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Register a new userA template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries
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Gravitational waveforms from the inspiral and ring-down stages of the binary black hole coalescences can be modelled accurately by approximation/perturbation techniques in general relativity. Recent progress in numerical relativity has enabled us to model also the non-perturbative merger phase of the binary black-hole coalescence problem. This enables us to emph{coherently} search for all three stages of the coalescence of non-spinning binary black holes using a single template bank. Taking our motivation from these results, we propose a family of template waveforms which can model the inspiral, merger, and ring-down stages of the coalescence of non-spinning binary black holes that follow quasi-circular inspiral. This two-dimensional template family is explicitly parametrized by the physical parameters of the binary. We show that the template family is not only emph{effectual} in detecting the signals from black hole coalescences, but also emph{faithful} in estimating the parameters of the binary. We compare the sensitivity of a search (in the context of different ground-based interferometers) using all three stages of the black hole coalescence with other template-based searches which look for individual stages separately. We find that the proposed search is significantly more sensitive than other template-based searches for a substantial mass-range, potentially bringing about remarkable improvement in the event-rate of ground-based interferometers. As part of this work, we also prescribe a general procedure to construct interpolated template banks using non-spinning black hole waveforms produced by numerical relativity.
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The standard post-Newtonian approximation to gravitational waveforms, called T-approximants, from non-spinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system. A new approximation, called P-approximants, is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit. In this study we apply P-approximants to the case of a test-particle in equatorial orbit around a Kerr black hole parameterized by a spin parameter q that takes values between -1 and 1. In order to assess the performance of the two approximants we measure their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole, T-approximant templates obtain an effectualness of ~ 0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q>0. For q<0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family.
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 ${lambda}$.
Gravitational waves from coalescing compact binaries are searched using the matched filtering technique. As the model waveform depends on a number of parameters, it is necessary to filter the data through a template bank covering the astrophysically interesting region of the parameter space. The choice of templates is defined by the maximum allowed drop in signal-to-noise ratio due to the discreteness of the template bank. In this paper we describe the template-bank algorithm that was used in the analysis of data from the Laser Interferometer Gravitational Wave Observatory (LIGO) and GEO 600 detectors to search for signals from binaries consisting of non-spinning compact objects. Using Monte-Carlo simulations, we study the efficiency of the bank and show that its performance is satisfactory for the design sensitivity curves of ground-based interferometric gravitational wave detectors GEO 600, initial LIGO, advanced LIGO and Virgo. The bank is efficient to search for various compact binaries such as binary primordial black holes, binary neutron stars, binary black holes, as well as a mixed binary consisting of a non-spinning black hole and a neutron star.
A waveform model for the eccentric binary black holes named SEOBNRE has been used to analyze the LIGO-Virgos gravitational wave data by several groups. The accuracy of this model has been validated by comparing it with numerical relativity. However, SEOBNRE is a time-domain model, and the efficiency for generating waveforms is a bottleneck in data analysis. To overcome this disadvantage, we offer a reduced-order surrogate model for eccentric binary black holes based on the SEOBNRE waveforms. This surrogate model (SEOBNRE_S) can simulate the complete inspiral-merger-ringdown waves with enough accuracy, covering eccentricities from 0 to 0.25 (0.1), and mass ratio from 1:1 to 5:1 (2:1) for nonspinning (spinning) binaries. The speed of waveform generation is accelerated about $10^2 sim 10^3$ times than the original SEOBNRE model. Therefore SEOBNRE_S could be helpful in the analysis of LIGO data to find potential eccentricities.
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.
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