modeling inaccuracies of SEOBNRv2 are found to be smaller than systematic uncertainties for moderately strong GW events up to roughly $rholesssim 15$. PhenomDs modeling errors are found to be smaller than SEOBNRv2s, and are generally irrelevant for $rholesssim 20$. Both models accuracy deteriorates with increased mass-ratio, and when at least one black hole spin is large and aligned. The SEOBNRv2 model shows a pronounced disagreement with the numerical relativity simulation in the merger phase, for unequal masses and simultaneously both black hole spins very large and aligned. Two older waveform models (PhenomC and SEOBNRv1) are found to be distinctly less accurate than the more recent PhenomD and SEOBNRv2 models. Finally, we quantify the bias expected from all GW models during parameter estimation for recovery of binarys masses and spins.
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Gravitational waves radiated by the coalescence of compact-object binaries containing a neutron star and a black hole are one of the most interesting sources for the ground-based gravitational-wave observatories Advanced LIGO and Advanced Virgo. Advanced LIGO will be sensitive to the inspiral of a $1.4, M_odot$ neutron star into a $10,M_odot$ black hole to a maximum distance of $sim 900$ Mpc. Achieving this sensitivity and extracting the physics imprinted in observed signals requires accurate modeling of the binary to construct template waveforms. In a NSBH binary, the black hole may have significant angular momentum (spin), which affects the phase evolution of the emitted gravitational waves. We investigate the ability of post-Newtonian (PN) templates to model the gravitational waves emitted during the inspiral phase of NSBH binaries. We restrict the black holes spin to be aligned with the orbital angular momentum and compare several approximants. We examine restricted amplitude waveforms that are accurate to 3.5PN order in the orbital dynamics and complete to 2.5PN order in the spin dynamics. We also consider PN waveforms with the recently derived 3.5PN spin-orbit and 3PN spin-orbit tail corrections. We compare these approximants to the effective-one-body model. For all these models, large disagreements start at low to moderate black hole spins, particularly for binaries where the spin is anti-aligned with the orbital angular momentum. We show that this divergence begins in the early inspiral at $v sim 0.2$ for $chi_{BH} sim 0.4$. PN spin corrections beyond those currently known will be required for optimal detection searches and to measure the parameters of neutron star--black hole binaries. While this complicates searches, the strong dependence of the gravitational-wave signal on the spin dynamics will make it possible to extract significant astrophysical information.
Spinning neutron stars acquire a quadrupole moment due to their own rotation. This quadratic-in-spin, self-spin effect depends on the equation of state (EOS) and affects the orbital motion and rate of inspiral of neutron star binaries. We incorporate the EOS-dependent self-spin (or monopole-quadrupole) terms in the spin-aligned effective-one-body (EOB) waveform model TEOBResumS at next-to-next-to-leading (NNLO) order, together with other (bilinear, cubic and quartic) nonlinear-in-spin effects (at leading order, LO). The structure of the Hamiltonian of TEOBResumS is such that it already incorporates, in the binary black hole case, the recently computed quartic-in-spin LO term. Using the gauge-invariant characterization of the phasing provided by the function $Q_omega=omega^2/dot{omega}$ of $omega=2pi f$ , where $f$ is the gravitational wave frequency, we study the EOS dependence of the self-spin effects and show that: (i) the next-to-leading order (NLO) and NNLO monopole-quadrupole corrections yield increasingly phase-accelerating effects compared to the corresponding LO contribution; (ii) the standard TaylorF2 post-Newtonian (PN) treatment of NLO (3PN) EOS-dependent self-spin effects makes their action stronger than the corresponding EOB description; (iii) the addition to the standard 3PN TaylorF2 post-Newtonian phasing description of self-spin tail effects at LO allows one to reconcile the self-spin part of the TaylorF2 PN phasing with the corresponding TEOBResumS one up to dimensionless frequencies $Momegasimeq 0.04-0.06$. By generating the inspiral dynamics using the post-adiabatic approximation, incorporated in a new implementation of TEOBResumS, one finds that the computational time needed to obtain a typical waveform (including all multipoles up to $ell=8$) from 10 Hz is of the order of 0.4 sec.
We develop new strategies to build numerical relativity surrogate models for eccentric binary black hole systems, which are expected to play an increasingly important role in current and future gravitational-wave detectors. We introduce a new surrogate waveform model, texttt{NRSur2dq1Ecc}, using 47 nonspinning, equal-mass waveforms with eccentricities up to $0.2$ when measured at a reference time of $5500M$ before merger. This is the first waveform model that is directly trained on eccentric numerical relativity simulations and does not require that the binary circularizes before merger. The model includes the $(2,2)$, $(3,2)$, and $(4,4)$ spin-weighted spherical harmonic modes. We also build a final black hole model, texttt{NRSur2dq1EccRemnant}, which models the mass, and spin of the remnant black hole. We show that our waveform model can accurately predict numerical relativity waveforms with mismatches $approx 10^{-3}$, while the remnant model can recover the final mass and dimensionless spin with absolute errors smaller than $approx 5 times 10^{-4}M$ and $approx 2 times10^{-3}$ respectively. We demonstrate that the waveform model can also recover subtle effects like mode-mixing in the ringdown signal without any special ad-hoc modeling steps. Finally, we show that despite being trained only on equal-mass binaries, texttt{NRSur2dq1Ecc} can be reasonably extended up to mass ratio $qapprox3$ with mismatches $simeq 10^{-2}$ for eccentricities smaller than $sim 0.05$ as measured at a reference time of $2000M$ before merger. The methods developed here should prove useful in the building of future eccentric surrogate models over larger regions of the parameter space.
A generic, non-eccentric binary black hole (BBH) system emits gravitational waves (GWs) that are completely described by 7 intrinsic parameters: the black hole spin vectors and the ratio of their masses. Simulating a BBH coalescence by solving Einsteins equations numerically is computationally expensive, requiring days to months of computing resources for a single set of parameter values. Since theoretical predictions of the GWs are often needed for many different source parameters, a fast and accurate model is essential. We present the first surrogate model for GWs from the coalescence of BBHs including all $7$ dimensions of the intrinsic non-eccentric parameter space. The surrogate model, which we call NRSur7dq2, is built from the results of $744$ numerical relativity simulations. NRSur7dq2 covers spin magnitudes up to $0.8$ and mass ratios up to $2$, includes all $ell leq 4$ modes, begins about $20$ orbits before merger, and can be evaluated in $sim~50,mathrm{ms}$. We find the largest NRSur7dq2 errors to be comparable to the largest errors in the numerical relativity simulations, and more than an order of magnitude smaller than the errors of other waveform models. Our model, and more broadly the methods developed here, will enable studies that would otherwise require millions of numerical relativity waveforms, such as parameter inference and tests of general relativity with GW observations.
Gravitational waves from binary neutron star (BNS) and black hole/neutron star (BHNS) inspirals are primary sources for detection by the Advanced Laser Interferometer Gravitational-Wave Observatory. The tidal forces acting on the neutron stars induce changes in the phase evolution of the gravitational waveform, and these changes can be used to constrain the nuclear equation of state. Current methods of generating BNS and BHNS waveforms rely on either computationally challenging full 3D hydrodynamical simulations or approximate analytic solutions. We introduce a new method for computing inspiral waveforms for BNS/BHNS systems by adding the post-Newtonian (PN) tidal effects to full numerical simulations of binary black holes (BBHs), effectively replacing the nontidal terms in the PN expansion with BBH results. Comparing a waveform generated with this method against a full hydrodynamical simulation of a BNS inspiral yields a phase difference of $<1$ radian over $sim 15$ orbits. The numerical phase accuracy required of BNS simulations to measure the accuracy of the method we present here is estimated as a function of the tidal deformability parameter ${lambda}$.
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