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Register a new userComparison of high-accuracy numerical simulations of black-hole binaries with stationary phase post-Newtonian template waveforms for Initial and Advanced LIGO
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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.
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Numerical simulations of 15 orbits of an equal-mass binary black hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasi-circular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first $sim 15$ cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, {em generic} time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6--7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly ($<1%$ amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.
Gravitational waves (GW) from coalescing stellar-mass black hole binaries (BBH) are expected to be detected by the Advanced Laser Interferometer Gravitational-wave Observatory and Advanced Virgo. Detection searches operate by matched-filtering the detector data using a bank of waveform templates. Traditionally, template banks for BBH are constructed from intermediary analytical waveform models which are calibrated against numerical relativity simulations and which can be aluated for any choice of BBH parameters. This paper explores an alternative to the traditional approach, namely the construction of template banks directly from numerical BBH simulations. Using non-spinning BBH systems as an example, we demonstrate which regions of the mass-parameter plane can be covered with existing numerical BBH waveforms. We estimate the required number and required length of BBH simulations to cover the entire non-spinning BBH parameter plane up to mass-ratio 10, thus illustrating that our approach can be used to guide parameter placement of future numerical simulations. We derive error bounds which are independent of analytical waveform models; therefore, our formalism can be used to independently test the accuracy of such waveform models. The resulting template banks are suitable for advanced LIGO searches.
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 the merger. An analytical formula for the dominant mode of the gravitational radiation of non-precessing black hole binaries is presented that captures the phenomenology of the hybrid waveforms. Its implementation in the current searches for gravitational waves should allow cross-checks of other inspiral-merger-ringdown waveform families and improve the reach of gravitational wave searches.
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.
Recent progress in numerical relativity has enabled us to model the non-perturbative merger phase of the binary black-hole coalescence problem. Based on these results, we propose a phenomenological family of waveforms which can model the inspiral, merger, and ring-down stages of black hole coalescence. We also construct a template bank using this family of waveforms and discuss its implementation in the search for signatures of gravitational waves produced by black-hole coalescences in the data of ground-based interferometers. This template bank might enable us to extend the present inspiral searches to higher-mass binary black-hole systems, i.e., systems with total mass greater than about 80 solar masses, thereby increasing the reach of the current generation of ground-based detectors.
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